bmeta.default: bmeta - Bayesian Meta Analysis/Meta-regression

In giabaio/bmeta: Bayesian Meta-Analysis and Meta-Regression

bmeta – Bayesian Meta Analysis/Meta-regression

Description

Function to fit the Bayesian fixed- and random-effects meta-analytic models with or without moderators. Models are designed to include non-informative priors.

Usage

## Default S3 method:
bmeta(
  data,
  outcome = c("bin", "ctns", "count"),
  model = c("std.norm", "std.dt", "reg.norm", "reg.dt", "std.ta", "std.mv", "reg.ta",
    "reg.mv", "std", "std.unif", "std.hc", "reg", "reg.unif", "reg.hc"),
  type = c("fix", "ran"),
  n.iter = 10000,
  n.burnin = 5000,
  n.samples = 1000,
  n.chains = 2,
  model.file = "model.txt",
  ...
)

Arguments

data	a data list containing information on observed data (including moderators). See 'details'.
outcome	type of outcome that needs to be specified. For binary, continuous and count data, "bin","ctns" and "count" need to be specified, respectively.
model	type of model that needs to be specified. See 'details'.
type	model type—either fixed-effects("fix") or random-effects model("ran") needs to be specified.
n.iter	number of iterations to be used in the simulation (default is 10000)
n.burnin	number of burn-in to be used in the simulation (default is 5000)
n.samples	number of total iterations to be saved
n.chains	number of Markov chains to be used in the simulation (default is 2)
model.file	file containing the appropriate model selected by user
...	additional (optional) arguments

Details

Specifying the data

The function can be used to evaluate odds ratios (or log odds ratios), mean difference and incidence rate ratios (or log incidence rate ratios). Users need to specify a list of data to be used in the function.

For binary data, the meta-analysis models require users to provide a list of values for events out of case arm (y1) and control arm (y0) and the sample size of case arm (n1) and control arm (n0). If there are additional covariates (when meta-regression should be applied), a matrix 'X' needs to be used with each column either containing a dummy variable (either '0' or '1') or a continuous variable. For binary and continuous covariates, the matrix 'X' can be specified by the command X=data$covariate or X=cbind(data$covariate1, data$covariate2). For categorical variables, users need to firstly choose a 'baseline' category as reference and then create dummies for each of the rest categories. For example, if there is a covariate 'ethnicity' with 3 categories —White, Black and Asian, and suppose we use Asian as our baseline reference group, then dummies for the rest 2 categories, White and Black, should be created, with 1 column containing either '0' or '1' indicating whether a study use White population or not and another one column in exactly the same format indicating whether as study use Black population or not. For the next step, the matrix 'X' should be specified by combining information from these two columns, i.e. X=cbind(data$White,data$Black).

For continuous data, mean (y1,y0) and standard errors (se1,se0) of case and control arm need to be listed, respectively, if information is available. However, if only mean difference and variance can be retrieved from each study, users need to list mean difference (y) and precision (prec)—defining as the inverse of variance. Notice that information of all the studies need to be provided in the same format for the function to work properly. For example, the function cannot work if some of the studies provide mean and standard errors of the two arms while the rest studies provide mean difference and variance. The meta-regression models require exactly the same format of covariates input as illustrated above for the binary data.

For count data, total number of events in the follow-up period of case arm (y1) and control arm (y0), total follow-up person-time in case arm (p1) and control arm (p0) should be listed. The meta-regression models require exactly the same format of input as illustrated above for the binary data.

Notice that for all meta-regression models, moderator effects can only be incorporated into the model through the matrix 'X'.

Model selection

Apart from 'null' models which apply Bayesian methods to obtain study-specific without pooling-effects, there are 22 models included in this package for pooling study-specific estimates together and producing summary estimate. The number of models designed for binary, continuous and count data are 8, 8 and 6, respectively. The model selection process for binary and count data requires users to specify not only whether meta-analysis or meta-regression is wanted but also the priors to be used.

For binary data, normal and Student t-distribution priors for summary estimates (on log scale) can be selected and it is indicated that Student t-distribution has heavier tails and is therefore more robust to outliers. The argument 'model' here includes 4 options —"std.norm","std.dt","reg.norm","reg.dt".

For continuous data, rather than specifying prior, users need to select whether all studies included report mean and standard errors of two arms separately or only mean difference and variance as discussed above in the 'Specifying the data' section. The argument 'model' here includes 4 options—"std.ta","std.mv","reg.ta","reg.mv"('model' ending with 'ta' represents 'two arms' and ending with 'mv' represents 'mean and variance').

For count data, uniform and half-Cauchy distribution priors for the variability of summary estimates (on log scale) can be selected. It is suggested that half-Cauchy distribution has heavier tails and allows for outliers and accommodates small variances closing to zero. It should be noticed that there is no need to specify priors for fixed-effects models for count data. The argument 'model' here includes 6 options —"std","std.unif","std.hc","reg","reg.unif","reg.hc". The meta-analysis models require users to provide a list of values for total number of events in case arm (y1) and control arm (y0) in the follow-up period and the total follow-up person-time in case arm (p1) and control arm (p0).

In conjunction with the argument 'type'—"fix" or "ran", users can select the specific model wanted for a certain type of data.

Value

mod	A rjags object with the results of the model
params	a list of monitored parameters to be saved
data	the original dataset
inits	a list with n.chains elements, with each element itself being a list of starting values for the model or a function generating initial values
outcome	selected type of outcome (i.e. bin/ctns/count)
type	selected type of model (either fixed-/random-effects)
model	selected model with specific priors
mod0	independent model without pooling effects

Author(s)

Tao Ding Gianluca Baio

References

Baio, G.(2012) Bayesian methods in health economics. Chapman Hall, CRC. Welton, N.J., Sutton, A.J., Cooper, N., Abrams, K.R. & Ades, A.E. (2012) Evidence synthesis for decision making in healthcare. Chichester, UK: John Wiley & Sons, Ltd.

Examples

### Read and format the data (binary)
data = read.csv(url("https://gianluca.statistica.it/software/bmeta/Data-bin.csv"))

### List data for binary outcome (for meta-analysis)
data.list <- list(y0=data$y0,y1=data$y1,n0=data$n0,n1=data$n1) 

### List data for binary outcome when there is a covariate (for meta-regression)
data.list <- list(y0=data$y0,y1=data$y1,n0=data$n0,n1=data$n1,X=cbind(data$X0)) 

### Select fixed-effects meta-analysis with normal prior for binary data 
bmeta(data.list, outcome="bin", model="std.norm", type="fix")

### Select random-effects meta-regression with t-distribution prior for binary
### data
bmeta(data.list, outcome="bin", model="reg.dt", type="ran")



### Read and format the data (continuous)
data = read.csv(url("https://gianluca.statistica.it/software/bmeta/Data-ctns.csv"))

### List data for continuous outcome for studies reporting two arms separately
### (for meta-analysis)
data.list <- list(y0=data$y0,y1=data$y1,se0=data$se0,se1=data$se1) 

### List data for continuous outcome for studies reporting mean difference and 
### variance with a covariate (for meta-regression)
data.list <- list(y=data$y,prec=data$prec,X=cbind(data$X0))

### Select fixed-effects meta-analysis with studies reporting information of 
### both arm for continuous data 
bmeta(data.list, outcome="ctns", model="std.ta", type="fix")

### Select random-effects meta-regression with studies reporting mean difference and 
### variance only for continuous data
bmeta(data.list, outcome="ctns", model="reg.mv", type="ran")



### Read and format the data (count)
data = read.csv(url("https://gianluca.statistica.it/software/bmeta/Data-count.csv"))

### List data for count outcome (for meta-analysis)
data.list <- list(y0=data$y0,y1=data$y1,p0=data$p0,p1=data$p1)

### List data for count outcome when there is a covariate (for meta-regression)
data.list <- list(y0=data$y0,y1=data$y1,p0=data$p0,p1=data$p1,X=cbind(data$X0)) 

### Select fixed-effects meta-analysis for count data
bmeta(data.list, outcome="count", model="std", type="fix")

### Select random-effects meta-analysis with half-Cauchy prior for count data
bmeta(data.list, outcome="count", model="std.hc", type="ran")

### Select random-effects meta-regression with uniform prior for count data
bmeta(data.list, outcome="count", model="reg.unif", type="ran")

giabaio/bmeta documentation built on May 4, 2023, 3:31 p.m.