# # Data: # CC CT TT # Cases 6 8 75 # Controls 10 66 163 # # Likelihood first # x <- c(0,1,2) y <- c(6,8,75) z <- c(10,66,163) logitmod <- glm(cbind(y,z)~x,family="binomial") thetahat <- logitmod\$coeff[2] # Log odds ratio V <- vcov(logitmod)[2,2] # se^2 exp(thetahat) exp(thetahat-1.96*sqrt(V)) exp(thetahat+1.96*sqrt(V)) summary(logitmod) # # Bayesian # source("http://faculty.washington.edu/jonno/BFDP.R") pi1 <- c(1/100,1/1000,1/10000,1/100000) # Prior on alternative Upper975 <- 1.5 W <- (log(Upper975)/1.96)^2 # 97.5 point of prior is log(1.5) so that we # believe with prior prob 0.95 that the odds # corresponding to one T allele more, # lies in (2/3,1.5) BFcall <- BFDPfunV(thetahat,V,W,pi1) r <- W/(V+W) exp(r*thetahat) exp(r*thetahat-1.96*sqrt(r*V)) exp(r*thetahat+1.96*sqrt(r*V)) cat("log odds, standard error and ratio: ",thetahat,sqrt(V), thetahat/sqrt(V),"\n") # Posterior distribution is asymptotically lognormal with mean r x thetahat # and variance r x thetahat RRseq <- seq(.1,4,.01) postseq <- dlnorm(RRseq,mean=r*thetahat,sd=sqrt(r*V)) plot(postseq~RRseq,type="n",xlab="Odds Ratio",ylab="Posterior") priorseq <- dlnorm(RRseq,mean=0,sd=sqrt(W)) lines(priorseq~RRseq,lty=2) lines(postseq~RRseq) legend("topright",legend=c("Prior Distribution","Posterior Distribution"), lty=2:1,bty="n") cat("Bayes Factor of H0 over H1: ",BFcall\$BF,"\n") cat("Posterior probs of the null, given priors on the null of: ",1-pi1," are ",BFcall\$BFDP,"\n")