Abstract: The randomized response technique (RRT) is used to reduce underreporting of sensitive characteristics in survey studies by enhancing privacy protection. Currently, the RRT is mainly applied for prevalence estimation of some sensitive event. We extend the application of the RRT to an analysis of a time-to-event outcome. Event time data collected from surveys are usually subject to case-I interval-censoring, so that only "current-status" data on the occurrence of the event by the examination time are available. As such, we focus on current-status (case-I interval-censored) event time data collected using the RRT. Based on the data, we propose a semiparametric maximum likelihood estimation procedure for the event time distribution given the covariates. The proposed method is assumed to follow a general class of semiparametric transformation models characterized by a parametric function for the relationship between the event time and the covariates, as well as an unspecified baseline function. We develop the asymptotic theory for the proposed estimation, including the consistency and asymptotic normality, and examine its finite-sample properties using simulation studies. We apply the proposed method to current-status data surveyed using the RRT to make statistical inferences on the time to incidence of extramarital relations since marriage.

Key words and phrases: Randomized response technique, semiparametric maximum likelihood estimation, semiparametric transformation model, sensitive issue.