Simultaneous Confidence Intervals For Multivariate Binomial Proportions

This paper considers construction of simultaneous confidence intervals for multivari-ate binomial proportions in one-sample and two-sample cases. Such problem often arises in safety analysis of clinical trial when several correlated adverse events are examined simultaneously. Unlike the approach through inequality-based corrections such as Bon-ferroni or Sidak method, we propose a method that takes the correlation structure into account. The simultaneous confidence intervals are built upon the Wilson type inter-vals for the individual parameter with equi-coordinate critical point approximated by the percentile of some maximum modulus distribution. And we also propose an effective two-point method, which is more accurate than Bonferroni method through simulation. When the dimension is large, the method of low dimension becomes computationally impractical to calculate the critical point directly because of time consumption and loss of precision. To circumvent such difficulty, we propose a parsimonious method to construct simulta-neous confidence intervals in the high dimensional case. Simulation studies demonstrate the effectiveness of the proposed methods in terms of precision of the coverage probability and computation time. At last, we also extend the methods to construct simultaneous confidence intervals for parameters in multivariate odds ratio and relative risk.