Package {epidist}

Title:	Estimate Epidemiological Delay Distributions with 'brms'
Version:	1.0.0
Description:	Understanding and accurately estimating epidemiological delay distributions is important for public health policy. These estimates influence epidemic situational awareness, control strategies, and resource allocation. This package provides methods to address the key challenges in estimating these distributions, including truncation, interval censoring, and dynamical biases, following Park et al. (2024) <doi:10.1101/2024.01.12.24301247> and Charniga et al. (2024) <doi:10.1371/journal.pcbi.1012520>. These issues are frequently overlooked, resulting in biased conclusions. Built on top of 'brms', it allows for flexible modelling including time-varying and spatial effects and partially pooled estimates of demographic characteristics.
License:	MIT + file LICENSE
URL:	https://epidist.epinowcast.org/, https://github.com/epinowcast/epidist/
BugReports:	https://github.com/epinowcast/epidist/issues/
Depends:	R (≥ 4.1.0)
Imports:	brms (≥ 2.23.0), checkmate, cli, dplyr, lubridate, primarycensored (≥ 1.6.0), purrr, rstan (≥ 2.26.0), stats, tibble, tidyr, utils
Suggests:	MASS, bayesplot, bookdown, collapse, distspec (≥ 0.2.0), flexsurv, ggplot2, knitr, loo, marginaleffects, patchwork, posterior, priorsense, reformulas, roxyglobals, scales, spelling, testthat (≥ 3.0.0), tidybayes, withr
Config/Needs/website:	r-lib/pkgdown, epinowcast/enwtheme
Config/testthat/edition:	3
Config/roxyglobals/filename:	globals.R
Config/roxyglobals/unique:	FALSE
LazyData:	true
VignetteBuilder:	knitr
Encoding:	UTF-8
Language:	en-GB
Config/roxygen2/version:	8.1.0
NeedsCompilation:	no
Packaged:	2026-09-29 18:46:17 UTC; lshsa2
Author:	Adam Howes [aut], Sang Woo Park [aut], Sam Abbott [aut, cre, cph], Sebastian Funk [ctb]
Maintainer:	Sam Abbott <contact@samabbott.co.uk>
Repository:	CRAN
Date/Publication:	2026-10-13 14:40:02 UTC

epidist: Estimate Epidemiological Delay Distributions with 'brms'

Description

Understanding and accurately estimating epidemiological delay distributions is important for public health policy. These estimates influence epidemic situational awareness, control strategies, and resource allocation. This package provides methods to address the key challenges in estimating these distributions, including truncation, interval censoring, and dynamical biases, following Park et al. (2024) doi:10.1101/2024.01.12.24301247 and Charniga et al. (2024) doi:10.1371/journal.pcbi.1012520. These issues are frequently overlooked, resulting in biased conclusions. Built on top of 'brms', it allows for flexible modelling including time-varying and spatial effects and partially pooled estimates of demographic characteristics.

Author(s)

Maintainer: Sam Abbott contact@samabbott.co.uk (ORCID) [copyright holder]

Authors:

• Sam Abbott contact@samabbott.co.uk (ORCID) [copyright holder]

• Adam Howes adamthowes@gmail.com (ORCID)

• Sang Woo Park swp2@princeton.edu (ORCID)

Other contributors:

• Sebastian Funk sebastian.funk@lshtm.ac.uk (ORCID) [contributor]

See Also

Useful links:

• https://epidist.epinowcast.org/

• https://github.com/epinowcast/epidist/

• Report bugs at https://github.com/epinowcast/epidist/issues/

Add a default grid cutoff to summary estimates

Description

The grid used to compute the implied summaries of an unbiased estimand must be finite. Where the study adjusted for right truncation there is no observation time to use, so a cutoff is derived from the reported values. A lognormal is matched to what each study reported by .estimates_lnorm_match(), and the cutoff is the delay beyond which one percent of its second moment lies, which for parameters meanlog and sdlog is exp(meanlog + 2 * sdlog^2 + sdlog * qnorm(0.99)). This is the same yardstick as the short cutoff check of .estimates_short_cutoff(), which fires at two percent, so the default never trips it. The cutoff is rounded up to a whole number of secondary windows with a floor of ten. Where nothing can be matched, which is a study reporting a single quantile or a mean with a standard error, the cutoff is five times the largest reported value.

Usage

.add_default_max_delay(data)

Arguments

Value

The input with an added max_delay column.

Add delay_min column to data

Description

Resolves the delay_min argument into a column on the data frame. If NULL, uses an existing delay_min column or defaults to 0. If numeric, uses that scalar. If character, looks up the named column.

Usage

.add_delay_min(data, delay_min = NULL)

Arguments

Value

The data frame with a delay_min column

Additional distributional parameter information for brms families

Description

Includes additional information (link functions and parameter bound) about the distributional parameters of a brms family which are not the conditional mean mu.

Usage

.add_dpar_info(family)

Arguments

Value

The family with other_links and other_bounds elements added.

Add the distributional parameters a primary event distribution needs

Description

Also records the distribution on the family so that the post-processing functions built from it use the same one.

Usage

.add_primary_dpars(family, data)

Arguments

Value

The family with any primary event parameters added.

Add weights to a data frame

Description

Helper function to add weights to a data frame, either from an existing column or defaulting to 1.

Usage

.add_weights(data, weight = NULL)

Arguments

Value

The data frame with an added 'n' column containing the weights

Analytic delay summaries for the families that have them

Description

Each gives the brms parameters of the family and functions of them returning the mean, the standard deviation, the quantile function and the density of the delay distribution, built by .analytic_family().

Usage

.analytic_delay_summaries(name)

Arguments

Value

A list of solutions, or NULL when the family has none.

Build the analytic delay summaries of a family

Description

Build the analytic delay summaries of a family

Usage

.analytic_family(dpars, dist, natural, mean, sd)

Arguments

Value

A list with dpars and the functions mean(d), sd(d), quantile(d, p) and density(d, x) of the brms parameters d.

Add summaries from an analytic solution

Description

Add summaries from an analytic solution

Usage

.analytic_summaries(data, analytic, probs = NULL)

Arguments

Value

The input with summary columns added.

Check that the distributional parameters of a family are present

Description

Check that the distributional parameters of a family are present

Usage

.assert_dpars(data, name, dpars)

Arguments

Value

The input, invisibly.

Check the parameters a study reported for its fitted distribution

Description

Check the parameters a study reported for its fitted distribution

Usage

.assert_estimates_parameters(family, parameters)

Arguments

Value

The parameters, ordered as the family expects.

Check the covariance matrices of an epidist_estimates_data object

Description

Each matrix must cover the rows sharing its mvn_id, be symmetric, and be positive definite, so that it has a Cholesky factor and defines a proper multivariate normal.

Usage

.assert_estimates_vcov(data)

Arguments

Value

NULL, invisibly.

Check that a fit is a meta model fitted with epidist()

Description

Check that a fit is a meta model fitted with epidist()

Usage

.assert_meta_fit(fit)

Arguments

Value

NULL, invisibly.

Assert that the group rows of an epidist_meta_model object are consistent

Description

A group row stands for several summaries reported by one study and indexes them in the flat member arrays. This checks that every index lands inside those arrays, that each kind of group has the members its likelihood needs, and that a set of quantiles is a partition of the delay axis.

Usage

.assert_meta_groups(data)

Arguments

Value

NULL, invisibly.

Check that a covariance matrix has a usable Cholesky factor

Description

A set of quantities that are deterministic functions of fewer underlying parameters has a covariance of the rank of those parameters, not of its own dimension. Five summaries of a two parameter fit are the common case. The message says so, because the alternative reading, that a column is constant or repeated, is usually not what happened. The rank is judged on the correlation matrix against .multivariate_eigen_floor(), because a covariance that is singular only up to the curvature of the map from parameters to summaries still has a Cholesky factor.

Usage

.assert_multivariate_definite(vcov)

Arguments

Value

NULL, invisibly.

Refuse a primary event distribution for a summaries only meta model

Description

The summaries only methods of as_epidist_meta_model() pass their extra arguments here. A primary among them would be silently ignored otherwise, since summary rows take their tilt from the growth_rate metadata.

Usage

.assert_no_meta_primary(...)

Arguments

Value

NULL, invisibly.

Check that a family is one the epidist helpers support

Description

Check that a family is one the epidist helpers support

Usage

.assert_supported_family(family)

Arguments

Value

The family, invisibly. Errors when the family is not supported.

Reject a grouped data.frame

Description

The ⁠as_epidist_*()⁠ constructors that build a model or aggregate object from epidist_linelist_data number rows or count observations in ways that go wrong silently on a grouped data.frame, for example dplyr::row_number() restarting within each group. Grouped input is rejected here rather than accepted and mishandled.

Usage

.assert_ungrouped(data)

Arguments

Value

NULL, invisibly. Called for the side effect of raising an error when data is a grouped data.frame.

Check a reporting window argument

Description

Accepts a single value or one value per observation, and recycles a single value so the caller can treat them the same.

Usage

.assert_window(window, n, name)

Arguments

Value

The window as a vector of length n.

Bin the delays of each stratum

Description

Bin the delays of each stratum

Usage

.bin_delays(delays, binwidth = 1, keep = NULL)

Arguments

Value

A tibble with one row per stratum and bin, holding the lower edge of the bin as delay, the weighted count n, the proportion of the stratum p and the density density.

The delay families whose brms post-processing epidist replaces

Description

The delay families whose brms post-processing epidist replaces

Usage

.brms_delay_families()

Value

A character vector of brms family names.

The stats distribution of a brms delay family

Description

Replaces the family specific parts of the brms internals ⁠log_lik_<family>()⁠ and ⁠posterior_predict_<family>()⁠ for the delay families brms provides and epidist supports. brms gives mu as the mean of the gamma, Weibull and exponential families and as the mean of the log delay for the lognormal family.

Usage

.brms_family_dist(family, prep, i)

Arguments

Value

A list with the stats distribution name dist, for example "lnorm", and its arguments args for observation i.

The post-processing functions of a delay family

Description

Gives the functions with the signatures brms expects of a custom family, for a delay family brms provides. Other families get functions that error when called, so a model can still be fitted with them.

Usage

.brms_family_fn(prefix, family)

Arguments

Value

A function.

The log likelihood of a brms delay family

Description

Replaces the brms internals ⁠log_lik_<family>()⁠, log_lik_censor() and log_lik_truncate(). Observation i may be left (cens of -1), right (1) or interval (2) censored, with the upper end of the interval in rcens, and truncated to lie between lb and ub.

Usage

.brms_family_log_lik(family, i, prep)

Arguments

Value

The log likelihood of observation i for every draw.

The mean of a brms delay family

Description

Replaces the brms internals ⁠posterior_epred_<family>()⁠.

Usage

.brms_family_posterior_epred(family, prep)

Arguments

Value

The mean delay for every draw and observation.

Draw from a brms delay family

Description

Replaces the brms internals ⁠posterior_predict_<family>()⁠ and rcontinuous(). When observation i is truncated to lie between lb and ub the delays are drawn by inverting the distribution function.

Usage

.brms_family_posterior_predict(family, i, prep)

Arguments

Value

A delay for observation i for every draw.

Expand variables into a grid and add the variables a model needs

Description

Used by the epidist_newdata() methods. Any epidist class is dropped before expanding so that the class methods documented in epidist_data do not warn about an object that was never meant to stay in its class.

Usage

.build_newdata(data, ..., .cols, .supplied = character())

Arguments

Value

A tibble::tibble() of newdata.

Capture the environment variables rstan leaks when compiling a model

Description

The rstan backend compiles through inline::cxxfunction(), which sets PKG_CPPFLAGS and PKG_LIBS and never restores them. The leaked flags make the next pkgbuild::has_build_tools() check fail, which prints a spurious compiler error before the model compiles and fits successfully. Restore them with .restore_compile_env() after a fit.

Usage

.capture_compile_env()

Value

A named character vector of the current values, NA where unset.

Check an object against the requirements of a single epidist class

Description

Check an object against the requirements of a single epidist class

Usage

.check_epidist_class(data, class)

Arguments

Value

NULL if data meets the requirements of class, or if class has no assert_epidist() method, and otherwise the message explaining why it does not.

Check that ggplot2 is installed

Description

ggplot2 is a suggested package, so the plot functions check for it before they use it.

Usage

.check_ggplot2()

Value

NULL, invisibly.

Model specific checks of user supplied prior distributions

Description

Dispatches on the class of data so that a model can reject or warn about prior distributions it does not support. By default no checks are made.

Usage

.check_model_prior(data, prior)

Arguments

Value

NULL, invisibly, called for the messages it may raise.

Check user supplied prior distributions for latent models

Description

The latent model reparameterises the event windows so that pwindow_raw and swindow_raw are on the unit interval. A non uniform prior on swindow_raw is not supported and a non uniform prior on pwindow_raw is only partially supported.

Usage

## S3 method for class 'epidist_latent_model'
.check_model_prior(data, prior)

Arguments

Value

NULL, invisibly, called for the messages it may raise.

Find the bins the data or the predictions put mass in

Description

Find the bins the data or the predictions put mass in

Usage

.delay_bins_with_mass(observed, predicted)

Arguments

Value

A tibble of the .stratum and delay of each bin to draw.

Draw the binned delays of each stratum as columns

Description

Draw the binned delays of each stratum as columns

Usage

.delay_column_plot(plot_data, legend, binwidth)

Arguments

Value

A ggplot object.

Evaluate the density of the delay distribution at each draw

Description

Uses the density of the family when there is an analytic solution, and otherwise simulates delays from each draw with .simulate_delays() and estimates their density with stats::density().

Usage

.delay_density_grid(family, dpars, max_delay = NULL, n_grid = 101, nsim = 1000)

Arguments

Value

A list with delays, the delays the density is evaluated at, and density, a matrix with one row per draw and one column per delay.

The delay distribution family of a fitted model

Description

The families epidist builds are brms custom families named after the model and the delay distribution, such as latent_lognormal. This returns the delay distribution part, which is what the summaries and the simulation need.

Usage

.delay_family(family)

Arguments

Value

A list with the delay distribution name and its distributional parameters dpars.

Find the minimum delay the datasets record

Description

Find the minimum delay the datasets record

Usage

.delay_min_of(datasets)

Arguments

Value

The single minimum delay the datasets record, or NULL when they do not all record the same one.

Label the axes of a delay plot and theme it

Description

Label the axes of a delay plot and theme it

Usage

.delay_plot_labs(p)

Arguments

Value

A ggplot object.

Draw the predicted delays over the observed delays

Description

Draw the predicted delays over the observed delays

Usage

.delay_predictive_layers(predicted, single)

Arguments

Value

A list of ggplot2 layers.

Draw a reference delay distribution over the observed delays

Description

Draw a reference delay distribution over the observed delays

Usage

.delay_reference_layer(reference, family, plot_data, binwidth)

Arguments

Value

A ggplot2 layer.

Label the strata of the observed delays of one or more datasets

Description

Takes the observed delay of each case, labels it with the dataset it came from, and hands the labelling to .draw_strata(). A single dataset with no by has one stratum, and a list of datasets is stratified by its names.

Usage

.delay_strata(datasets, by = NULL)

Arguments

Value

A list as returned by .draw_strata(), holding the observed delay of each case, its weight n and its .stratum.

Describe prior distributions for use in messages

Description

Gives each prior as its distribution followed by the parameter it applies to, dropping the matching columns which are empty. Braces are escaped so that the result can be passed to cli.

Usage

.describe_prior(prior)

Arguments

Value

A character vector with one entry per prior.

The functions of a primarycensored distribution name

Description

.pdist() gives the distribution function, .ddist() the density and .qdist() the quantile function, all found by swapping the leading p of the name.

Usage

.dist_fn(dist, type)

.pdist(dist)

.ddist(dist)

.qdist(dist)

Arguments

Value

The function of that name from the package that provides the distribution.

The distspec constructor and natural parameters of a delay family

Description

Maps the name of a delay distribution family to the distspec constructor that represents it and to a function turning draws of its brms parameters into draws of the natural parameters of that constructor.

Usage

.dist_spec_family(name)

Arguments

Value

A list with the family name, the constructor name, the brms parameters dpars it needs, and a function natural taking a list of draws of them and returning a named list of draws of the natural parameters.

Summarise draws of the delay parameters into a ⁠<dist_spec>⁠

Description

Summarise draws of the delay parameters into a ⁠<dist_spec>⁠

Usage

.dist_spec_from_draws(draws, family, max = Inf, cdf_max = 1)

Arguments

Value

A ⁠<dist_spec>⁠.

Natural scale bounds of a distributional parameter

Description

Replaces brms:::dpar_bounds() for the non-mixture families that epidist supports. Guarantees a list with character elements lb and ub giving the lower and upper bound of dpar on the natural scale, where "" means unbounded. A custom family, such as gengamma(), records its own bounds, which are returned as brms does. Unlike the brms internal, an unrecognised parameter is an error rather than NULL, because epidist cannot generate Stan code without a bound.

Usage

.dpar_bounds(dpar, family = NULL)

Arguments

Value

A list with character elements lb and ub.

Draws of each distributional parameter in a long data.frame

Description

Draws of each distributional parameter in a long data.frame

Usage

.dpar_draws(object, newdata = NULL, ...)

Arguments

Value

A data.frame with columns .row, .chain, .iteration, .draw and one column per distributional parameter.

Chain and iteration index of each posterior draw

Description

brms stores draws ordered by chain, so the chain and iteration of a draw follow from its position. A subset of draws cannot be placed this way, so both are NA in that case, as they are in tidybayes.

Usage

.draw_chain_iteration(object, pp)

Arguments

Value

A list with chain and iteration elements.

Label the strata of a data.frame of draws

Description

Label the strata of a data.frame of draws

Usage

.draw_strata(object, by = NULL)

Arguments

Value

A list with data, an ungrouped tibble of the draws with a .stratum factor column, by, the columns the strata are defined by or NULL when there is a single stratum, and legend, a legend title.

Drop the epidist_delay_draws class from an object

Description

Drop the epidist_delay_draws class from an object

Usage

.drop_delay_draws_class(data)

Arguments

Value

data without the epidist_delay_draws class.

Drop epidist classes from an object

Description

Removes class from data, and also removes the shared epidist_data class once no specific epidist class is left.

Usage

.drop_epidist_class(data, class = NULL)

Arguments

Value

data with the requested classes removed.

Remove one study from the model data of a meta model

Description

An epidist_meta_model object is subset through the epidist_data methods, which check the result, and then transformed with epidist_transform_data() so that its rows are summarised as they were for the full fit. The plain model data stored in a fit has already been transformed, so it is subset directly.

Usage

.drop_study(data, study, fit)

Arguments

Value

The model data without the rows of study.

Extract the specific epidist classes of an object

Description

Extract the specific epidist classes of an object

Usage

.epidist_classes(data)

Arguments

Value

A character vector of the epidist classes of data, excluding the shared epidist_data class.

The discrete colour scale the package plots use

Description

Uses .epidist_palette() when it holds enough colours and the viridis scale otherwise. The scale covers both the colour and the fill aesthetic, so that a variable mapped to each gets one legend.

Usage

.epidist_colour_scale(n)

Arguments

Value

A ggplot2 scale.

The families epidist defines itself

Description

brms names a custom family "custom" and keeps its own name in name, so these are looked up by that name where brms would be asked for one of its own families.

Usage

.epidist_families()

Value

A named list of family constructors.

The colour palette the package plots use

Description

The Okabe-Ito palette, ordered so that the first two colours are the blue and green the vignettes use for the primary and secondary events. It is colour blind friendly and holds eight colours.

Usage

.epidist_palette()

Value

A character vector of colours.

The theme the package plots use

Description

ggplot2::theme_minimal() with the legend below the plot, as the package documentation draws its plots.

Usage

.epidist_plot_theme()

Value

A ggplot2 theme.

A column of an epireview table, or NA where it is absent

Description

A column of an epireview table, or NA where it is absent

Usage

.epireview_column(data, names)

Arguments

Value

The first of the columns present, or a vector of NA with one entry per record where none is.

The default as_epidist_estimates_data() assumes for a metadata column

Description

Reads from .estimates_default_values so the fallback matches .fill_estimates_defaults() without restating each value here.

Usage

.epireview_default(col, meta)

Arguments

Value

A vector with one default per record.

The family epidist calls a distribution epireview names

Description

The family epidist calls a distribution epireview names

Usage

.epireview_family(type)

Arguments

Value

A character vector of families, NA where the family is not one epidist_estimates_parameters() supports.

Resolve the study metadata of each epireview record

Description

Starts from the metadata shared by every record, replaces it with the values metadata gives for each study, and fills the studies a column leaves blank with the default as_epidist_estimates_data() would assume. A column no study has a value for is left out, so that as_epidist_estimates_data() assumes it and messages once. The studies filled are reported by .epireview_report_gaps() once the records kept are known, so that a dropped record is not named.

Usage

.epireview_metadata(studies, n, metadata, shared)

Arguments

Value

A list holding meta, a tibble with one row per record and the study, n and metadata columns that were given, and filled, a list with one logical vector per column filled marking the records filled.

The metadata columns epidist_estimates_epireview() takes

Description

The metadata columns epidist_estimates_epireview() takes

Usage

.epireview_metadata_cols()

Value

A character vector of column names.

The parameter name epidist uses for a parameter type epireview names

Description

The parameter name epidist uses for a parameter type epireview names

Usage

.epireview_parameter_name(type)

Arguments

Value

A character vector of parameter names, NA where the type is not recognised. A mean is "mean" and a standard deviation "sd", which are the moments a fit is often recorded by rather than natural parameters.

The natural parameters of the distribution an epireview record fitted

Description

The natural parameters of the distribution an epireview record fitted

Usage

.epireview_parameters(data)

Arguments

Value

A list with one element per record, NULL where the record does not report a supported family by a supported set of parameters, and otherwise a list holding the family and the named parameters.

Message about the epireview records that were dropped

Description

Message about the epireview records that were dropped

Usage

.epireview_report_dropped(studies, reason)

Arguments

Value

NULL, invisibly, called for the message it may raise.

Message about the studies a metadata column left blank

Description

A study assumed to have adjusted for right truncation is warned about, as as_epidist_estimates_data() warns.

Usage

.epireview_report_gaps(meta, filled, kept)

Arguments

Value

NULL, invisibly, called for the messages it may raise.

The rows of the long format one epireview record contributes

Description

The rows of the long format one epireview record contributes

Usage

.epireview_row(record, type, value, se = NA_real_, p = NA_real_)

Arguments

Value

A data.frame with one row per value.

Map each epireview record to the rows of the long format

Description

Map each epireview record to the rows of the long format

Usage

.epireview_rows(data, meta)

Arguments

Value

A data.frame with a .record column indexing the records and the type, value, se and p of each row.

The standard deviation an epireview record reports alongside its mean

Description

The standard deviation an epireview record reports alongside its mean

Usage

.epireview_sd(data, i, spread, spread_type)

Arguments

Value

The standard deviation, or NA where none is reported. A standard deviation of zero is treated as not reported by the caller, because as_epidist_estimates_data() rejects it.

Check the shared study metadata passed to epidist_estimates_epireview()

Description

Check the shared study metadata passed to epidist_estimates_epireview()

Usage

.epireview_shared_metadata(...)

Arguments

Value

A named list with one value per metadata column given.

Escape braces so that cli does not interpolate them

Description

Messages from checkmate contain braces, which cli would otherwise treat as glue interpolation.

Usage

.escape_braces(x)

Arguments

Value

x with each brace doubled.

Advise on summary estimates the meta model will fit poorly

Description

Runs the advisory checks on a freshly built epidist_estimates_data object and messages about each study they flag. They run once, here, when the object is first built, rather than in assert_epidist(), so that passing the finished object on to as_epidist_meta_model() does not repeat them. The pointer to the Checks section of as_epidist_estimates_data.data.frame(), which describes the checks, prints once after the messages when at least one check fired.

Usage

.estimates_advise(data)

Arguments

Value

NULL, invisibly, called for the messages it may raise.

Bind coerced contributions into one epidist_estimates_data object

Description

Covariance matrices are keyed by mvn_id, so a key used by two contributions is renamed before the rows are bound.

Usage

.estimates_bind(parts)

Arguments

Value

An epidist_estimates_data object.

The pointer that follows the advisory messages

Description

The pointer that follows the advisory messages

Usage

.estimates_checks_pointer()

Value

A named character vector for cli::cli_inform().

Studies whose quadrature nodes are far apart relative to their delays

Description

The number of quadrature intervals of .estimates_n_quad() is capped, so a study whose grid cutoff is very long relative to the spread it reported is left with nodes further apart than a quarter of that spread. This covers a study that did not adjust for right truncation and used a continuous adjustment (cens_adjusted of 1, 2 or 4), a study that did adjust but whose primary events were not uniform within their window (cens_adjusted of 2 or 4 with a non zero or estimated growth_rate), and the quantile members of a covariance matrix group, which are read off the same nodes.

Usage

.estimates_coarse_quadrature(data)

Arguments

Value

A character vector of study identifiers whose quadrature is coarse.

Studies reporting quantiles on a coarse delay grid

Description

The studies flagged by .estimates_coarse_rows().

Usage

.estimates_coarse_quantiles(data)

Arguments

Value

A character vector of study identifiers reporting quantiles on a coarse grid.

The smallest quantile of each study on a coarse delay grid

Description

A study that summarised interval censored delays without adjusting for censoring (cens_adjusted of 0 or 3) reports quantiles of a discrete distribution, which the model interpolates through the mid points of its cells. The reported value is still rounded to that grid, and what the interpolation leaves behind does not shrink with the study sample size. It is a few percent once a reported quantile sits a few tens of cells above the smallest delay the study counted, and tens of percent when it sits within about ten. A study is flagged on its smallest reported quantile, the one nearest that edge of the grid, because the residual on that quantile is what biases the fitted spread even when the larger quantiles of the same study sit well up the grid. A reported mean and standard deviation of the same delays do not carry this residual, so they should be fitted in preference where the study gives them.

Usage

.estimates_coarse_rows(data)

Arguments

Value

A logical vector, one entry per row, marking the smallest reported quantile of each flagged study.

Default values as_epidist_estimates_data() assumes for metadata columns

Description

Shared by .fill_estimates_defaults() and .epireview_default() so the two stay in step.

Usage

.estimates_default_values

A numerical Jacobian of the map from parameters to summaries

Description

Uses a central difference with a step relative to each parameter, held away from zero so that a parameter reported as zero still moves. The step of a parameter constrained to be positive is held below half its value, so the lower evaluation stays inside the support.

Usage

.estimates_delta_jacobian(fn, x, positive)

Arguments

Details

A numerical Jacobian is used because the derivative of a quantile with respect to the shape of a gamma or a weibull has no closed form.

Value

A matrix with one row per summary and one column per parameter.

Build an epidist_estimates_data object from one study's summaries

Description

Build an epidist_estimates_data object from one study's summaries

Usage

.estimates_from_summaries(study, value, type, p, se, n, ...)

Arguments

Value

An epidist_estimates_data object.

The grid cutoff implied by a set of summary estimates

Description

Studies that did not adjust for right truncation are evaluated on a grid running to their observation time. Studies that did are evaluated on a grid running to max_delay.

Usage

.estimates_grid_cutoff(data)

Arguments

Value

A numeric vector of grid cutoffs.

Which summary estimates estimate their growth rate

Description

A study whose growth_rate is NA, or which reported it with a positive growth_rate_sd, takes its rate from the pgrowth distributional parameter of the meta model rather than from a number. See as_epidist_estimates_data().

Usage

.estimates_growth_estimated(data)

Arguments

Value

A logical vector, one entry per row.

Which summary estimates have a tilted primary event

Description

The primary event is uniform within its window only for a known growth rate of zero. A non zero rate tilts it, and an estimated rate is taken to tilt it whatever value the parameter holds, so that the choice of path does not depend on a parameter.

Usage

.estimates_growth_tilted(data)

Arguments

Value

A logical vector, one entry per row.

Reported standard deviations with a heavy tailed sampling error

Description

The sampling standard error of a reported standard deviation is \sigma \sqrt{(\kappa - 1) / (4 n)}, with \kappa the kurtosis of the delays. The normal approximation behind it holds while that relative standard error is below about a quarter. Above it the sampling distribution of a sample standard deviation is far from normal, the asymptotic standard error overstates its spread by up to two times, and the joint likelihood of a mean and standard deviation pair is biased by about a standard error. The kurtosis is taken from the reported mean and standard deviation under a lognormal delay, which is a plausible tail for a delay of that coefficient of variation.

Usage

.estimates_heavy_tail_rows(data)

Arguments

Value

A logical vector, one entry per row, marking each reported standard deviation with a heavy tailed sampling error.

Studies whose reported standard deviation has a heavy tailed sampling error

Description

The studies flagged by .estimates_heavy_tail_rows().

Usage

.estimates_heavy_tail_sd(data)

Arguments

Value

A character vector of study identifiers.

A lognormal matched to the summaries a study reported

Description

Matches a lognormal to a reported mean and standard deviation by its moments. Where the study reported only quantiles, its median is the location and its largest quantile above the median, at the level the study reported it, sets the scale. A study reporting neither pair, or one whose quantiles do not increase, gives NULL.

Usage

.estimates_lnorm_match(data, rows)

Arguments

Value

A list with meanlog and sdlog elements, or NULL.

The moments a reported fit is summarised by

Description

The moments a reported fit is summarised by

Usage

.estimates_moments(moments, probs)

Arguments

Value

The moments, ordered as the summary vector expects.

What each element of a multivariate representation reports

Description

What each element of a multivariate representation reports

Usage

.estimates_multivariate_types(params)

Arguments

Value

A list with the type and p of each element.

Summarise draws of a study's fitted parameters

Description

Summarise draws of a study's fitted parameters

Usage

.estimates_mvn_summarise(data, family, moments, probs, ...)

Arguments

Value

A list with the type, p, value and vcov of the summaries.

The number of quadrature intervals each summary row is evaluated on

Description

The moments and distribution function of a continuous estimand that is truncated at the grid cutoff are computed by Simpson's rule on equally spaced intervals running from delay_min to the cutoff, so the node spacing is set by the cutoff and not by the scale of the delay. A fixed number of intervals leaves a narrow delay unresolved on a wide grid, which pins its implied kurtosis at its floor and can put its implied standard deviation out by a factor of two. The number is therefore chosen per study so that the spacing is at most a quarter of the spread the study reported, see .estimates_spread(), with options(epidist.meta_n_quad) as its floor and .meta_n_quad_max() as its cap unless the option is set above it. It is even, because the quadrature uses Simpson's rule.

Usage

.estimates_n_quad(data)

Arguments

Details

Every row gets a number, including rows on the discrete grid, which do not use it.

Value

An integer vector of interval counts, one per row.

The primarycensored distribution function name of a reported family

Description

The primarycensored distribution function name of a reported family

Usage

.estimates_parameter_dist(family)

Arguments

Value

A distribution function name.

Which reported parameters are constrained to be positive

Description

Which reported parameters are constrained to be positive

Usage

.estimates_parameter_positive(names)

Arguments

Value

A logical vector, one entry per parameter.

The parameterisations supported for a reported distribution

Description

Each family lists the sets of parameter names a study may report it with. The first set of each family is the one used internally.

Usage

.estimates_parameter_sets()

Value

A named list of character vectors of parameter names.

The summaries a reported distribution implies

Description

The summaries a reported distribution implies

Usage

.estimates_parameter_summary(
  family,
  parameters,
  moments,
  probs,
  lower = 0,
  cutoff = Inf
)

Arguments

Value

A numeric vector of summaries, the moments first.

The largest reported quantile a set of summary estimates can support

Description

A quantile reported at or beyond the top of the estimand's support has an implied cumulative probability of one and an implied density of zero, so the delta method conversion of a delay scale standard error hits its floor and the row contributes a constant to the likelihood instead of information. The limit is the top of the discrete grid for a study that did not adjust for censoring, allowing for the half cell the continuity correction adds and for the half window midpoint imputation shifts by, and the grid cutoff otherwise.

Usage

.estimates_quantile_limit(data)

Arguments

Value

A numeric vector of limits, one per row.

The range of delays a study's reported distribution describes

Description

A study that fitted a distribution to right truncated data without correcting for the truncation reported a distribution with more spread than the delays it saw, because its family carries a tail beyond the point its data stop. Summaries of the reported distribution are therefore taken over the range of delays the study could have seen, which is the same range the meta model computes its implied summaries over. The metadata that gives that range is already on its way onto the returned rows, so it is read from there rather than asked for again.

Usage

.estimates_reported_support(...)

Arguments

Value

A list with the study's lower and cutoff delays.

Label flagged summary rows by study and position in the input

Description

Label flagged summary rows by study and position in the input

Usage

.estimates_row_labels(data, rows)

Arguments

Value

A character vector such as ⁠"A" (row 2)⁠, one entry per selected row.

Attach reported covariance matrices to an epidist_estimates_data object

Description

The matrices are held alongside the data rather than in it, because a covariance matrix spans several rows. They are keyed by the mvn_id column, which names the multivariate object the rows came from, so one study may contribute more than one. Their Cholesky factors are built once by as_epidist_meta_model() and passed to Stan, so the sampler never decomposes them.

Usage

.estimates_set_vcov(data, vcov)

Arguments

Details

Only as_epidist_estimates_data.epidist_multivariate() writes to this.

Value

The input with the matrices attached.

Studies whose grid cutoff is short relative to their reported tail

Description

The implied summaries of a study that did not adjust for censoring but did adjust for right truncation are computed on a grid running to max_delay. A cutoff that the delay distribution has not decayed by biases them downwards, and the standard deviation most, because the tail beyond the cutoff carries a share of the second moment out of all proportion to its mass. A lognormal is matched to what each study reported, through its mean and standard deviation, or its median and largest quantile above the median where it reported only quantiles, and the study is flagged when more than 2% of the second moment of that lognormal lies beyond the cutoff. That is where the standard deviation on the grid falls about 1% short, and the shortfall grows with the share. Studies reporting neither pair are not checked.

Usage

.estimates_short_cutoff(data)

Arguments

Value

A character vector of study identifiers with a short cutoff.

The spread each study reported, as a proxy for its delay standard deviation

Description

The quadrature a summary row uses has to resolve the delay distribution, whose scale is only known once the model is fitted. The spread the study itself reported stands in for it. That is its reported standard deviation where it gave one, the range of its reported quantiles divided by the same range of a standard normal where it gave two or more, and otherwise a quarter of the smallest location it reported, which is the coefficient of variation below which a delay is narrow. The proxy only has to be within a factor of two or so, because the resolution is chosen well inside where Simpson's rule converges.

Usage

.estimates_spread(data)

Arguments

Value

A numeric vector of spreads, one per row.

The reported covariance matrices of an epidist_estimates_data object

Description

The reported covariance matrices of an epidist_estimates_data object

Usage

.estimates_vcov(data)

Arguments

Value

A named list of covariance matrices, empty when no study reported one.

Which rows of an epidist_estimates_data object have a covariance matrix

Description

Which rows of an epidist_estimates_data object have a covariance matrix

Usage

.estimates_vcov_rows(data)

Arguments

Value

A logical vector, one entry per row.

The unit the advisory messages count a study's censoring windows in

Description

The unit the advisory messages count a study's censoring windows in

Usage

.estimates_window_unit(swindow)

Arguments

Value

"days" for daily windows, "weeks" for weekly ones, and "censoring windows" otherwise.

Expand a dot in a model formula

Description

Replaces the part of brms:::expand_dot_formula() that epidist needs. A formula containing . on the right hand side is expanded against data, keeping the attributes of the original formula.

Usage

.expand_dot_formula(formula, data = NULL)

Arguments

Value

The expanded formula.

Extract distributional parameter terms from a brms formula

Description

This function extracts all unique terms from the right-hand side of all distributional parameters in a brms formula.

Usage

.extract_dpar_terms(formula)

Arguments

Value

A character vector of unique terms.

Build the Stan functions block shared by the marginal and meta models

Description

Both models read a functions.stan chunk with the same placeholders (family, dist_id, dpars_A, dpars_B, and the pair ⁠primary_id, primary_params⁠), filled in with the target distribution's details and the primary event distribution. dpars_B is the parameter order of primarycensored, which a family may record as pcd_param where it differs from the order of its Stan density. Used within epidist_stancode() methods for the marginal and meta models, which differ only in the chunk path, the family name prefix, and any further placeholders they need substituted.

Usage

.family_functions_stanvar(
  chunk_path,
  family,
  family_prefix,
  primary = .primary_spec("uniform"),
  extra = character()
)

Arguments

Value

A brms stanvars object holding the substituted functions chunk.

The name of a delay distribution family

Description

A family built with brms::custom_family(), such as gengamma(), is named "custom" for brms to dispatch on and records its own name in name. Every other family is named by family.

Usage

.family_name(family)

Arguments

Value

A character string.

Stan functions a family defines itself

Description

A family brms does not have, such as gengamma(), carries the Stan density and distribution function brms and the latent model call. They are read from the ⁠stan/family/⁠ folder of the installed package.

Usage

.family_stanvars(family)

Arguments

Value

A brms stanvars object, or NULL for a brms family.

Fill in the optional columns of an epidist_estimates_data object

Description

Applies the documented defaults for study metadata that was not supplied, informing the user about each assumption made on their behalf.

Usage

.fill_estimates_defaults(data)

Arguments

Value

The input with all of .estimates_required_cols() present.

Give every distributional parameter after mu a link

Description

brms::custom_family() recycles a single link over every parameter, and a family such as brms::brmsfamily()'s Gamma carries no link for its other parameters, so a link appended for a further parameter would be matched to the wrong one. The missing links are filled with the link of mu, which is what the recycling gives.

Usage

.fill_other_links(family)

Arguments

Value

The family with one entry of other_links per parameter after mu.

The name of the brms family a fit was made with

Description

The families epidist builds are custom families named after the model and the delay distribution, such as meta_lognormal.

Usage

.fit_family_name(fit)

Arguments

Value

A string.

Default newdata for a fitted model

Description

Expands the variables in the distributional parameter formulas into a grid with epidist_newdata(), so there is one row per unique combination of the predictors with no censoring and no truncation. brms keeps the data a model was fitted to as a plain data.frame, so the epidist class is restored from the family name first.

Usage

.fit_newdata(object)

Arguments

Value

A tibble::tibble() of newdata.

Take the observed delays of a fitted model

Description

Reads the response and the case weights of the model data, and the strata to colour by, which default to the variables in the distributional parameter formulas as they do in epidist_strata().

Usage

.fitted_delays(x, by = NULL)

Arguments

Value

A list with data, a tibble of the observed delay of each case, its weight n and the columns in by, and by, the columns the strata are defined by or NULL when there are none.

Round to the nearest multiple

Description

This function rounds an input x down to the nearest multiple of some number f. For example, if f = 0.2 and x = 1.5 then the output would be 1.4. If f = 1 then floor_mult behaves as floor. If f = 0 then x is returned.

Usage

.floor_mult(x, f = 1)

Arguments

Value

x rounded down to the nearest multiple of f.

The Stacy parameters of a brms prep object for gengamma()

Description

The Stacy parameters of a brms prep object for gengamma()

Usage

.gengamma_dpars(prep, i = NULL)

Arguments

Value

A named list of shape, scale and k.

The brms post-processing functions of the gengamma() family

Description

The brms post-processing functions of the gengamma() family

Usage

.gengamma_log_lik(i, prep)

.gengamma_posterior_predict(i, prep, ...)

.gengamma_posterior_epred(prep)

Arguments

Value

The log likelihood of observation i for every draw, a delay drawn for observation i for every draw, and the mean of the delay for every draw and observation.

The mean and standard deviation of the generalised gamma distribution

Description

From the raw moments E[T^r] = scale^r \Gamma(k + r / shape) / \Gamma(k) of the Stacy form.

Usage

.gengamma_mean(scale, shape, k)

.gengamma_sd(scale, shape, k)

Arguments

Value

A numeric vector.

Convert the generalised gamma from the Prentice to the Stacy form

Description

primarycensored and flexsurv::dgengamma.orig() use the Stacy (1962) form with shape, scale and k. It has no counterpart for Q of zero or below, which is why gengamma() keeps Q positive.

Usage

.gengamma_stacy(mu, sigma, Q)

Arguments

Value

A named list of shape, scale and k.

Get the post-processing function of a family by prefix

Description

Gets the function brms would call for a family, such as log_lik or posterior_predict. A family epidist defines itself, such as gengamma(), carries these functions, so they are taken from it, whether it is given as the family or as a model family built on it. For a brms family they come from .brms_family_fn().

Usage

.get_brms_fn(prefix, family)

Arguments

Value

The requested function

Check for a non uniform prior on a latent model event window

Description

Check for a non uniform prior on a latent model event window

Usage

.has_non_uniform_window_prior(prior, parameter)

Arguments

Value

A logical, TRUE if a non uniform prior has been supplied.

Are the infinite values of data all observation times?

Description

Are the infinite values of data all observation times?

Usage

.inf_is_obs_time_only(data)

Arguments

Value

TRUE when data holds at least one infinite value and every column holding one is an .obs_time_cols() column, and FALSE otherwise.

The brms warning about infinite values in the data

Description

A substring of the message brms:::validate_data() warns with, which brms::prepare_predictions() reaches through brms:::validate_newdata(). Matching a substring rather than the whole message keeps the match narrow enough not to catch another warning, while surviving a change to the rest of the sentence. A reworded message brings the warning back rather than muffling something else.

Usage

.infinite_data_warning()

Value

A string to match against a warning message.

Inform users about data summarisation

Description

This function informs users when data has been summarised by unique combinations of variables, providing information about the variables used and the reduction in number of rows.

Usage

.inform_data_summarised(data, trans_data, required_cols)

Arguments

Value

Nothing, called for side effects only

Combine the model and family specific prior distributions

Description

Model specific priors from epidist_model_prior() overwrite family specific priors from epidist_family_prior(). The result is then restricted to the parameters brms recognises, so that priors for parameters which are not in the model are dropped.

Usage

.internal_prior(data, family, formula, default)

Arguments

Value

A brmsprior object, or NULL when there are no internal priors.

Identify manually specified brms priors

Description

Manual priors are written using the parameter ~ distribution syntax and are passed through to the Stan model block unchanged. They cannot be matched on parameter metadata in the way that standard brms priors can.

Usage

.is_manual_prior(prior)

Arguments

Value

A logical vector flagging the manually specified priors.

Attach the model's predictors from newdata to a comparison

Description

study in out already names the held out study, so a study predictor in newdata, such as one built with epidist_newdata(meta, study), is excluded to avoid a second column of the same name.

Usage

.leave_one_out_bind_predictors(out, newdata, formula)

Arguments

Value

out with any predictors of formula present in newdata, other than study, added after .row.

Compare the summaries of leave one out refits with the full fit

Description

Compare the summaries of leave one out refits with the full fit

Usage

.leave_one_out_compare(held, full)

Arguments

Value

held with the full fit values added as full_estimate, full_lower and full_upper, and the refit's median and interval minus the full fit's median as difference, difference_lower and difference_upper.

The cores of each leave-one-out refit

Description

brms does not store the cores a model was fitted with, so this gives cores, else the mc.cores option, else one core per chain.

Usage

.leave_one_out_cores(cores, chains)

Arguments

Value

An integer.

The model data used to hold each study out of a meta model fit

Description

The model data used to hold each study out of a meta model fit

Usage

.leave_one_out_data(fit, data = NULL)

Arguments

Value

The epidist_meta_model object given as data, or the plain data.frame of model data stored in fit.

The default newdata for comparing leave one out refits

Description

A single row giving the population level delay with no censoring and no truncation. epidist_newdata() only reads its data argument to expand variables, so a copy of the model data carrying the class is enough.

Usage

.leave_one_out_newdata(fit)

Arguments

Value

A tibble::tibble() of one row.

The studies of a meta model to hold out

Description

The studies of a meta model to hold out

Usage

.leave_one_out_studies(data, studies = NULL)

Arguments

Value

A character vector of study labels, in order of first appearance, or studies in the order given.

Posterior summaries of the delay mean and standard deviation of a fit

Description

Posterior summaries of the delay mean and standard deviation of a fit

Usage

.leave_one_out_summaries(fit, newdata, re_formula = NA, width)

Arguments

Value

A tibble with one row per row of newdata and summary, with columns .row, summary, estimate (the posterior median), lower and upper.

Apply observation weights to a log likelihood

Description

Replaces brms:::log_lik_weight(). Multiplies x by the weight of observation i, if the model has weights, and returns x unchanged otherwise.

Usage

.log_lik_weight(x, i, prep)

Arguments

Value

The weighted log likelihood values.

Include implicit intercepts in brms formula as explicit

Description

This function detects the distributional parameters in a brms formula object, and alters to formula to include explicit intercept parameters for them i.e. ~ 1.

Usage

.make_intercepts_explicit(formula)

Arguments

Value

The formula with an explicit intercept for every distributional parameter that had none.

Extract the parameter name of a manually specified brms prior

Description

Extract the parameter name of a manually specified brms prior

Usage

.manual_prior_parameter(prior)

Arguments

Value

A character vector of parameter names.

The density of a continuous estimand under an accrual design

Description

The distribution function is interpolated linearly between quadrature nodes, so its slope on the interval containing the reported value is the density there.

Usage

.meta_accrual_density(
  y,
  dist,
  args,
  lower = 0,
  cutoff,
  pwindow,
  cens_adjusted,
  growth_rate,
  n_quad = .meta_n_quad()
)

Arguments

Value

A density on the delay scale.

Whether accrual weighting applies to a summary row

Description

The truncation design only matters for a study that did not adjust for right truncation, because a study that did has already removed the effect the design would have had.

Usage

.meta_accrual_flag(trunc_adjusted, trunc_design)

Arguments

Value

1 if the accrual weight applies, 0 otherwise.

The accrual weighted distribution function on the quadrature grid

Description

The weight is offset by half a primary window for the uniform single interval approximation, matching .meta_pcens_trunc_moments(), so that the reported quantile and the reported moments describe the same estimand.

Usage

.meta_accrual_nodes(
  dist,
  args,
  lower = 0,
  cutoff,
  pwindow,
  cens_adjusted,
  growth_rate,
  n_quad = .meta_n_quad()
)

Arguments

Value

A distribution function at n_quad + 1 equally spaced nodes.

The distribution function of a continuous estimand under an accrual design

Description

Interpolates the accrual weighted distribution function of .meta_accrual_nodes() linearly at the reported value.

Usage

.meta_accrual_prob(
  y,
  dist,
  args,
  lower = 0,
  cutoff,
  pwindow,
  cens_adjusted,
  growth_rate,
  n_quad = .meta_n_quad()
)

Arguments

Value

A probability.

Reweight a distribution function for an accrual design

Description

Weights the probability mass between consecutive quadrature nodes by the follow up available at the midpoint of the interval, then renormalises, so that the returned distribution function is that of the delays a study collecting up to a calendar stop would have seen. The midpoint is used rather than a node because it makes the quadrature second order accurate.

Usage

.meta_accrual_reweight(cdf, lower, cutoff, growth_rate, weight_offset = 0)

Arguments

Details

The follow up available to a primary event depends on the calendar time of the event itself, which is only known to within its censoring window. Where the quantity being weighted already includes the offset of the primary event within that window, as it does for the uniform single interval approximation, weight_offset shifts the weight so that it is evaluated at the underlying primary event time. Averaging over the window makes the shift half its width. Without it the follow up is systematically half a window short, which biases the implied summaries downwards.

Value

A distribution function at the same nodes, running from zero to one.

The follow up available to a delay under an accrual design, up to a constant

Description

Every use of the accrual weight renormalises afterwards, so the weights are returned relative to their largest value to avoid overflow. A growth rate of zero makes the follow up linear in the delay, which is taken directly rather than through the log scale form.

Usage

.meta_accrual_weight(d, window, growth_rate)

Arguments

Value

A numeric vector of relative weights with a maximum of one.

Add the pgrowth parameter a summary row with an estimated growth rate needs

Description

A summary row whose growth rate is estimated reads the pgrowth distributional parameter, which the family only carries where the individual level rows use an exponential growth primary event. It is added here otherwise, with the link and bounds of that primary event, while the primary event of the individual level rows is left as it is.

Usage

.meta_add_growth_dpar(family, data)

Arguments

Value

The family with pgrowth among its distributional parameters where a summary row needs it.

Add an independent uniform primary window to a set of summaries

Description

The uniform single interval approximation leaves the primary interval uncorrected, so the study effectively summarised the delay plus an independent draw from a uniform distribution over the primary window. This convolution is exact when the study also adjusted for right truncation and the primary events were uniform within their window.

Usage

.meta_add_uniform(moments, pwindow)

Arguments

Value

A named numeric vector with elements mean, sd, kurtosis and skewness.

Assign summary estimates to joint likelihood groups

Description

Summaries reported by the same study are fitted jointly, so they must be collected into groups before the model rows are built. Two summaries share a group only when they agree on every column other than the summary itself, that is on the study, its metadata, and any covariates the user supplied. This keeps the grouping correct for any brms formula, because a linear predictor built from those columns cannot vary within a group.

Usage

.meta_assign_groups(estimates, mvn = NULL)

Arguments

Details

A study with a continuous estimand (cens_adjusted 1, 2 or 4) has every kind of summary in one group, because the sampling covariance of its mean, standard deviation and quantiles is available from the implied distribution. See .meta_joint_covariance(). On the discrete grid (cens_adjusted 0 or 3) the mean and standard deviation group together and the quantiles group together, but the two are not mixed because the quantiles are fitted as discrete statistics, so such a study is counted twice where it reports both kinds. A study reporting more than one mean, or more than one standard deviation, with otherwise identical metadata has the repeats split into further groups. A summary with its own reported standard error is left on its own, because that standard error replaces the sampling uncertainty the joint likelihood would derive.

The summaries covered by one covariance matrix are one group, whatever their types, because the matrix is what ties them together. They are identified by their shared mvn_id, so one study may contribute more than one such group.

Value

An integer vector of group identifiers, one per row.

The half width of the band of counts the forward pass keeps

Description

The forward pass of .meta_grid_box_ll() sums over the counts within six standard deviations and eight counts of the most likely path, plus the stride of the grid that path was found on. The mass beyond six standard deviations is below 1e-9 of the total for every binomial, including the Poisson like tail of a step with a small mean, which the eight counts cover. Matches meta_family_band_half_width() in Stan.

Usage

.meta_band_half_width(variance, stride)

Arguments

Value

An integer number of counts.

The counts of a coarse grid within a box

Description

The box boundaries and every multiple of the stride between them, so that a most likely count sitting on a boundary is on the grid.

Usage

.meta_box_grid(lower, upper, stride)

Arguments

Value

An increasing integer vector of counts.

The most likely path of the constrained chain of cumulative counts

Description

A Viterbi pass over the coarse grid of .meta_box_grid() at every edge, which finds the counts a study most probably had at each edge given every box, to within a stride. The forward pass of .meta_grid_box_ll() is then kept to a band around them. Centring on the counts the boxes pull the chain to, rather than on the counts the parameters expect at each edge, is what keeps the pass accurate where a later quantile forces an earlier count far from its mean. The distribution function is rounded to 2^{-20} by .meta_fixed_point() first, as Stan must to keep the search off the autodiff stack. Matches meta_family_box_mode_path() in Stan.

Usage

.meta_box_mode_path(study_n, cdf, lower, upper, stride)

Arguments

Value

An integer vector of counts, one per edge, or NULL when no path satisfies every box.

One step of the forward pass over the cumulative counts

Description

Carries the log probabilities of the counts in one band to the counts in the next, through the binomial step of the chain. The step is a matrix product of .meta_step_kernel() with the exponentiated source vector, each scaled so that the arithmetic stays in range, and a sum on the log scale over every pair of counts where the kernel would underflow at the most likely step. Both give the same probabilities. Matches meta_family_box_step() in Stan.

Usage

.meta_box_step(alpha, a, b, a2, b2, r, study_n, m_prev, m, lg)

Arguments

Value

The log probabilities of the target counts a2:b2.

The stride of the coarse grid of counts the forward pass centres on

Description

The most likely path of the constrained chain of counts is found on a grid of every strideth count, about half a standard deviation of a binomial apart, so that a search over it costs about four times the sample size per edge. Matches meta_family_box_stride() in Stan.

Usage

.meta_box_stride(study_n)

Arguments

Value

An integer stride of at least one.

The smallest probability a multinomial cell is given

Description

A cell whose implied probability underflows to zero while the study saw delays in it would give a log likelihood of -Inf. Stan differences log distribution functions and so keeps a tiny mass in such a cell, where R differences them on the natural scale and gets exactly zero. Both floor the cell here, so that a single badly misfitting draw is rejected in practice but leaves loo() a finite value.

Usage

.meta_cell_floor()

Value

A probability.

The censoring adjustment whose estimand a code is built on

Description

Two adjustment codes are another code's estimand moved along the delay axis by a fixed amount, because the study replaced an event time with the midpoint of its window. Midpoint imputation of the secondary interval (code 3) moves the naive discrete grid of code 0. Midpoint imputation of the primary event (code 4) moves the primary censored estimand of code 2. Both are evaluated by calling the base code and moving the result, so each estimand is implemented once.

Usage

.meta_cens_base(cens_adjusted)

Arguments

Details

Matches meta_family_cens_base in inst/stan/meta_model/functions.stan.

Value

The code whose estimand is evaluated.

The left truncation point of the base estimand a midpoint code is built on

Description

delay_min is the smallest delay a study counted on the scale it reported, so a midpoint code that moved its estimand along the delay axis dropped the records whose moved delay fell below it. The base estimand is therefore left truncated at delay_min moved back by the same shift. A delay_min of zero means the study counted every delay and is left alone, because it is the sentinel that selects the untruncated formulas, even for code 4 whose reported delays can be negative.

Usage

.meta_cens_lower(lower, cens_adjusted, pwindow, swindow)

Arguments

Details

The right truncation point is not moved, because the observation time bounds the underlying event, not the midpointed value.

Matches meta_family_cens_lower in inst/stan/meta_model/functions.stan.

Value

The left truncation point of the base estimand.

The delay a midpoint imputation moves the base estimand by

Description

Midpoint imputation of the secondary interval (code 3) assigns each delay to the centre of the interval it was seen in, moving it up by half a secondary window. Midpoint imputation of the primary event (code 4) anchors the delay at the centre of the primary window rather than at its lower edge, moving it down by half a primary window. Every other code leaves its estimand where it is.

Usage

.meta_cens_shift(cens_adjusted, pwindow, swindow)

Arguments

Details

Matches meta_family_shift in inst/stan/meta_model/functions.stan.

Value

A signed delay.

The slots of the base estimand a midpoint code is built on

Description

Replaces the censoring adjustment code by the code it is built on and moves the left truncation point with it. See .meta_cens_base() and .meta_cens_lower().

Usage

.meta_cens_slots(slots)

Arguments

Value

The slots of the base estimand.

A central difference of the implied distribution function

Description

Used where the density of the biased estimand has no closed form, which is the primary censored delay of a study whose primary events were not uniform within their window.

Usage

.meta_central_difference(
  y,
  dist,
  args,
  lower = 0,
  cutoff,
  pwindow,
  swindow,
  trunc_adjusted,
  cens_adjusted,
  growth_rate,
  trunc_design = 0L,
  n_quad = .meta_n_quad()
)

Arguments

Value

A density on the delay scale.

Summarise a distribution from its first four raw moments

Description

Summarise a distribution from its first four raw moments

Usage

.meta_central_from_raw(moments)

Arguments

Value

A named numeric vector with elements mean, sd, kurtosis and skewness.

The flat Cholesky factors of an epidist_meta_model object

Description

A group covered by a covariance matrix has the Cholesky factor of that matrix stored here, in column major order, and its row indexes into this vector with chol_start. Factoring once here rather than inside the likelihood keeps the matrix out of every gradient evaluation.

Usage

.meta_chol(data)

Arguments

Value

A numeric vector of Cholesky factor entries.

Analytic summaries of a delay distribution

Description

The mean and standard deviation mirror the formulas used by add_summaries(). A draw wide enough to overflow a moment, such as a lognormal whose exp(4 * sdlog^2) is infinite, is returned as .meta_moment_failure() so that the row is rejected rather than carrying a NaN into its standard error. Matches the reject in meta_family_moments() in inst/stan/meta_model/functions.stan, where an infinite intermediate would otherwise leave a finite density with a non finite gradient.

Usage

.meta_continuous_moments(dist, args)

Arguments

Value

A named numeric vector with elements mean, sd, kurtosis and skewness.

The box constraints a set of integer day quantiles puts on a study

Description

A type 1 quantile at probability p of n delays is their \lceil n p \rceilth smallest, so two reported at probabilities that name the same order statistic cannot land on different days. Such a group would give every parameter a log likelihood of -Inf, so it is refused here with a message that says why.

Usage

.meta_crossing_box(estimates, study_n)

Arguments

Value

A list of the count and lower member columns of .meta_member_table().

The order statistics a set of type 1 quantiles stand for

Description

A type 1 quantile at probability p of n delays is the \lceil n p \rceilth smallest of them. A quantile of integer day delays reported as day y therefore says the study saw fewer than that many delays below y and at least that many at or below it, which are the box constraints .meta_grid_box_ll() fits. The rounding guard matches .meta_grid_crossing_ll(), so that n p landing on an integer up to floating point error is not pushed up a count.

Usage

.meta_crossing_counts(p, study_n)

Arguments

Value

An integer vector of counts.

Whether a delay is certainly below the cut of the distribution function

Description

Decided from a closed form bound on the parameters rather than from the distribution function, because in Stan the distribution function must not be evaluated where it underflows: its autodiff partial is then 0 / 0, and Stan's reverse pass chains every node on the stack, so the NaN poisons the gradient even when the value is discarded. The bounds are Phi(z) < exp(-100) for z < -14 for the lognormal, P(a, x) <= x^a / Gamma(a + 1) for the gamma and 1 - exp(-y) <= y for the weibull. The generalised gamma uses the gamma bound at x = (q / scale)^shape with a = k. Mirrors meta_family_deep_tail() in Stan.

Usage

.meta_deep_tail(q, dist, args)

Arguments

Value

A logical vector.

Deep lower tail bounds of the delay distributions

Description

One per family with a closed form bound, see .meta_deep_tail(). They mirror the Stan functions of the same name in inst/stan/meta_model/functions.stan.

Usage

.meta_deep_tail_lognormal(q, args)

.meta_deep_tail_gamma(q, args)

.meta_deep_tail_weibull(q, args)

.meta_deep_tail_gengamma(q, args)

Arguments

Value

A logical vector.

The distribution function of the delay, severed deep in its lower tail

Description

The distribution function of the delay, severed deep in its lower tail

Usage

.meta_dist_cdf(q, dist, args)

Arguments

Value

A numeric vector of cumulative probabilities, zero at or below a delay of zero, where .meta_deep_tail() holds, and below the cut of .meta_log_cdf_floor().

The largest number of entries the implied summary cache holds

Description

The cache is bounded so that it cannot grow without limit over a long session. Passing the limit clears it rather than evicting one entry, which keeps the bookkeeping to a single check. Each entry holds one summary vector per posterior draw, so the limit is small.

Usage

.meta_draw_cache_limit()

Value

An integer number of entries.

The slots of one meta model row for one posterior draw

Description

A row with an estimated growth rate holds one rate per draw, see .meta_row_slots(), and the implied summaries of a draw are computed from the rate of that draw. A row with a known rate is returned as it is.

Usage

.meta_draw_slots(slots, draw)

Arguments

Value

The slots with a single growth_rate.

Implied summaries shared by meta model rows with the same study design

Description

Holds one entry per study design, each a list of the parameter draws it was built from and the summaries they imply. It lives in the package namespace, so it is never written into a fitted model object. See .meta_row_draw_moments().

Usage

.meta_draws

Format

An environment.

An empty table of grouped summary members

Description

An empty table of grouped summary members

Usage

.meta_empty_members()

Value

A zero row tibble with the member columns.

Build the summary estimate rows of an epidist_meta_model object

Description

One row is built per group from .meta_assign_groups(). A group of one is a single reported summary, and a larger group is fitted with the joint likelihood of its members. The members of a group are held in flat arrays that the row indexes with group_start and group_len, because a study may report any number of quantiles and a row has a fixed number of slots. Row order is irrelevant to the index, so aggregating or reordering rows later cannot break it.

Usage

.meta_estimate_rows(estimates)

Arguments

Value

A list with a tibble of summary rows using the meta model slots, a tibble of their members, and the flat chol vector of Cholesky factors for the groups covered by a covariance matrix.

A number as a multiple of a power of two, for a data only scaling

Description

The forward pass scales each step around the expected size of the step, and centres its bands on the most likely path, both of which depend on the parameters. Stan can only build data from integers, so each is carried as the integer part of 2^{20} times the number, found there by bisection on comparisons. Neither has to be exact: the result of a step does not depend on its scaling, and the bands are wide. Matches meta_family_fixed_point() in Stan.

Usage

.meta_fixed_point(x)

Arguments

Value

An integer vector within \pm 2^{29}.

The joint log likelihood of several quantiles of integer day delays

Description

Each quantile reported at probability p and landing on day y says that the empirical distribution function crossed p between the day below and the day itself, N_{\le y - w_s} \le \lceil n p \rceil - 1 and N_{\le y} \ge \lceil n p \rceil, with N_{\le y} the number of delays at or below y. The counts at the integer edges the reported quantiles name form a Markov chain,

N_{e_{i+1}} \mid N_{e_i} \sim N_{e_i} + \text{Binomial}\left(n - N_{e_i}, \frac{G_0(e_{i+1}) - G_0(e_i)}{1 - G_0(e_i)}\right),

with G_0 the uncorrected grid distribution function, and the likelihood is the probability that every count fell in its box. It is a forward pass over the counts on the log scale, one step of .meta_box_step() per edge, kept to a band of .meta_band_half_width() counts around the most likely path of .meta_box_mode_path(), so its cost grows like the number of edges times the sample size to the power one and a half rather than squared. Two quantiles reported at the same value are two constraints at one edge, and reporting the same count at two values is a box no chain can satisfy, which gives -Inf.

Usage

.meta_grid_box_ll(y, upper, lower, study_n, dist, args, slots)

Arguments

Details

This is the joint form of .meta_grid_crossing_ll(), which it reduces to for a single quantile. Like it, the information it carries saturates as the study grows, and at a thousand delays it is close to an indicator of the parameters that put the population quantiles in the reported cells, a box rather than a peak. The multinomial of .meta_quantile_set_ll() on the continuity corrected grid keeps sharpening with the sample size instead, so it is not used for such a study.

Matches meta_family_grid_box_ll() in Stan.

Value

A log probability mass.

The uncorrected grid distribution function at a set of cells

Description

The number of delays a study saw at or below a grid cell is binomial on the grid distribution function at that cell, which is the mass of the cells up to and including it. A cohort grid is normalised by the mass it holds, so only the cells asked for, the top of the grid and its first cell are evaluated, as in .meta_grid_edges(). An accrual grid reweights every cell before renormalising, so it is built in full by .meta_grid_pmf().

Usage

.meta_grid_cdf(
  cell,
  dist,
  args,
  lower = 0,
  cutoff,
  pwindow,
  swindow,
  growth_rate,
  accrual = 0L
)

Arguments

Value

The grid distribution function at each cell, or infinities if the grid mass underflows to zero.

The log likelihood of a single quantile of integer day delays

Description

A quantile of delays counted in whole censoring windows is a discrete statistic. "The median is 5 days" says that the empirical distribution function crossed one half between 4 and 5 days, that is N_{\le y - w_s} < \lceil n p \rceil \le N_{\le y} with N_{\le y} the number of delays at or below y, which reads the reported value as a type 1 quantile. Each count is binomial on the uncorrected grid distribution function, so the probability of the event is a difference of two binomial upper tails, computed on the log scale.

Usage

.meta_grid_crossing_ll(y, p, study_n, dist, args, slots)

Arguments

Details

Unlike the continuity corrected forms, the information this carries saturates as the study grows: once the binomial spread of the crossing is narrower than a window the reported integer stops moving, and the likelihood tends to an indicator of the parameters that put the population quantile in the reported cell.

Matches meta_family_grid_crossing_ll() in Stan.

Value

A log probability mass.

The cohort grid distribution function at the two edges of one cell

Description

A cohort grid is normalised by the mass it holds, so its cumulative sum at cell k is (F(k \times swindow) - F(L)) / (F(n_{grid} \times swindow) - F(L)). A reported quantile therefore needs four distribution function evaluations rather than the whole grid, and three where the study counted every delay. This does not hold under an accrual design, which reweights each cell before renormalising and so must keep the full grid.

Usage

.meta_grid_edges(
  cell,
  dist,
  args,
  lower = 0,
  cutoff,
  pwindow,
  swindow,
  growth_rate
)

Arguments

Value

The grid distribution function at the lower and upper cell edges, or two infinities if the grid mass underflows to zero.

The index of the first grid cell a left truncated study could have seen

Description

A study that only counted delays of at least lower never saw the grid cells recording a shorter delay, so they are dropped before the grid is renormalised. The index counts cells from zero, so it is zero when the study counted every delay.

Usage

.meta_grid_first(lower, swindow)

Arguments

Value

An integer cell index.

Summaries of a discrete delay grid

Description

Summaries of a discrete delay grid

Usage

.meta_grid_moments(mass, first_delay, swindow)

Arguments

Value

A named numeric vector with elements mean, sd, kurtosis and skewness.

The discrete delay distribution a naive study would observe

Description

Builds the probability mass function of the interval censored delays a study that took date differences directly would have summarised. The grid runs over delays of 0, swindow, 2 * swindow, and so on up to the largest multiple of swindow whose upper bound is within cutoff, and is renormalised so that it conditions on delays falling within the grid. This renormalisation is what applies the study's right truncation, and it discretises the truncation point to the nearest grid boundary.

Usage

.meta_grid_pmf(
  dist,
  args,
  lower = 0,
  cutoff,
  pwindow,
  swindow,
  growth_rate,
  accrual = 0L
)

Arguments

Details

Cells recording a delay below lower are dropped before the grid is renormalised, which conditions it on the study's left truncation point. The normaliser is then the mass of the kept cells, which is F(D) - F(L) whenever lower falls on a grid boundary.

Under an accrual design the cell masses are additionally weighted by the follow up available to the cases each cell holds, before renormalising. A case is seen when its primary event fell early enough for its delay to complete before the calendar stop, and the primary event is known only to its window. A complete primary window starting at k w_p holds a delay of x from its start when k w_p + x \le A, so the growth weighted mass of the complete windows eligible for x is a step function of x that steps down at A - j w_p. Each cell is cut at those points and every piece is weighted by that mass. When cutoff is not a multiple of pwindow the last primary window is partial, of length l = A - w_p \lfloor A / w_p \rfloor. It only holds delays up to l, and the offset of its primary events runs over l rather than w_p, so its cases follow the primary censored distribution function with a window of l, weighted by the growth weighted length of the window, and are added to the cells below l. This is exact for any cutoff, pwindow and swindow, and reduces to the weight at the cell's lower edge when pwindow and swindow are equal and cutoff is a multiple of both.

A cohort grid is normalised by the distribution function at its top, which is already known. An accrual grid reweights each cell first, so its normaliser is not known in advance.

Value

A numeric vector of probabilities summing to one, one per kept cell, or a vector of NA the same length if the grid mass underflows to zero.

The continuity corrected distribution function of a discrete delay grid

Description

The step distribution function of the grid is replaced by the version that interpolates it linearly through the mid points of its cells. Without this correction a quantile of day resolution data, which must land on a jump of the step function, biases the implied probability upwards by several sampling standard errors.

Usage

.meta_grid_prob(
  y,
  dist,
  args,
  lower = 0,
  cutoff,
  pwindow,
  swindow,
  growth_rate,
  accrual = 0L
)

Arguments

Details

A cohort grid only needs the two cell edges the value falls between, so it takes the three evaluation shortcut of .meta_grid_edges(). An accrual grid must be built in full.

Value

A probability, or Inf if the grid mass underflows to zero, which forces a -Inf log likelihood rather than a NaN one.

The continuity corrected cohort grid distribution function at several delays

Description

The vectorised form of .meta_grid_prob() for a cohort study. Every cell edge a set of reported quantiles needs is evaluated in one call, because a call to primarycensored::pprimarycensored() costs the same whether it is given one delay or a hundred.

Usage

.meta_grid_probs(
  y,
  dist,
  args,
  lower = 0,
  cutoff,
  pwindow,
  swindow,
  growth_rate
)

Arguments

Value

A numeric vector of probabilities, or infinities if the grid mass underflows to zero.

Build a single meta model row from one group of summary estimates

Description

The group_start slot is filled in by .meta_estimate_rows() once every group has been built.

Usage

.meta_group_row(estimates, vcov = NULL, n_quad = .meta_n_quad())

Arguments

Value

A list with a one row tibble row, a tibble of its members, and the flat chol entries of its covariance matrix.

Pass the grouped summary members of a meta model to Stan

Description

A row that stands for several summaries reported by one study cannot carry them in its own slots, because a study may report any number of quantiles. They are passed instead as flat arrays that the row indexes into with its group_start and group_len slots. See .meta_estimate_rows().

Usage

.meta_group_stanvars(data)

Arguments

Value

A brms stanvars object holding the flat member arrays.

Whether any summary row of a meta model estimates its growth rate

Description

Whether any summary row of a meta model estimates its growth rate

Usage

.meta_growth_estimated(data)

Arguments

Value

TRUE where a summary row has a growth_known slot of 0.

The default pgrowth formula of a meta model

Description

See epidist_formula_model.epidist_meta_model().

Usage

.meta_growth_formula(data, formula)

Arguments

Value

The formula, with pgrowth ~ 0 + study, or pgrowth ~ 1 for a single study, added where a summary row estimates its growth rate and no pgrowth formula was given.

Prior distributions for the growth rate of summary rows

Description

See epidist_model_prior.epidist_meta_model().

Usage

.meta_growth_prior(data, formula, default = NULL)

Arguments

Value

A brmsprior object, or NULL where no summary row estimates its growth rate.

The density of the biased estimand at a reported quantile value

Description

Used to convert a quantile standard error reported on the delay scale to the cumulative probability scale the model works on, by the delta method. For a discrete estimand the density is the mass of the grid cell the value falls in divided by the grid spacing, which is exactly the slope of the continuity corrected distribution function there. For a continuous estimand it is the closed form density of the estimand over its truncation normaliser, or, under an accrual design, the slope of the interpolated distribution function. A primary censored delay with a non uniform primary event has no closed form density, so it falls back to a central difference.

Usage

.meta_implied_density(
  y,
  dist,
  args,
  lower = 0,
  cutoff,
  pwindow,
  swindow,
  trunc_adjusted,
  cens_adjusted,
  growth_rate,
  trunc_design = 0L,
  n_quad = .meta_n_quad()
)

Arguments

Value

A density on the delay scale, or Inf if the grid mass or the distribution function underflows to zero, which forces a -Inf log likelihood rather than a NaN one.

The summaries a study using a given procedure would report

Description

Forward models the summaries that a study would converge to given the biases in its estimation procedure. See as_epidist_estimates_data.data.frame() for what the adjustment codes mean.

Usage

.meta_implied_moments(
  dist,
  args,
  lower = 0,
  cutoff,
  pwindow,
  swindow,
  trunc_adjusted,
  cens_adjusted,
  growth_rate,
  trunc_design = 0L,
  n_quad = .meta_n_quad()
)

Arguments

Details

Under the uniform single interval approximation (cens_adjusted of 2) the study summarised the delay plus the uncorrected primary event offset. Where the study also adjusted for right truncation and the primary events were uniform within their window this is the analytic convolution, which adds pwindow / 2 to the mean and pwindow^2 / 12 to the variance. Otherwise the moments of the primary censored delay, truncated at cutoff, are used directly.

A study that adjusted for right truncation and counted only delays above lower has its analytic moments left truncated by .meta_left_moments(), so they do not depend on cutoff. A study whose primary events were not uniform within their window has no analytic moments, so it is truncated at cutoff by quadrature instead.

Under midpoint imputation (cens_adjusted of 3) the study assigned each delay to the centre of the interval it was observed in, so the estimand is the naive discrete grid shifted up by swindow / 2. The shift moves the mean and leaves every central moment unchanged.

Under midpoint imputation with a uniform interval (cens_adjusted of 4) the study placed the primary event at the midpoint of its window instead of at its lower edge, so the estimand is that of cens_adjusted of 2 shifted down by pwindow / 2. Both midpoint codes are evaluated by calling the code they shift. See .meta_cens_base() and .meta_cens_shift().

Value

A named numeric vector with elements mean, sd, kurtosis and skewness.

The implied distribution function at equally spaced delays

Description

Returns the implied distribution function on a grid of delays, together with where that grid starts and how far apart its points are. Reading an implied quantile off the delay scale needs the inverse of the implied distribution function, which has no closed form on the discrete grid, so it is interpolated from these points instead. See .meta_node_quantile().

Usage

.meta_implied_nodes(dist, args, slots)

Arguments

Value

A list with the distribution function values, the delay origin of the first value, and the spacing between values.

The cumulative probability a study using a given procedure would report

Description

Evaluates the distribution function of the biased estimand at a reported quantile value. Working on the probability scale avoids inverting the distribution function, which has no closed form on the discrete grid.

Usage

.meta_implied_prob(
  y,
  dist,
  args,
  lower = 0,
  cutoff,
  pwindow,
  swindow,
  trunc_adjusted,
  cens_adjusted,
  growth_rate,
  trunc_design = 0L,
  n_quad = .meta_n_quad()
)

Arguments

Details

For a naive study (cens_adjusted of 0) the estimand is discrete, so the continuity corrected grid distribution function of .meta_grid_prob() is used. Midpoint imputation (cens_adjusted of 3) uses the same function evaluated half a secondary window lower, because the study shifted every delay up by that amount.

For the uniform single interval approximation (cens_adjusted of 2) the distribution function of the primary censored delay is used, so that it matches the moments used for reported means and standard deviations. Midpoint imputation with a uniform interval (cens_adjusted of 4) uses that function evaluated half a primary window higher, because the study anchored every delay at the centre of the primary window rather than at its lower edge.

Value

A probability, or Inf if the distribution function underflows to zero at cutoff, which forces a -Inf log likelihood rather than a NaN one.

The cumulative probabilities a study would report at several quantiles

Description

The vectorised form of .meta_implied_prob(), used for the set of quantiles one study reported. A cohort study on a discrete grid needs only the cell edges the reported values fall between, so all of them are evaluated in one call. Every other design falls back to evaluating each value on its own.

Usage

.meta_implied_probs(y, dist, args, slots)

Arguments

Value

A numeric vector of probabilities.

The summaries a study would report, one per multivariate normal member

Description

Member types are 1 for a mean, 2 for a standard deviation and 3 for a quantile at the matching probability. Quantile members are read off the implied distribution function by .meta_node_quantile(), so they are on the delay scale, matching the reported values and the covariance matrix supplied with them.

Usage

.meta_implied_summary_vector(dist, args, slots, moments = NULL)

Arguments

Value

A numeric vector of implied summaries.

Build the individual level rows of an epidist_meta_model object

Description

Build the individual level rows of an epidist_meta_model object

Usage

.meta_individual_rows(data)

Arguments

Value

A tibble of individual level rows using the meta model slots.

Interpolate a distribution function held at equally spaced points

Description

Both the discrete grid and the accrual quadrature give the implied distribution function at equally spaced delays, and a reported quantile is read off by linear interpolation between them. Delays below the first point are given zero and delays at or beyond the last are given one.

Usage

.meta_interpolate(y, values, spacing, offset)

Arguments

Value

A numeric vector of probabilities.

The sampling covariance of the summaries one study reports

Description

The asymptotic covariance of a sample mean, a sample standard deviation and sample quantiles computed from the same study_n delays. The mean and standard deviation block is that of .meta_moment_pair_ll(). By the Bahadur representation a sample quantile at probability p is Q_p - (\hat{G}(Q_p) - p) / f(Q_p) up to a smaller order term, so with f_i = f(Q_{p_i}) the implied density at each implied quantile

\text{Cov}(q_i, q_j) = \frac{p_i (1 - p_j)}{n f_i f_j}, \quad p_i \le p_j,

\text{Cov}(\bar{x}, q_i) = -\frac{1}{n f_i} \int_L^{Q_{p_i}} (x - \mu) \text{d}G(x),

\text{Cov}(s, q_i) = -\frac{1}{2 \sigma n f_i} \int_L^{Q_{p_i}} \left((x - \mu)^2 - \sigma^2\right) \text{d}G(x),

the last carried from the sample variance to the standard deviation by the delta method. The integrals are the centred partial moments of .meta_quantile_partials(). Matches meta_family_joint_covariance() in Stan.

Usage

.meta_joint_covariance(types, probs, moments, density, partial, study_n)

Arguments

Value

A covariance matrix over the members.

The joint log likelihood of the summaries of one continuous study

Description

The multivariate normal of .meta_joint_study_terms(). A covariance that is not positive definite, which quadrature error can produce for a draw far from the reported summaries, is rejected with a log likelihood of -Inf, as are the failures listed there. Matches meta_family_joint_study_lpdf() in Stan.

Usage

.meta_joint_study_ll(y, dist, args, slots, moments = NULL)

Arguments

Value

A log density.

The implied summaries of a joint study group and their sampling covariance

Description

A continuous estimand reporting a mean or a standard deviation alongside quantiles has every summary fitted jointly, with the covariance of .meta_joint_covariance() derived from the implied distribution rather than supplied. The quantiles are read off the implied nodes as for a covariance matrix group, see .meta_implied_summary_vector(), and the density and centred partial moments at each are taken from the same nodes.

Usage

.meta_joint_study_terms(dist, args, slots, moments = NULL)

Arguments

Value

A list with the implied summary vector and the covariance matrix sigma, or NULL where the implied moments are not finite, the nodes underflow or a quantile sits where the estimand has no density, which the caller rejects.

Summaries of a distribution left truncated at lower

Description

A study that adjusted for right truncation and only counted delays above lower reported the moments of the delay conditioned on exceeding it. They are taken from the untruncated moments by removing the part below lower, E[\tau^k 1(\tau \le L)] = L^k F(L) - \int_0^L k t^{k - 1} F(t) dt, by Simpson's rule on [0, L], and dividing by 1 - F(L). The integral is over a bounded interval the quadrature resolves well, so the result does not depend on max_delay, and it matches the distribution function (F(y) - F(L)) / (1 - F(L)) used for the same study's quantile rows. It applies to any distribution whose untruncated moments and distribution function are available, which is the delay itself and the uniform single interval approximation of .meta_add_uniform(). Matches meta_family_left_moments in inst/stan/meta_model/functions.stan.

Usage

.meta_left_moments(full, cdf, lower)

Arguments

Value

A named numeric vector with elements mean, sd, kurtosis and skewness.

The log follow up available to a delay under an accrual design

Description

A study that collected primary events over a window of length window and stopped at its calendar end could only observe a delay of d for the primary events that occurred at least d before the stop. With primary events arriving at a rate proportional to \exp(r t) the amount of such follow up is w(d) = \int_0^{window - d} \exp(r t) \text{d}t = (\exp(r (window - d)) - 1) / r, which tends to window - d as r tends to zero. This is the dynamical bias of Park et al. (2024); for a long window and a growing epidemic it approaches an exponential tilt of the delay distribution by \exp(-r d).

Usage

.meta_log_accrual_weight(d, window, growth_rate)

Arguments

Details

Working on the log scale keeps the weight finite for a fast growing epidemic observed over a long window, where the weight itself would overflow.

Value

A numeric vector of log follow up times.

The log mass of a binomial count with floored probabilities

Description

The binomial mass with the success and failure probabilities floored at 1e-300, so that a count the parameters make all but impossible is very unlikely rather than impossible and a chain can start from a random initial value. Matches the arithmetic of meta_family_grid_box_ll() in Stan.

Usage

.meta_log_binom(x, size, prob)

Arguments

Value

A vector of log masses.

The log upper tail of a binomial count, stable far into the tail

Description

P(M >= m) for M ~ Binomial(size, prob). Nine standard deviations above the mean, or below a probability of 1e-12, the tail is summed term by term on the log scale until the terms fall forty nats below the first, or two hundred terms in with a geometric bound on the rest, which is exact to that tolerance and, unlike the distribution function, has finite partial derivatives there in Stan. Elsewhere it is the distribution function of the complement. Matches meta_family_log_binom_upper() in Stan.

Usage

.meta_log_binom_upper(m, size, prob)

Arguments

Value

The log tail probabilities, recycled to the longest argument.

The log distribution function below which a node is severed

Description

Every grid and quadrature path evaluates the distribution function from the study's minimum delay upwards, so for a narrow delay it reaches deep into the lower tail, where the Stan primary censored distribution function of primarycensored returns a finite value with a non finite gradient. A node whose plain log distribution function is below this value holds a probability below exp(-100), which no moment or probability the model forms can resolve, so it is treated as holding no mass before that function is called. Matches the cut in meta_family_pcens_lcdf() and meta_family_dist_prob() in inst/stan/meta_model/functions.stan.

Usage

.meta_log_cdf_floor()

Value

A log probability.

The log of a difference of two exponentials

Description

Matches Stan's log_diff_exp(), returning -Inf where the difference is zero or negative rather than NaN.

Usage

.meta_log_diff_exp(upper, lower)

Arguments

Value

log(exp(upper) - exp(lower)).

A numerically stable log of a sum of exponentials

Description

A numerically stable log of a sum of exponentials

Usage

.meta_log_sum_exp(x)

Arguments

Value

log(sum(exp(x))), or -Inf when every element is -Inf.

The largest correlation the joint moment likelihood will use

Description

The asymptotic correlation between a sample mean and a sample standard deviation is the skewness over the square root of the excess kurtosis, and \kappa \geq \gamma_1^2 + 1 holds for every distribution, so it never leaves [-1, 1]. Moments taken from a discrete grid or from quadrature can sit a little outside that bound, which would make the covariance matrix singular, so the correlation is held inside it.

Usage

.meta_max_correlation()

Details

Matches the value hard coded in inst/stan/meta_model/functions.stan so that the R and Stan implementations agree.

Value

A correlation.

Build the member table of one joint likelihood group

Description

The member type and probability are carried alongside the reported value because a group covered by a covariance matrix may mix means, standard deviations and quantiles, so the likelihood needs to know which implied summary each member is.

Usage

.meta_member_table(estimates, count, lower = 0L)

Arguments

Details

A set of quantiles of integer day delays carries the box each reported day puts on the study's cumulative counts: count is the largest number of delays the study can have seen below the day and lower the smallest at or below it. See .meta_grid_box_ll().

Value

A tibble of member value, count, lower, type and p columns.

The grouped summary members of an epidist_meta_model object

Description

The grouped summary members of an epidist_meta_model object

Usage

.meta_members(data)

Arguments

Value

A tibble of member value, count, lower, type and p columns.

The smallest quantile standard error the model will use

Description

A quantile standard error supplied on the delay scale is used as reported, held at or above this value as a guard against a standard error of zero, which would give a degenerate likelihood.

Usage

.meta_min_prob_se()

Value

A delay scale standard error.

The correlation between a reported mean and a reported standard deviation

Description

The correlation between a reported mean and a reported standard deviation

Usage

.meta_moment_correlation(moments)

Arguments

Value

A correlation strictly inside [-1, 1].

The summary vector returned when a normaliser underflows to zero

Description

An infinite mean and standard deviation make the normal log likelihood evaluate to -Inf for any finite reported value, so a draw that hits this case is rejected rather than turning the log likelihood into NaN.

Usage

.meta_moment_failure()

Value

A named numeric vector with elements mean, sd, kurtosis and skewness.

The joint log likelihood of a mean and a standard deviation from one study

Description

A sample mean and a sample standard deviation computed from the same delays are correlated, so fitting them as two independent normal terms overstates how much a study reporting both tells us. They are instead given the asymptotic bivariate normal of the pair, with \text{Cov}(\bar{x}, s^2) = \mu_3 / n carried onto the standard deviation scale by the delta method, giving \text{Cov}(\bar{x}, s) = \mu_3 / (2 n \sigma) and a correlation of \gamma_1 / \sqrt{\kappa - 1}. See .meta_moment_correlation().

Usage

.meta_moment_pair_ll(y_mean, y_sd, moments, study_n)

Arguments

Value

A log density.

Summarise a distribution from its mean and central moments

Description

The kurtosis is needed as well as the mean and standard deviation because the sampling error of a reported standard deviation depends on it. See .meta_summary_terms(). The skewness is needed because the sampling covariance of a reported mean and a reported standard deviation from the same study depends on it. See .meta_moment_pair_ll().

Usage

.meta_moment_vector(mean, variance, third, fourth)

Arguments

Value

A named numeric vector with elements mean, sd, kurtosis and skewness.

Central moments of the delay distributions with analytic summaries

Description

Each returns the mean, the variance and the third and fourth central moments. They mirror the Stan functions of the same name in inst/stan/meta_model/functions.stan. The weibull and generalised gamma share .meta_moments_scaled(), since their raw moments are E[T^r] = scale^r g_r.

Usage

.meta_moments_lognormal(args)

.meta_moments_gamma(args)

.meta_moments_scaled(scale, g)

.meta_moments_weibull(args)

.meta_moments_gengamma(args)

Arguments

Value

A numeric vector of length four.

The log density of a study's summaries under a supplied covariance

Description

A study that cannot share its delays can report a vector of summaries with a covariance matrix over them, which keeps the correlation between the quantities it reports. The Cholesky factor of that matrix is built once when the model data are prepared and passed to Stan, so the sampler never decomposes it.

Usage

.meta_multi_normal_ll(y, implied, chol)

Arguments

Value

A log density.

The smallest number of quadrature intervals used for a summary row

Description

Set with options(epidist.meta_n_quad = ), as an even number of at least two. Each summary row carries its own number of intervals in its n_quad slot, chosen by .estimates_n_quad() from the spread the study reported so that the quadrature resolves the delay, and this is the floor of that choice. Set it before building the model data, since the slot is filled in then. It also lifts the cap of .meta_n_quad_max() when set above it.

Usage

.meta_n_quad()

Value

An integer number of intervals.

The default number of quadrature intervals for truncated continuous moments

Description

The default number of quadrature intervals for truncated continuous moments

Usage

.meta_n_quad_default()

Value

An integer number of intervals.

The largest number of quadrature intervals chosen for a summary row

Description

Every quadrature node costs a distribution function evaluation on each gradient, so the number of intervals .estimates_n_quad() chooses for a study is capped here unless options(epidist.meta_n_quad = ) is set higher. as_epidist_estimates_data() warns about a study the cap leaves unresolved.

Usage

.meta_n_quad_max()

Value

An integer number of intervals.

The number of Newton steps taken from the chord inverse

Description

Matches meta_family_node_quantile() in Stan. Each step squares the error of the chord, which is of the order of the node spacing squared, so two steps leave a residual well below the sampling standard error of any reported quantile.

Usage

.meta_newton_steps()

Value

An integer.

The index of the node interval holding a delay

Description

Interval i runs from node i to node i + 1. It is found by stepping through the nodes rather than by rounding, because in Stan the delay is a parameter and cannot be converted to an integer. Matches meta_family_node_interval() in Stan.

Usage

.meta_node_interval(nodes, q)

Arguments

Value

An integer between 1 and the number of intervals.

The delay at which an implied distribution function reaches p

Description

Inverts the distribution function of .meta_implied_nodes() by linear interpolation between the two points that bracket p. On the discrete grid that interpolant is the model's own definition of the continuity corrected quantile, so the chord is exact there. For a continuous estimand the chord is only as accurate as the node spacing, which for a truncation adjusted study is about a day, so it is refined by .meta_refine_quantile() when the design is supplied. The result stays a differentiable function of the delay distribution parameters, which a root search would not be.

Usage

.meta_node_quantile(nodes, p, dist = NULL, args = NULL, slots = NULL)

Arguments

Value

A delay.

Map summary types to their observation type codes

Description

Map summary types to their observation type codes

Usage

.meta_obs_type(type)

Arguments

Value

An integer vector of observation type codes.

Order the summaries within a joint likelihood group

Description

Members are stored as the mean, then the standard deviation, then the quantiles in increasing probability, so that the bivariate normal knows which member is which and a joint study group is laid out as its covariance is built. The quantiles must be non decreasing in the reported value for the cells of the multinomial to be a partition of the delay axis. Coincident values are merged into one cell by the likelihood.

Usage

.meta_order_group(estimates, vcov = NULL)

Arguments

Details

A group covered by a covariance matrix keeps the order its rows were given in, because that is the order the matrix is indexed by.

Value

The input, reordered.

The primary censored distribution function, guarded against underflow

Description

Primary distributions without an analytical solution are integrated numerically, which can return a non finite or negative cumulative probability deep in the lower tail. Those cases carry negligible probability and are treated as zero, matching the guard in inst/stan/meta_model/functions.stan. A delay whose plain distribution function is below the cut of .meta_log_cdf_floor() is severed to zero before the primary censored function is called, as it is in Stan, since the primary censored distribution function is never above the plain one.

Usage

.meta_pcens_cdf(q, dist, args, pwindow, growth_rate)

Arguments

Value

A numeric vector of cumulative probabilities.

Summaries of a right truncated primary censored delay distribution

Description

The estimand is the delay plus the primary event offset within its window, conditioned on falling below the cutoff. Under an accrual design the quadrature is reweighted by the follow up available to each delay, offset by half a primary window because the estimand already includes the primary event offset. See .meta_accrual_reweight().

Usage

.meta_pcens_trunc_moments(
  dist,
  args,
  lower = 0,
  cutoff,
  pwindow,
  growth_rate,
  accrual = 0L,
  n_quad = .meta_n_quad()
)

Arguments

Value

A named numeric vector with elements mean, sd, kurtosis and skewness.

The primary event distribution implied by a growth rate

Description

A growth rate of zero corresponds to a uniform primary event within its censoring window. Any other value uses the exponential growth primary distribution from primarycensored.

Usage

.meta_primary(growth_rate)

Arguments

Value

A list with elements dprimary and dprimary_args.

The cumulative counts implied by a set of reported quantiles

Description

The multinomial likelihood of .meta_quantile_set_ll() needs the number of delays a study saw at or below each reported quantile. Rounding the cumulative probabilities rather than the increments keeps the counts non decreasing and bounded by the sample size, so the cell counts are non negative and sum to the sample size however the probabilities round.

Usage

.meta_quantile_counts(p, study_n)

Arguments

Value

An integer vector of cumulative counts.

The entries of the joint sampling covariance of one study's summaries

Description

.meta_quantile_covariance() gives the Bahadur covariance of two quantiles, .meta_cross_covariance() that of a mean or a standard deviation and a quantile, and .meta_moment_covariance() that of two moment summaries, see .meta_joint_covariance(). They mirror the Stan functions meta_family_quantile_covariance(), meta_family_cross_covariance() and meta_family_moment_covariance() in inst/stan/meta_model/functions.stan.

Usage

.meta_quantile_covariance(prob_i, prob_j, density_i, density_j, study_n)

.meta_cross_covariance(moment_type, prob, density, partial, spread, study_n)

.meta_moment_covariance(type_i, type_j, se_mean, se_sd, rho)

Arguments

Value

A covariance.

The density of a continuous estimand at its implied quantile

Description

Where the quantile is left on its chord, see .meta_quantile_on_chord(), the estimand is the linear interpolant of its nodes and its density is the slope of the interval holding the quantile. Otherwise it is the closed form density of .meta_implied_density(). Matches meta_family_quantile_density() in Stan.

Usage

.meta_quantile_density(q, index, nodes, dist, args, slots)

Arguments

Value

A density on the delay scale.

Whether the implied quantile of a design is left on its chord

Description

The chord inverse of .meta_node_quantile() is refined only where the implied distribution function and density exist in closed form. A discrete grid, an accrual estimand and a uniform single interval estimand with a growing primary event are defined by the interpolation between their nodes, so their chord is the implied quantile and the slope of the interval holding it is the implied density. See .meta_refine_quantile(). Matches the early returns of meta_family_node_quantile() in Stan.

Usage

.meta_quantile_on_chord(slots)

Arguments

Value

A logical scalar.

The centred partial moments of an estimand below its implied quantile

Description

The sampling covariance of a reported mean or standard deviation with a reported quantile depends on \int_L^{q} (x - \mu)^k \text{d}G(x) for k = 1, 2, with G the implied distribution function, \mu the implied mean and L the smallest delay the study counted. Integrating by parts gives (q - \mu)^k p - \int_L^{q} k (x - \mu)^{k - 1} G(x) \text{d}x, and the remaining integral is taken by the trapezoid rule over the linear interpolant of the nodes, which reaches p at q. Its error is of the order of the node spacing squared, which .estimates_n_quad() holds to a quarter of the reported spread. Matches meta_family_quantile_partials() in Stan.

Usage

.meta_quantile_partials(nodes, q, p, index, centre)

Arguments

Value

A numeric vector of the first and second centred partial moments.

The joint log likelihood of a set of quantiles from one study

Description

Quantiles reported at probabilities p_1 < \dots < p_k with values y_1 \le \dots \le y_k split the delay axis into the cells (0, y_1], \dots, (y_{k-1}, y_k], (y_k, \infty), and the number of delays falling in each cell is multinomial with probabilities given by the increments of the implied distribution function. This is the joint version of the empirical distribution function likelihood used for a single quantile, and it reduces to the exact binomial when only one quantile of a continuous estimand is reported. Fitting each quantile separately ignores the positive correlation between the empirical distribution function at different points, which over weights a study reporting a median with an interquartile range.

Usage

.meta_quantile_set_ll(
  y,
  cum_count,
  study_n,
  dist,
  args,
  slots,
  p = slots$group_p,
  lower = slots$group_lower
)

Arguments

Details

Two quantiles reported at the same value are two constraints on the empirical distribution function at one cell, so they are merged into that cell with their combined count.

Quantiles of integer day delays (cens_adjusted 0 or 3) are discrete statistics, and the multinomial on the continuity corrected distribution function keeps sharpening with the study size while a rounded quantile stops moving. A single such quantile is fitted by .meta_grid_crossing_ll() as the cell in which the empirical distribution function crossed its probability, and several by .meta_grid_box_ll() as the joint probability of every such crossing, with cum_count and lower read as the box each crossing puts on the counts below and at the reported day. Both start the grid at delay_min moved back by .meta_cens_lower(), as the mean and standard deviation of the same study do. For a midpoint imputed grid (cens_adjusted 3) the reported delay_min sits on the midpointed scale, so an off grid value would otherwise drop the lowest counted cell.

A cell whose implied probability underflows to zero while the study saw delays in it is floored at .meta_cell_floor().

Value

A log probability mass.

The first four raw moments of a set of summaries

Description

Inverts .meta_central_from_raw().

Usage

.meta_raw_from_central(moments)

Arguments

Value

A numeric vector of the first four raw moments.

Refine the chord inverse of a continuous implied distribution function

Description

Where the family quantile function is available, that is for a lognormal or weibull delay reported by a study that adjusted for censoring and did not use an accrual design, the implied quantile is Q(F(L) + p (F(D) - F(L))) exactly. Otherwise Newton steps are taken from the chord using the implied distribution function and density of .meta_implied_prob() and .meta_implied_density(), which exist in closed form for every remaining continuous design with a uniform primary event. An accrual estimand, or a uniform single interval estimand with a growing primary event, is defined by linear interpolation between its nodes, so its chord is left alone, as is a discrete grid.

Usage

.meta_refine_quantile(chord, p, dist, args, slots, floor, ceiling)

Arguments

Details

The Stan mirror meta_family_node_quantile() cannot evaluate the primary censored distribution function at a parameter dependent delay, so the cases refined here are exactly those it can refine with closed forms.

Value

A delay.

The implied summaries of one meta model row for every posterior draw

Description

Rows sharing a study design, the same parameter draws and the same quadrature resolution imply the same summaries, so they are computed once and reused. The cache is bounded and lives in the package namespace, so it is never written into a fitted model object. See .meta_draws. A row with an estimated growth rate holds one rate per draw, so the rates are part of what a cached entry is compared against, and each draw is summarised at its own rate.

Usage

.meta_row_draw_moments(slots, dist, dist_args)

Arguments

Details

Only reported means and standard deviations need implied summaries. Quantile rows work on the cumulative probability scale, so they get a list of NULL and nothing is computed for them.

Value

A list of summary vectors, one per posterior draw.

The log likelihood of one meta model summary row for one draw

Description

Ungrouped rows use the normal approximations of .meta_summary_terms(). A group row, which stands for several summaries reported by one study, uses the joint likelihood of its members: .meta_moment_pair_ll() for a mean and a standard deviation, .meta_quantile_set_ll() for a set of quantiles, which hands quantiles of integer day delays to .meta_grid_crossing_ll() or .meta_grid_box_ll(), and .meta_joint_study_ll() for a continuous estimand reporting both kinds.

Usage

.meta_row_log_lik(slots, dist, args, moments = NULL)

Arguments

Details

A draw whose implied moments are not all finite, which an extreme delay distribution parameter can produce by overflowing the analytic kurtosis, is rejected with a log likelihood of -Inf rather than NaN, for every row that uses the moments. Matches the guard in meta_family_lpmf in inst/stan/meta_model/functions.stan.

Value

A log density.

The log of a sum of exponentials over each row of a matrix

Description

The log of a sum of exponentials over each row of a matrix

Usage

.meta_row_log_sum_exp(m)

Arguments

Value

A numeric vector, one value per row, -Inf where every element of the row is -Inf.

The summaries implied by one meta model row for one draw

Description

The summaries implied by one meta model row for one draw

Usage

.meta_row_moments(slots, dist, args)

Arguments

Value

A named numeric vector with elements mean, sd, kurtosis and skewness.

Extract the meta model slots for a single row

Description

Group rows point into the flat member arrays passed to Stan as data, so the reported values and cumulative counts of the group are read back out here for the R mirrors of the joint likelihoods.

Usage

.meta_row_slots(i, prep)

Arguments

Details

A row whose growth_known slot is 0 estimates its growth rate as the pgrowth distributional parameter, so its growth_rate element holds one value per posterior draw rather than the number in the slot. Everything that works one draw at a time takes the slots of that draw from .meta_draw_slots(). A fit made before the slot existed has no growth_known and every row of it is known.

Value

A named list of the observation type, study metadata and reported values for row i.

The sampling standard error of a reported standard deviation

Description

Uses the asymptotic standard error of the sample standard deviation, \sigma \sqrt{(\kappa - 1) / (4 n)}, where \kappa is the kurtosis of the estimand the study was summarising. The normal theory expression \sigma / \sqrt{2 (n - 1)} is not used because it is far too narrow for the skewed distributions delays usually follow.

Usage

.meta_sd_se(moments, study_n)

Arguments

Value

The standard error of the reported standard deviation.

Attach the grouped summary members to an epidist_meta_model object

Description

The members of a group row cannot be stored in the row itself because a study may report any number of quantiles, so they are held alongside the data and passed to Stan as flat arrays that the group row indexes into. See .meta_estimate_rows().

Usage

.meta_set_members(data, members, chol = numeric(0))

Arguments

Value

The input with the members attached.

The number of quadrature intervals a row's slots ask for

Description

Rows built by as_epidist_meta_model() carry it in their n_quad slot. A slots list assembled by hand without one uses the floor.

Usage

.meta_slots_n_quad(slots)

Arguments