Multiple comparisons for analyzing dichotomous response

Dichotomous response models are common in many experimental settings. Statistical parameters of interest are typically the probabilities, p(i), that an experimental unit will respond at the various treatment levels. Herein, simultaneous procedures are considered for multiple comparison among these probabilities, with attention directed at construction of simultaneous confidence intervals for various functions of the p(i). The inferences are based on the asymptotic normality of the maximum likelihood estimator of p(i). Specific applications include all pairwise comparisons and comparisons with a fixed (control) treatment. Monte Carlo evaluations are undertaken to examine the small-sample properties of the various procedures. It is seen that use of the usual estimates of variance consistently leads to less-than-nominal empirical coverage for most sample sizes examined. For very large samples (total size greater than about 300), nominal coverage is achieved. A reformulation of the pairwise comparisons using a construction noted by Beal (1987, Biometrics 43, 941-950) is shown to exhibit generally nominal empirical coverage characteristics, and is recommended for use with small-to-moderate sample sizes.