Estimating and comparing correct-use failure probabilities in clinical studies of condom functionality

In a clinical study comparing the failure probabilities of two condom types, the sample of all reported acts of intercourse in which a study condom was used by a randomized participant is typically defined to be the primary analysis sample. However, it may also be desirable to make comparisons among only those acts in which the participants correctly followed all condom use instructions before, during, and after the act of intercourse (i.e., the "correct-use" subset). The timing associated with the definition of correct use creates a dilemma in that an act cannot be classified as a "correct-use act" until after the completion of both intercourse and withdrawal; if a condom fails (e.g., breaks or slips completely off of the penis) during intercourse then the couple has no chance at correct use during withdrawal. As a result of the implicitly conditional nature of this problem, it is not a simple matter to specify a correct-use subset of the primary analysis sample. With this in mind, we develop estimators for the correct-use failure probabilities, the corresponding standard errors, and test statistics for comparing the correct-use failure probabilities between condom groups. We demonstrate the utility of the proposed methods by applying them to data from a clinical study of condom contraceptive effectiveness, and we use simulated data to investigate the finite sample properties of the proposed methods. The simulation results indicate that one of our proposed estimators is at least approximately unbiased, even in small samples. Furthermore, one-sided noninferiority tests performed using this estimator tend to have sizes that are only marginally larger than the nominal test size in moderate to large samples.