Analysis of randomized response survival data in discrete-time

Event time data collected in sensitive survey studies are often subject to case-I interval censoring and response misreporting. To mitigate these issues, such data are frequently gathered as current status data using the randomized response technique (RRT). When event times are recorded on a discrete time scale, applying continuous-time methods to RRT data may result in substantial bias, underscoring the need for methodologies specifically tailored to discrete-time analysis. In this study, we propose a discrete time-to-event analysis framework for current status data obtained via the unrelated-question RRT. The event time is modeled using a general discrete-time transformation model, which encompasses widely used formulations such as the proportional continuation ratio and grouped proportional hazards models, with the baseline hazard specified in either a discrete or smooth form. Recognizing that the exact failure time and the indicator of whether a respondent answered the sensitive question are latent under the current status censoring and RRT design, we develop a novel, tailored expectation–maximization algorithm for efficient computation. We establish the asymptotic properties of the proposed estimators and demonstrate the utility of the method through comprehensive simulation studies and applications to two real-world datasets.