Modeling Time-to-Diagnosis from HIV Infection of Truncated Observations: An Applied Comparison Of Survival Models

In this paper, we model the delay from HIV infection to AIDS diagnosis using data collected by the Centers for Disease Control and Prevention. The study population consists of 295 AIDS patients of different ages who were infected with HIV through blood transfusion. Patients were observed before July 1, 1986 and were identified only after developing AIDS, resulting in a right-truncation observation scheme. We recast the problem as a left-truncation problem by modeling the intensity of the reverse-time counting process, which enables feasible inference. We compute risk predictions and evaluate out-of-sample performance for two semiparametric models: a proportional hazards model with linear covariate effects and a proportional hazards model with spline-based effects. The performance of these models is compared with that of a Bayesian log-logistic parametric model estimated using MCMC methods. The main real-data application is based on an open-source dataset. We complement the real-data analysis with a simulation study.