A Transfer Learning Approach to Semiparametric Probit Regression for Interval-Censored Failure Times Data

Regression analysis of interval-censored failure time data commonly arises in biomedical studies, particularly when the available sample size is limited. Although many methods have been proposed for the semiparametric probit model with interval-censored data, there does not appear to exist an established approach that effectively borrows information from external sources to improve estimation efficiency. Such external information may arise, for example, in clinical trials where an auxiliary dataset from a related population is available but may differ from the target population in certain aspects, leading to heterogeneity between populations. To address this issue, a sieve maximum likelihood estimation procedure is developed for the semiparametric probit model with interval-censored data, and a transfer learning method is proposed to leverage auxiliary information from a source domain to improve estimation efficiency in the target domain while accounting for population heterogeneity. The proposed approach is based on a penalized likelihood formulation and uses monotone splines to approximate the unknown baseline function, providing flexibility in both modeling and computation. Simulation studies show that the proposed estimator substantially improves estimation accuracy compared with methods that rely solely on the target data, particularly when the target sample size is small. An application to an Alzheimer’s disease dataset further illustrates the practical usefulness of the proposed approach in biomedical studies.