Estimating Simultaneous Confidence Intervals for Multiple Contrasts of Proportions by the Method of Variance Estimates Recovery

Many questions in biomedical research can be addressed effectively with simultaneous confidence intervals for multiple contrasts. While procedures for normal outcome data are readily available, there is still a need for developing practical methods for binary outcomes. In this article, we construct simultaneous confidence intervals for multiple contrasts of binomial proportions using the two-step method of variance estimates recovery (Zou and Donner 2008; Zou 2008; Zou et al. 2009a). First, we obtain confidence limits about single proportions using critical values from the multivariate normal distribution that account for correlations among contrasts. Second, we set confidence limits for these contrasts using variance estimates recovered from the limits. Simulation results show this approach performs well in small to moderate sample sizes when either the Wilson or Jeffreys method is used for constructing confidence limits about a single proportion. We illustrate the procedure with examples.