Bayesian Meta Analysis/Meta-regression

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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

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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")

## 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

The total number of MCMC simulations saved (including thinning). Default at 1000

n.chains

number of Markov chains to be used in the simulation (default is 2)

model.file

Name of the text file to which the model is saved

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, events out of case and control arm and sample size of case and control arm need to be listed. For continuous data, mean and standard errors of case and control arm need to be listed if information is available. However, if only mean difference and variance can be retrieved from each study, users need to list mean difference and precision (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. For count data, total number of events in the follow-up period of case and control arm, total follow-up person-time in case and control arm should be listed.

If additional impacts of a variable or more than one variable are observed (when meta-regression is expected to be used), users need to provide a matrix with each column either containing a dummy variable or a continuous variable. In case that categorical variables (i.e. ethnicity, age band) are observed and included, users need to first choose a 'baseline' category as reference and then create dummies for each of the rest categories.

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.

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

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

### List data for binary outcome (for meta-analysis)
d1 <- 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)
d1 <- 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 
m1 <- bmeta(d1, outcome="bin", model="std.norm", type="fix",n.iter=100)

### Select random-effects meta-regression with t-distribution prior for binary
### data
m2 <- bmeta(data.list, outcome="bin", model="reg.dt", type="ran",n.iter=100)



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

### List data for continuous outcome for studies reporting two arms separately
### (for meta-analysis)
d1 <- 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)
d2 <- data.list2 <- 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 
m1 <- bmeta(data.list, outcome="ctns", model="std.ta", type="fix",n.iter=100)

### Select random-effects meta-regression with studies reporting mean difference and 
### variance only for continuous data
m2 <- bmeta(data.list2, outcome="ctns", model="reg.mv", type="ran",n.iter=100)



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

### List data for count outcome (for meta-analysis)
d1 <- data.list <- list(y0=data$y0,y1=data$y1,p0=data[,6],p1=data[,10])

### List data for count outcome when there is a covariate (for meta-regression)
d2 <- data.list <- list(y0=data$y0,y1=data$y1,p0=data[,6],p1=data[,10],X=cbind(data$X0)) 

### Select fixed-effects meta-analysis for count data
m1 <- bmeta(d1, outcome="count", model="std", type="fix",n.iter=100)

### Select random-effects meta-analysis with half-Cauchy prior for count data
m2 <- bmeta(d1, outcome="count", model="std.hc", type="ran",n.iter=100)

### Select random-effects meta-regression with uniform prior for count data
m3 <- bmeta(d2, outcome="count", model="reg.unif", type="ran",n.iter=100)