Estimation of the short-term and long-term hazard ratios for interval-censored and truncated data

Survival analysis is a vital field in statistics with widespread applications. The short-term and long-term hazard ratio model is a novel semiparametric framework designed to handle crossing survival curves, encompassing the proportional hazards and proportional odds models as special cases. In this paper, we extend the short-term and long-term hazard ratio model to accommodate interval-censored and truncated data with covariates. The identifiability challenges arising from truncation are also discussed. We first prove that the nonparametric maximum likelihood estimation of the baseline survival function retains piecewise constant. Then an efficient iterative convex minorant algorithm, enhanced with a half-stepping strategy, is developed for computation. Additionally, we present a straightforward Wald test for hypothesis testing under a simplified yet commonly encountered practical scenario. Extensive simulation studies under diverse censoring and truncation scenarios demonstrate the robustness and accuracy in estimation of the proposed approach, particularly when traditional proportional hazards or proportional odds assumptions are violated. Applications to three real-world datasets further demonstrate the model's ability to capture varying covariate effects on survival probabilities across early and late stages, offering valuable insights for clinical practice and decision-making.