Semiparametric estimation of a nested random effects model for the analysis of multi-level clustered failure time data

Multi-level clustered failure time data arise when the clustering of data occurs at more than one level. It is of interest to estimate the relative risks of covariates and clustering effect of failure times at each level. We consider a nested random effect proportional hazards model, where a subcluster-specific frailty operates multiplicatively on the conditional hazard model, and its distribution function depends on a cluster-specific random frailty. Under this model, we propose a Monte-Carlo EM-based semiparametric estimation procedure to estimate regression coefficients, nonparametric baseline cumulative hazard and the association parameters. In addition, we derive a covariance matrix of the parameter estimates. We illustrate the proposed method using clustered survival data collected from a vitamin A supplementation trial in Nepal, where it is of scientific interest to assess the clustering effect of mortality within households and within villages. We use simulations to study the performance of the proposed estimation procedure.