Blinded sample size review for McNemar's test based on primary and surrogate endpoints

Abstract

We develop blinded sample size re-estimation strategies for McNemar's test based on paired binary primary and secondary short-term surrogate endpoints. The development is motivated by a prospective randomized clinical trial on childhood glaucoma. A conditional power expression for McNemar's test given the primary endpoint at an interim analysis is derived and complemented by a sample size re-estimation rule. We show that this procedure preserves the type I error rate while allowing the second-stage sample size to be chosen to attain a prespecified target power. In the case where for some patients only a short-term surrogate endpoint is available at interim, we introduce a surrogate-based re-estimation approach that conditions on all possible numbers of primary-endpoint discordant pairs using transition rates from the surrogate to the primary outcome. We show how these transition rates can be estimated from data on a subsample for which both surrogate and primary endpoint are available. We derive the resulting surrogate endpoint-based conditional power and sample size rule and illustrate their use with the example of the motivating trial.