NAPrior: Network Meta-Analytic Predictive Priors

Description

<one-line summary + longer description>

Author(s)

Maintainer: Chunyi Zhang czhang12@mdanderson.org

Turn a single model input (object with JAGS text OR path) into a file path

Description

Turn a single model input (object with JAGS text OR path) into a file path

Usage

.model_path_from(model)

Simulation for operating-characteristics applying NAP-based priors

Description

Runs Monte Carlo simulations of an E vs C2 trial and performs Bayesian analysis with a NAP-based prior constructed by NAP_prior(). The routine supports both single external study setting and multiple external studies settings as encoded in the provided NAP_prior object, and works with either a fixed mixture weight (mNAP) or an elastic, data-adaptive weight (eNAP).

Usage

NAP_oc(
  NAP_prior = NULL,
  theta_EC2 = 0,
  n_EC2 = 200,
  lambda = 2,
  sim_model = c("Exponential", "Weibull"),
  model_param = 0.05,
  iter = 2000,
  chains = 4,
  seed = 123,
  nsim = 100,
  jags_model = NULL
)

Arguments

Value

A data frame with one row per replicate containing:

• post_mean, post_sd, low95, hi95 — posterior mean, SD, and 95\

• prob_E_better — posterior probability theta_{E,C2} < 0.

• prior_weight, post_weight — prior and updated weights used in the mixture (for eNAP, prior_weight is w(Z)).

• sigma_hat — posterior mean of between-study SD (RE only; NA for FE).

Conduct posterior inference with NAP-based priors

Description

Draw posterior via MCMC (JAGS) with derived NAP priors from NAP_prior function both setting (one external trial/multiple external trials) and NAP method (NAP/mNAP/eNAP) will be determined by the provided NAP_prior object. If using eNAP, make sure the tuning parameter used to derive NAP_prior are calibrated by tune_param_eNAP function.

Usage

NAP_posterior(
  NAP_prior = NULL,
  y_EC2,
  s_EC2,
  iter = 2000,
  chains = 4,
  model = NULL
)

Arguments

Value

A list of class "NAP_posterior_result" with elements:

• posterior_sum: data frame with posterior summaries for \theta_{E,C2} (mean, sd, 95\ weights (prior_weight, post_weight).

• enap_prior: For eNAP only: data frame describing the eNAP prior with calculated data-dependent weight: columns for NAP (Informative) and Vague, rows for Mixing Weight, Mean, Variance, and ESS (events) if available.

• jags_fit: the R2jags fit object.

#'

Examples

# Create a NAP_prior object
my_naprior <- NAP_prior(
  weight_mtd = "fixed", w = 0.50,       # fixed mixture weight
  y_EC1  = -0.36, s_EC1  = 0.16^2,
  y_C2C1 = -0.30, s_C2C1 = 0.14^2,      # single external trial
  tau0   = 1000
)

# Calculate posterior
out <- NAP_posterior(
  NAP_prior = my_naprior,
  y_EC2 = -0.20, s_EC2 = 0.18^2,
  iter = 1000, chains = 2
)
out$posterior_sum
out$enap_prior

NAP_prior: Derive NAP/mNAP/eNAP priors

Description

Builds the informative NAP component (mean/variance from the indirect path) and the vague component, and reports the mixing weight depending on the mode:

• weight_mtd = "fixed": use the supplied fixed weight w in [0,1].

• weight_mtd = "adaptive" (eNAP): if y_EC2 is provided, compute the data-dependent weight via the elastic link; otherwise, print a formula note.

Derive NAP-based prior (s) based on indirect evidence

Derive the NAP-based posteriors with provided summary statistics on indirect evidence edges By default, the function assumes a vague component is desired, as a result, to obtain NAP/mNAP/eNAP:

• NAP Set weight_mtd="fixed" and w=1, use the NAP (informative component) column results

• mNAP Set weight_mtd="fixed" and w as pre-specified fixed weight. The resulting mNAP is w\pi_{NAP}+(1-w)\pi_0

• eNAP Set weight_mtd="adaptive" and provide calibrated a and b as from tune_param_eNAP function, then either: 1). Provide assumed value for y_EC2 and s_EC2 (i.e., as for sample size calculation): return a calculated dynamic weight w(Z), the resulting eNAP is then w(Z)\pi_{NAP}+(1-w(Z))\pi_0; OR 2). Leave y_EC2 and s_EC2 as NULL, return the NAP (informative component) and Vague component, with description for protocol reference

Usage

NAP_prior(
  weight_mtd = c("adaptive", "fixed"),
  w = NULL,
  a = NULL,
  b = NULL,
  y_EC2 = NULL,
  s_EC2 = NULL,
  y_EC1,
  s_EC1,
  y_C2C1,
  s_C2C1,
  mu0 = 0,
  tau0 = 1000,
  lambda = 1,
  sigma2_hat = NULL
)

Arguments

Details

This function automatically selects one external trial vs multiple external trials setting:

• One external trial if length(y_C2C1) == 1 & length(s_C2C1)==1 (one external trial).

• Multiple external trials if length(y_C2C1) > 1 & length(s_C2C1)==length(y_C2C1). By default uses metafor::rma.uni(..., method="REML") to obtain REML estimate; Otherwise please provide sigma2_hat

Value

Displays the NAP prior as a mixture of an informative prior (constructed based on the indirect evidence path) and a vague prior.

An object of class "NAPrior" (data.frame + attributes).

Examples

## ------------------------------------------------------------
## Example 1: One external trial setting with fixed mixing weight of 0.5 (mNAP)
## ------------------------------------------------------------
mNAP_test1 <- NAP_prior(
  weight_mtd = "fixed", w = 0.50,                  # fixed mixture weight
  y_EC1  = -0.36, s_EC1  = 0.16^2,
  y_C2C1 = -0.30, s_C2C1 = 0.14^2,                  # single external trial
  tau0   = 1000
)
print(mNAP_test1)  
plot(mNAP_test1)   

## ------------------------------------------------------------
## Example 2: RE case (multiple historical), ADAPTIVE weight
## ------------------------------------------------------------
eNAP_test1 <- NAP_prior(
  weight_mtd = "adaptive",
  a = -2, b = 10,            # from calibration
  y_EC1  = -0.36, s_EC1  = 0.16^2,                 # E:C1 (current, pre-change)
  y_C2C1 = c(-0.28, -0.35, -0.31),                 # C2:C1 (external trials)
  s_C2C1 = c(0.12^2, 0.11^2, 0.15^2),
  tau0   = 1000                                     # vague variance
)
print(eNAP_test1)

   

Posterior mixture weight calculation

Description

Computes posterior updated mixture weights for a two-component normal–normal model using the standard logit-additive update. The prior mixing weight is either a fixed weight w \in (0,1) or a dynamic mixing weight as for eNAP prior: Z = |y_{\mathrm{dir}} - y_{\mathrm{ind}}| / s_{\mathrm{link}}:

w_(Z) = 1/exp(a + b \log (Z+1)), \quad a<0, \; b > 0.

Usage

post_w(
  w,
  a,
  b,
  s_EC2,
  s_EC1,
  s_C2C1,
  y_EC2,
  y_EC1 = -0.5,
  y_C2C1 = -0.5,
  tau0 = 1000,
  mu0 = 0,
  eps = 1e-12
)

Arguments

Details

• Fixed prior mixing weight (Robust NMAP Prior): requires ⁠0 < w < 1⁠.

• Adaptive branch (Adaptive NMAP Prior): triggered by w > 1, requires a<0 and b > 0. This corresponds to a decreasing prior weight as the inconsistency grows.

• All variance/SD arguments may be given as scalars or vectors; scalars are recycled.

Value

A numeric vector of posterior weights in ⁠(0,1)⁠ reflecting realized borrowing fraction of the informative component.

Examples

y_EC2  <- -0.5; y_EC1  <- -0.8; y_C2C1 <- -0.3
s_EC2 <- 0.2; s_EC1 <- 0.18; s_C2C1 <- 0.18

# Fixed mixing weight 0.5
post_w(w = 0.5, a = NA, b = NA,s_EC2,s_EC1,s_C2C1,
       y_EC2,y_EC1,y_C2C1)

# Dynamic weight with elastic function of (a=-4.6, b=3):
post_w(w = 2, a = -2.5, b = 10,s_EC2,s_EC1,s_C2C1,
       y_EC2,y_EC1,y_C2C1)

Calibrate (a, b) for eNAP prior

Description

Calibrates the tuning parameters (a,b) of the elastic NAP prior. This function supports both the one external trial setting and multiple external trials setting:

• Single external trial provide y_C2C1 and s_C2C1 as scalars.

• Multiple external trials provide y_C2C1 and s_C2C1 as vectors of same lengths. by default the cross-trial variance will be automatically calculated by REML, otherwise please provide the cross-trial variance as input parameter: sigma2_hat

Usage

tune_param_eNAP(
  s_EC2,
  s_EC1,
  s_C2C1,
  tau0 = 1000,
  delta = 0.5,
  t1 = 0.999,
  t0 = 0.05,
  clip_a = c(-5, -0.5),
  clip_b = c(1e-05, 50),
  exact = FALSE,
  y_EC1 = -0.5,
  y_C2C1 = -0.5,
  mu0 = 0,
  sigma2_hat = NULL,
  verbose = FALSE
)

Arguments

Details

Calibration procedure:

• Consistency case (Z = 0). Enforce near-full borrowing at exact consistency by solving w'(Z = 0) = t_1 for a.

• Strong inconsistency case (Z(\delta)=\frac{|\delta|}{\sqrt{s_{E,C_2}+s_{E,C_1}+s_{C_2,C_1}}}). Enforce minimal borrowing at a clinically significant difference by targeting the updated weight w'(Z(\delta)) = t_0, with calibrated a from step 1, solve for b.

For further details, see the original NAP paper by Zhang and et al. (manuscript).

Value

list with a, b, mode ("FE" or "RE"), and simple check summary.

Examples

s_EC2 <- 0.2^2; s_EC1 <- 0.18^2; s_C2C1 <- 0.18^2
tau0 <- 1000

# One external trial setting
tune_param_eNAP(
  s_EC2,s_EC1,s_C2C1, tau0=1000,
  delta=0.5, t1 = 0.999, t0 = 0.05)

# Multiple external trials setting
s_C2C1=c(0.19^2,0.18^2,0.20^2)
y_C2C1=c(-0.5,-0.45,-0.6)
tune_param_eNAP(
  s_EC2,s_EC1,s_C2C1, tau0=10,
  delta=0.5, t1 = 0.999, t0 = 0.05,
  exact=TRUE,y_EC1=-0.8,y_C2C1=y_C2C1)