Evaluating factors associated with STD infection in a study with interval-censored event times and an unknown proportion of participants not at risk for disease.

Sexually transmitted diseases (STD) are a major cause of morbidity and mortality world-wide. Because of their association with an increased risk of infection with human immunodeficiency virus, the prevention and control of STD are particularly important. Studies designed to evaluate factors associated with the transmission of STD can pose a number of statistical challenges, however. Two such concerns are the interval-censored event times that result from spacing between follow-up test visits, and an unknown proportion of study participants who are not at risk for infection. Researchers in various fields of study have used parametric mixture models to account for individuals not at risk. Owing to non-identifiability concerns within the mixture model framework, however, it is not always possible to distinguish between effects of explanatory variables on the distribution of event times for at-risk individuals and their effects on the probability of being at risk. We address these issues using data from a clinical trial designed to investigate the effectiveness of an intravaginal microbicide in preventing male-to-female transmission of STD. Factors associated with time to infection among at-risk women are initially identified by fitting right-truncated models to the interval-censored event times of participants who tested positive for STD, and hence are known to have been at risk. Subsequently, factors associated with the probability of being at risk are evaluated using mixture models that incorporate information contributed by the right-censored event-free times of uninfected study participants.