Semiparametric accelerated failure time models under unspecified random effect distributions

Accelerated failure time (AFT) models with random effects, a useful alternative to frailty models, have been widely used for analyzing clustered (or correlated) time-to-event data. In the AFT model, the distribution of the unobserved random effect is conventionally assumed to be parametric, often modeled as a normal distribution. Although it has been known that a misspecfied random-effect distribution has little effect on regression parameter estimates, in some cases, the impact caused by such misspecification is not negligible. Particularly when our focus extends to quantities associated with random effects, the problem could become worse. In this paper, we propose a semi-parametric maximum likelihood approach in which the random-effect distribution under the AFT models is left unspecified. We provide a feasible algorithm to estimate the random-effect distribution as well as model parameters. Through comprehensive simulation studies, our results demonstrate the effectiveness of this proposed method across a range of random-effect distribution types (discrete or continuous) and under conditions of heavy censoring. The efficacy of the approach is further illustrated through simulation studies and real-world data examples.