Simultaneous confidence intervals for comparing margins of multivariate binary data

In many applications two groups are compared simultaneously on several correlated binary variables for a more comprehensive assessment of group differences. Although the response is multivariate, the main interest is in comparing the marginal probabilities between the groups. Estimating the size of these differences under strong error control allows for a better evaluation of effects than can be provided by multiplicity adjusted P-values. Simultaneous confidence intervals for the differences in marginal probabilities are developed through inverting the maximum of correlated Wald, score or quasi-score statistics. Taking advantage of the available correlation information leads to improvements in the joint coverage probability and power compared to straightforward Bonferroni adjustments. Estimating the correlation under the null is also explored. While computationally complex even in small dimensions, it does not result in marked improvements. Based on extensive simulation results, a simple approach that uses univariate score statistics together with their estimated correlation is proposed and recommended. All methods are illustrated using data from a vaccine trial that investigated the incidence of four pre-specified adverse events between two groups and with data from the General Social Survey.