Adaptive lasso for current status survival data under randomized response: application to extramarital behaviour in Taiwan

Abstract Surveys on sensitive topics frequently yield current status survival data that are subject to response bias. The randomized response technique (RRT) offers a principled approach to mitigating such bias by enhancing respondent privacy. In this paper, we develop an adaptive lasso procedure for variable selection in current status survival data collected under various RRT designs. The underlying event time distribution is modelled using a flexible class of transformation models, encompassing proportional hazards and proportional odds structures. We establish the oracle property of the proposed estimator and provide analytical expressions for standard error estimation, enabling valid inference. To address the latent structure introduced by RRT, specifically, the unobserved indicator of whether the sensitive question was asked, we devise a modified shooting algorithm embedded within an expectation-maximization framework. Simulation studies confirm that the method achieves consistent variable selection and asymptotically normal estimates. The proposed approach is applied to data from the Taiwan Social Change Survey on extramarital sex, demonstrating its practical relevance and interpretability.