R: Fit Bayesian Network Meta-Regression Models

bayes_nmr {metapack}

R Documentation

Fit Bayesian Network Meta-Regression Models

Description

This is a function the fits the model introduced in Bayesian Network Meta-Regression Models Using Heavy-Tailed Multivariate Random Effects with Covariate-Dependent Variances. The first seven arguments are required except ZCovariate. If not provided, ZCovariate will be assigned a vector of ones, rep(1, length(Outcome)). ZCovariate is the centerpiece of the modeling of variances and the heavy-tailed random effects distribution.

Usage

bayes_nmr(
  Outcome,
  SD,
  XCovariate,
  ZCovariate,
  Treat,
  Trial,
  Npt,
  prior = list(),
  mcmc = list(),
  control = list(),
  init = list(),
  Treat_order = NULL,
  Trial_order = NULL,
  scale_x = FALSE,
  verbose = FALSE
)

Arguments

`Outcome`	the aggregate mean of the responses for each arm of every study.
`SD`	the standard deviation of the responses for each arm of every study.
`XCovariate`	the aggregate covariates for the fixed effects.
`ZCovariate`	the aggregate covariates associated with the variance of the random effects.
`Treat`	the treatment identifiers for trial arm. This is equivalent to the arm labels in each study. The elements within will be coerced to consecutive integers
`Trial`	the study/trial identifiers. The elements within will be coerced to consecutive integers.
`Npt`	the number of observations/participants for a unique `⁠(k,t)⁠`, or each arm of every trial.
`prior`	(Optional) a list of hyperparameters. The hyperparameters include `df`, `c01`, `c02`, `a4`, `b4`, `a5`, and `b5`. `df` indicates the degrees of freedom whose value is 20. The hyperparameters `⁠a⁠` and `⁠b⁠` will take effect only if `sample_df=TRUE`. See `control`.
`mcmc`	(Optional) a list of MCMC specification. `ndiscard` is the number of burn-in iterations. `nskip` configures the thinning of the MCMC. For instance, if `nskip=5`, `bayes_nmr` will save the posterior sample every 5 iterations. `nkeep` is the size of the posterior sample. The total number of iterations will be `ndiscard + nskip * nkeep`.
`control`	(Optional) a list of parameters for the Metropolis-Hastings algorithm. `lambda`, `phi`, and `Rho` are sampled through the localized Metropolis algorithm. `⁠*_stepsize⁠` with the asterisk replaced with one of the names above specifies the stepsize for determining the sample evaluation points in the localized Metropolis algorithm. `sample_Rho` can be set to `FALSE` to suppress the sampling of `Rho`. When `sample_Rho` is `FALSE`, `Rho` will be fixed using the value given by the `init` argument, which defaults to an equicorrelation matrix of `0.5\boldsymbol{I}+0.5\boldsymbol{1}\boldsymbol{1}^\prime` where `\boldsymbol{1}` is the vector of ones. When `sample_df` is `TRUE`, `df` will be sampled.
`init`	(Optional) a list of initial values for the parameters to be sampled: `theta`, `phi`, `sig2`, and `Rho`.
`Treat_order`	(Optional) a vector of unique treatments to be used for renumbering the `Treat` vector. The first element will be assigned treatment zero, potentially indicating placebo. If not provided, the numbering will default to an alphabetical/numerical order.
`Trial_order`	(Optional) a vector unique trials. The first element will be assigned trial zero. If not provided, the numbering will default to an alphabetical/numerical order.
`scale_x`	(Optional) a logical variable indicating whether `XCovariate` should be scaled/standardized. The effect of setting this to `TRUE` is not limited to merely standardizing `XCovariate`. The following generic functions will scale the posterior sample of `theta` back to its original unit: `plot`, `fitted`, `summary`, and `print`. That is `theta[j] <- theta[j] / sd(XCovariate[,j])`.
`verbose`	(Optional) a logical value indicating whether to print the progress bar during the MCMC sampling.

Value

bayes_nmr returns an object of class "bayesnmr". The functions summary or print are used to obtain and print a summary of the results. The generic accessor function fitted extracts the posterior mean, posterior standard deviation, and the interval estimates of the value returned by bayes_nmr.

An object of class bayesnmr is a list containing the following components:

Outcome - the aggregate response used in the function call.
SD - the standard deviation used in the function call.
Npt - the number of participants for ⁠(k,t)⁠ used in the function call.
XCovariate - the aggregate design matrix for fixed effects used in the function call. Depending on scale_x, this may differ from the matrix provided at function call.
ZCovariate - the aggregate design matrix for random effects. bayes_nmr will assign rep(1, length(Outcome)) if it was not provided at function call.
Trial - the renumbered trial indicators. Depending on Trial_order, it may differ from the vector provided at function call.
Treat - the renumbered treatment indicators. Depending on Treat_order, it may differ from the vector provided at function call.
TrtLabels - the vector of treatment labels corresponding to the renumbered Treat. This is equivalent to Treat_order if it was given at function call.
TrialLabels - the vector of trial labels corresponding to the renumbered Trial. This is equivalent to Trial_order if it was given at function call.
K - the total number of trials.
nT - the total number of treatments.
scale_x - a Boolean indicating whether XCovariate has been scaled/standardized.
prior - the list of hyperparameters used in the function call.
control - the list of tuning parameters used for MCMC in the function call.
mcmctime - the elapsed time for the MCMC algorithm in the function call. This does not include all the other preprocessing and post-processing outside of MCMC.
mcmc - the list of MCMC specification used in the function call.
mcmc.draws - the list containing the MCMC draws. The posterior sample will be accessible here.

Author(s)

Daeyoung Lim, daeyoung.lim@uconn.edu

References

Li, H., Chen, M. H., Ibrahim, J. G., Kim, S., Shah, A. K., Lin, J., & Tershakovec, A. M. (2019). Bayesian inference for network meta-regression using multivariate random effects with applications to cholesterol lowering drugs. Biostatistics, 20(3), 499-516.

Li, H., Lim, D., Chen, M. H., Ibrahim, J. G., Kim, S., Shah, A. K., & Lin, J. (2021). Bayesian network meta-regression hierarchical models using heavy-tailed multivariate random effects with covariate-dependent variances. Statistics in Medicine.

Examples

library(metapack)
data(TNM)
groupInfo <- list(c("PBO"), c("R"))
nz <- length(groupInfo)
ns <- nrow(TNM)
XCovariate <- model.matrix(~ 0 + bldlc + bhdlc + btg + age +
 white + male + bmi + potencymed + potencyhigh + durat, data = TNM)
XCovariate <- scale(XCovariate, center = TRUE, scale = FALSE)
ZCovariate <- matrix(0, ns, nz)
for (j in 1:length(groupInfo)) {
    for (i in 1:ns) {
        if (TNM$treat[i] %in% groupInfo[[j]]) {
            ZCovariate[i, j] <- 1
        }
    }
}
addz <- scale(cbind(TNM$bldlc, TNM$btg), center=TRUE, scale=TRUE)
ZCovariate <- cbind(1, ZCovariate, addz)
theta_init <- c(0.05113, -1.38866, 1.09817, -0.85855, -1.12056, -1.14133,
             -0.22435, 3.63453, -2.09322, 1.07858, 0.80566, -40.76753,
             -45.07127, -28.27232, -44.14054, -28.13203, -19.19989,
             -47.21824, -51.31234, -48.46266, -47.71443)
set.seed(2797542)
fit <- bayes_nmr(TNM$ptg, TNM$sdtg, XCovariate, ZCovariate, TNM$treat,
    TNM$trial, TNM$n, prior = list(c01 = 1.0e05, c02 = 4, df = 3),
    mcmc = list(ndiscard = 1, nskip = 1, nkeep = 1),
    init = list(theta = theta_init),
    Treat_order = c("PBO", "S", "A", "L", "R", "P", "E", "SE",
         "AE", "LE", "PE"),
    scale_x = TRUE, verbose = FALSE)

[Package metapack version 0.3 Index]