Bayesia analysis of cluster randomised trials Using vague priors.
Description
crtBayes
performs analysis of cluster randomised trial using multilevel model within the Bayesian framework
assuming vague priors.
Usage
1 
Arguments
formula 
specifies the model to be analysed. It is of the form form y ~ x1+x2 +..., where y is the outcome variable and X's are the predictors. 
random 
a string variable specifying the "clustering" variable as contained in the data. This must be put between quotes. For example, "school". 
intervention 
specifies the name of the intervention variable as appeared in formula. This must be put between quotes. For example "intervention" or "treatment" or "group"... 
nSim 
number of MCMC simulations to generate samples from full conditional posterior distributions. A minimum of 10,000 is recommended. 
data 
specifies data frame containing the data to be analysed. 
Value
S3 mcpi
object; a list consisting of

Beta
. Estimates and confidence intervals for the predictors specified in the model. It will be a slope for a continuous predictor and a mean difference for a dummy variable or a categorical predictor. 
ES
. Effect size for the intervention effect. 
covParm
. A vector of variance decomposition into betweenvariance (Schools), withinvariance (Pupils) and total variance. It also contains the intracluster correlation (ICC). 
ProbES
. A maxtrix containing the probability of observing ES greater than a prespecified value. First column is for withinvariance, second column for betweenvariance and the third column for totalvariance. 
SchEffects
. Individual school effects at baseline.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56  data(iwq)
########################################################
## Bayesian analysis of cluster randomised trials ##
########################################################
output < crtBayes(Posttest~ Intervention+Prettest,
random="School",intervention="Intervention",
nSim=10000,data=iwq)
### Fixed effects
beta < output$Beta
beta
### Effect size
ES1 < output$ES
ES1
## Covariance matrix
covParm < output$covParm
covParm
### random effects for schools
randOut < output$"SchEffects"
randOut < randOut[order(randOut$Estimate),]
barplot(randOut$Estimate,ylab="Deviations from Overall Average",
names.arg=randOut$Schools,las=2)
### Posterior probability given a fixed threshold
probES < output$ProbES
str(probES )
plot(probES[,1] ,probES[,2],ylim=c(0,max(probES)),
ylab="Probability",cex.lab=1,cex.axis=1,
type="n", xlab=expression("Effect size" >= "x"),
cex=1)
lines(probES[,1],probES[,2],col="chartreuse3",cex=1.5,
lwd=1.5,lty=2)
lines(probES[,1],probES[,3],col="violetred",cex=1.5,
lwd=1.5,lty=3)
lines(probES[,1],probES[,4],col="cornflowerblue",cex=1.5,
lwd=1.5,lty=1)
points(probES[,1],probES[,2],col="chartreuse3",cex=1.5,
lwd=1.5,pch=7)
points(probES[,1],probES[,3],col="violetred",cex=1.5,
lwd=1.5,pch=1)
points(probES[,1],probES[,4],col="cornflowerblue",
cex=1.5,lwd=1.5,pch=12)
legend(0,0.4,legend=c("Within ","Between ","Total "),
lty=c(2,3,1),cex=1.5, pch=c(7,1,12),
col=c("chartreuse3","violetred","cornflowerblue"),
title="Variance Type")

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