Compute a Bayesian random-effects meta-analysis

Compute a Bayesian meta-analysis using the Markov chain Monte Carlo (MCMC) engine BEAST. A normal and half-normal prior are used for the mu and tau parameters, respectively, with standard deviations as defined by the priorSd argument.

computeBayesianMetaAnalysis(
  data,
  chainLength = 1100000,
  burnIn = 1e+05,
  subSampleFrequency = 100,
  priorSd = c(2, 0.5),
  alpha = 0.05,
  robust = FALSE,
  df = 4,
  seed = 1,
  showProgressBar = TRUE
)

Arguments

data

A data frame containing either normal, skew-normal, custom parametric, or grid likelihood data, with one row per database.

chainLength

Number of MCMC iterations.

burnIn

Number of MCMC iterations to consider as burn in.

subSampleFrequency

Subsample frequency for the MCMC.

priorSd

A two-dimensional vector with the standard deviation of the prior for mu and tau, respectively.

alpha

The alpha (expected type I error) used for the credible intervals.

robust

Whether or not to use a t-distribution model; default: FALSE.

df

Degrees of freedom for the t-model, only used if robust is TRUE.

seed

The seed for the random number generator.

showProgressBar

Showing a progress bar for MCMC?

Value

A data frame with the point estimates and 95% credible intervals for the mu and tau parameters (the mean and standard deviation of the distribution from which the per-site effect sizes are drawn). Attributes of the data frame contain the MCMC trace and the detected approximation type.

See also

approximateLikelihood, computeFixedEffectMetaAnalysis

Examples

# Simulate some data for this example:
populations <- simulatePopulations()

# Fit a Cox regression at each data site, and approximate likelihood function:
fitModelInDatabase <- function(population) {
  cyclopsData <- Cyclops::createCyclopsData(Surv(time, y) ~ x + strata(stratumId),
    data = population,
    modelType = "cox"
  )
  cyclopsFit <- Cyclops::fitCyclopsModel(cyclopsData)
  approximation <- approximateLikelihood(cyclopsFit,
                                         parameter = "x",
                                         approximation = "grid with gradients")
  return(approximation)
}
approximations <- lapply(populations, fitModelInDatabase)

# At study coordinating center, perform meta-analysis using per-site approximations:
estimate <- computeBayesianMetaAnalysis(approximations)
#> Detected data following grid with gradients distribution
#> Performing MCMC. This may take a while
estimate
#>         mu     mu95Lb   mu95Ub      muSe       tau     tau95Lb  tau95Ub
#> 1 0.456537 -0.4352229 1.231871 0.4238033 0.4477577 0.001885051 1.017906
#>      logRr   seLogRr predictionInterval95Lb predictionInterval95Ub
#> 1 0.456537 0.4238033             -0.9953475               1.934389

# (Estimates in this example will vary due to the random simulation)