################################################## ## Introduction to Sampling & Variability ## Steve Bellan ## Meaningful Modeling of Epidemiological Data 2015 ## African Institute of Mathematical Sciences, Muizenberg, South Africa ## Pick a research question: ## ## Does having HIV affect TB set.seed(1) n <- 200 ## sample size hivstatus <- rep(c(0,1), each = n/2) table(hivstatus) tbIncRate <- c(.05, .15) myDat <- data.frame(hiv = hivstatus, tb = NA) numPerms <- 999 myDat\$tb <- rbinom(n, 1, prob = rep(tbIncRate, each = n/2)) xtabs(~hiv + tb, myDat) idr <- function(dat) with(dat, mean(tb[hiv==1])/mean(tb[hiv==0])) Null_IDR_Vector <- rep(NA, numPerms) for(ii in 1:numPerms) { permDat <- myDat permDat\$tb <- sample(permDat\$tb, n) xtabs(~hiv + tb, permDat) Null_IDR_Vector[ii] <- idr(permDat) } idr(myDat) Full_IDR_Vector <- c(Null_IDR_Vector, idr(myDat)) par('ps' = 24) hist(log(Full_IDR_Vector), xlab = 'null IDR', ylab = 'frequency', bty = 'n', col = 'gray', main = '', xaxt='n') axis(1, at = log(c(.2,.5,1,2,5)), lab = c(.2,.5,1,2,5)) abline(v = log(idr(myDat)), col = 'red', lwd =2) 2*min(mean(Full_IDR_Vector >= idr(myDat)), mean(Full_IDR_Vector <= idr(myDat))) pValFxn <- function(FullVector, ObsVal) 2*min(mean(FullVector >= ObsVal), mean(FullVector <= ObsVal)) trueIDRvals <- seq(1, 5, l = 10) noHIV_tb_inc <- .05 n <- 500 ## sample size hivstatus <- rep(c(0,1), each = n/2) numSims <- 1000 numPerms <- 999 powerChiSqVector <- rep(NA, length(trueIDRvals)) for(rr in 1:length(trueIDRvals)) { print(paste0('on IDR ', rr, ' of ', length(trueIDRvals))) trueIDR <- trueIDRvals[rr] ## Power Analysis tbIncRate <- c(noHIV_tb_inc, trueIDR * noHIV_tb_inc) myDat <- data.frame(hiv = hivstatus, tb = NA) pValueVectorChiSq <- pValueVector <- rep(NA, numSims) for(jj in 1:numSims) { if(jj %% 20 == 0) print(paste0('on simulation ', jj, ' of ', numSims)) myDat\$tb <- rbinom(n, 1, prob = rep(tbIncRate, each = n/2)) ## Null_IDR_Vector <- rep(NA, numPerms) ## for(ii in 1:numPerms) { ## permDat <- myDat ## permDat\$tb <- sample(permDat\$tb, n) ## Null_IDR_Vector[ii] <- idr(permDat) ## } ## Full_IDR_Vector <- c(Null_IDR_Vector, idr(myDat)) ## pValueVector[jj] <- pValFxn(Full_IDR_Vector, idr(myDat)) myTab <- xtabs(~hiv + tb, myDat) chisqResult <- chisq.test(myTab) pValueVectorChiSq[jj] <- chisqResult\$p.value ## if(pValueVector[jj] > 1) browser() } ## debug(pValFxn) ## undebug(pValFxn) ## pValueVector ## pValueVectorChiSq ## plot(data.frame(pValueVector, pValueVectorChiSq)) ## abline(a = 0, b = 1) ## power <- mean(pValueVector <= .05) powerChiSqVector[rr] <- mean(pValueVectorChiSq <= .05) } par(mar = c(6,6,1,1)) powerTable <- data.frame(idr = trueIDRvals, power = powerChiSqVector) plot(powerTable, xlab = 'IDR', ylab = 'statistical power', main = '', type = 'b', col = 'blue', lwd = 3, bty = 'n') abline(h=.05, col = 'red', lty = 2, lwd = 4)