A Semiparametric Single-Index Modelling Approach to Learning Optimal Treatment Regimens with Interval-Censored Data

Precision medicine tailored to individual patient characteristics is crucial for improving long-term health outcomes. In survival analysis, a significant challenge for learning an optimal treatment regimen is to handle censoring, which is ubiquitous due to insufficient follow-up or other reasons. While there exist some ready-made methods under right censoring, learning an optimal treatment regimen with the more complicated interval censoring mechanism is still unexplored. To address this significant gap, this work proposes a novel semiparametric single-index modeling method, in which the interaction between the treatment and a single-index combination of covariates is linked through an unknown monotonic function. The proposed approach can capture complex, nonlinear treatment–covariate relationships while maintaining interpretability for clinical decision-making. Our estimation strategy employs sieve maximum likelihood, utilizing monotone splines to approximate the cumulative baseline hazard and B-splines for the unknown link function. To tackle the challenge of maximizing the complicated likelihood, we develop a stable and computationally efficient EM algorithm. The consistency and asymptotic distribution of the resultant estimators are established through the empirical process theory. Simulation studies demonstrate that the proposed approach performs well in finite samples. An application to a clinical trial data set on AIDS highlights the practical utility of the proposed method.