Estimating cycle pregnancy probability with incomplete data in contraceptive studies

In studies on the effectiveness of barrier method contraceptives, researchers need to estimate the risk of pregnancy during consistent use of these methods. However, participants may not use assigned methods consistently, and only consistent-use cycles are included in the estimates. Inconsistent-use cycles are considered missing intervals, and a subject's early discontinuation from the study or pregnancy during inconsistent use is censored from the analysis. In this article, we consider a semiparametric maximum likelihood approach to estimate survival probability for grouped survival data with missing and censored data. The method is flexible in that it is nonparametric with respect to the underlying survival function, yet it can be easily extended to accommodate the covariates in a parametric way. Results from our simulation study show that the proposed method works well in practical sample sizes. Our findings support the U.S. Food and Drug Administration's (FDA) sample size requirements for contraceptive studies. We use data from an effectiveness trial on vaginal contraceptive film (VCF) to illustrate the proposed methods.