Question

Consider the anorexia dataset in the MASS package. This data considers two treatments for anorexia, one based on Cognitive Behavorial Treatment (CBT) sessions from a professional therapist and another based on family oriented treatment sessions (FT). The Treat variable is a factor with three levels: Cont (control, no treatment), CBT, and FT. For each subject two weights (in lbs) were measured, one before (Prewt) and one after (Postwt) treatment.

(a) Create a new variable, Outcome, that indicates if the post-weight is higher than the pre-weight, thus denoting whether or not the treatment was successful. Design a figure that compares the success of the three treatment groups graphically (e.g. a barplot).

(b) Using a uniform prior, compute and plot the posterior densities of the proportion of successes for each treatment level.

(c) Use Monte Carlo with your posterior distributions to obtain confidence/credible intervals for the difference in success proportions when comparing CBT to Cont and FT to Cont. What can you conclude in terms of the data?

Answer 1

> library(MASS)
> d=anorexia
> Outcome=ifelse(d$Postwt>d$Prewt,1,0)
> d1=cbind(d,Outcome)
> d2=d1[which(d1$Treat=="Cont"),]
> d3=d1[which(d1$Treat=="CBT"),]
> d4=d1[which(d1$Treat=="FT"),]
> s1=sum(d2$Outcome);s2=sum(d3$Outcome);s3=sum(d4$Outcome)
> s=c(s1,s2,s3)
> S=c(dim(d2)[1],dim(d3)[1],dim(d4)[1])
> b1=barplot(as.matrix(t(cbind(s,S))),xlab = "trt")
> b1
[1] 0.7 1.9 3.1