Sample size determination and re-estimation for matched pair designs with multiple binary endpoints

Motivated by a recent symptom management trial to simultaneously assess multiple binary endpoints for cancer chemotherapy, we extend the univariate McNemar test to multivariate cases for doubly blinded clinical trials with matched pairs. We propose a general method to test noninferiority or equivalence. The method employs the intersection-union principle on the marginal score statistics to obtain an asymptotic α-level test. Power formula and sample size calculation are provided by a simple numerical method that accounts for the correlation structure among the endpoints. We further consider sample size re-estimation through internal pilot study. To avoid the need of unblinding for doubly blinded trials, we also propose a blinded approach for nuisance parameter estimation. The effectiveness of the proposed methods is demonstrated by simulation studies. Application to the cancer chemotherapy trial is illustrated.