Estimating the mean hazard ratio parameters for clustered survival data with random clusters.

We consider a latent variable hazard model for clustered survival data where clusters are a random sample from an underlying population. We allow interactions between the random cluster effect and covariates. We use a maximum pseudo-likelihood estimator to estimate the mean hazard ratio parameters. We propose a bootstrap sampling scheme to obtain an estimate of the variance of the proposed estimator. Application of this method in large multi-centre clinical trials allows one to assess the mean treatment effect, where we consider participating centres as a random sample from an underlying population. We evaluate properties of the proposed estimators via extensive simulation studies. A real data example from the Studies of Left Ventricular Dysfunction (SOLVD) Prevention Trial illustrates the method.