Estimation of a failure time distribution based on imperfect diagnostic tests

Sequentially-administered diagnostic tests used to determine the occurrence of a silent event are sometimes subject to error, leading to false positive and false negative test results. In such cases, standard methods for interval censored data do not give valid estimates of the distribution of the time to the event. We present methods for estimating the distribution of the time to the event that account for multiple types of imperfect diagnostic test, as well as differing periods at risk. We illustrate the methods with simulated data and results from a clinical trial for the prevention of mother-to-infant transmission of HIV in Tanzania.