Monte Carlo modified profile likelihood in survival models for clustered censored data

When analyzing failure time datasets within stratified contexts, the main focus is usually not on the clustering variables and hence the group-specific parameters are treated as nuisance. If a fixed e↵ects formulation is preferred and the total number of clusters is large relative to the single-stratum sizes, standard frequentist techniques are often misleading and the use of adjustments to make reliable inference on the parameter of interest is complicated by the presence of censored data. Here we show how Monte Carlo simulation may be exploited to compute a modification of the profile likelihood in general regression settings for survival models with unspecified censoring mechanism.