Abstract: A Proportional Hazards Mixed-effects Model (PHMM) was recently proposed, which associates general random effects with arbitrary covariates and includes the univariate frailty model as a special case. In this paper, we establish the asymptotic properties of the nonparametric maximum likelihood estimator (NPMLE) of the parameters of the PHMM. This estimator is computed using a Monte Carlo Expectation-Maximization algorithm. The finite sample performance of the NPMLE is examined in a series of simulations and compared with the performance of a penalized partial likelihood estimator and an approximate Laplace EM estimator. The model and NPMLE are applied to an analysis of twin data.
Key words and phrases: Asymptotic efficiency, clustered survival data, consistency, identifiability.