ABSTRACT
Chapter 2 introduces the all-important 2x2 table summarizing the comparison of two groups with respect to a binary outcome. We discuss different measures of treatment effect: the risk difference, relative risk, and odds ratio. We show why it is more natural to log transform two measures of relative treatment effect, the relative risk and odds ratio. This segues into the use of the delta method to derive the asymptotic distribution of estimates of the log relative risk and log odds ratio. We also relate the log odds ratio to logistic regression and introduce the ‘O minus E except after V’ principle for estimating the log odds ratio. Also featured in Chapter 2 are Fisher's exact test and its associated confidence interval for the odds ratio via the noncentral hypergeometric distribution. We show how Fisher's exact test, like other exact tests, can exhibit strange behavior and have lower power when sample sizes are small. For this reason, we briefly discuss exact unconditional tests, which are often more powerful than Fisher's exact test.
