An h-likelihood approach to fitting accelerated failure time models for clustered heavily censored data

Abstract

Motivated by oral health time-to-event outcomes, we focus on the analysis of clustered (tooth within subjects), heavily right-censored, survival data, where the event of interest is tooth failure. The generalized extreme value (GEV) distribution is widely used for analyzing extreme events. To mitigate heavy censoring (about 93%), we propose the use of the GEV distribution by treating uncensored observations as extreme events. To further quantify the straightforward association between the survival time and covariates, we develop an accelerated failure time random effects model with GEV errors (as opposed to the usual Cox proportional hazards route), where the random effects capture the correlation among the clustered survival times. Our method of inference is via h-likelihood – an appealing alternative to the more popular Monte Carlo EM, or Markov chain Monte Carlo based estimation in terms of achieving computational tractability under a random effects framework. The performance of the proposed method in terms of parameter estimation and robustness is evaluated on synthetic data. Finally, the methodology is illustrated via application to a database of electronic health records from Creighton University capturing tooth loss events, and other covariates.