Analyzing time-to-event data in a clinical trial when an unknown proportion of subjects has experienced the event at entry

In some clinical trials, where the outcome is the time until development of a silent event, an unknown proportion of subjects who have already experienced the event will be unknowingly enrolled due to the imperfect nature of the diagnostic tests used to screen potential subjects. For example, commonly used diagnostic tests for evaluating HIV infection status in infants, such as DNA PCR and HIV Culture, have low sensitivity when given soon after infection. This can lead to the inclusion of an unknown proportion of HIV-infected infants into clinical trials aimed at the prevention of transmission from HIV-positive mothers to their infants through breastfeeding. The infection status of infants at the end of the trial, when they are more than a year of age, can be determined with certainty. For those infants found to be infected with HIV at the end of the trial, it cannot be determined whether this occurred during the study or whether they were already infected when they were enrolled. In these settings, estimates of the cumulative risk of the event by the end of the study will overestimate the true probability of event during the study period and hypothesis tests comparing two or more intervention strategies can also be biased. We present inference methods for the distribution of time until the event of interest in these settings, and investigate issues in the design of such trials when there is a choice of using both imperfect and perfect diagnostic tests.