Integrated likelihoods in survival models with stratum nuisance parameters

When inference is about a parameter of interest in presence of many nuisance parameters, in general prole likelihoods perform very poorly and lead to serious bias. For stratied data, this problem is particularly evident in models with stratum nuisance parameters, when the number of strata is relatively high with respect to the within-stratum size. Stratied data are very frequent in many applied settings, such as in cohort studies based on multi-center clinical trials. We consider stratied survival data in a parametric framework under the general assumption of noninformative independent censoring (both type I censoring and random censoring schemes), and for such data an inferential approach based on integrated likelihood is proposed. Appropriately dened integrated likelihoods provide very accurate results in all circumstances. Test statistics based on them provides very accurate inference even in extreme settings. These conclusion were strongly supported by simulation studies. Therefore, the paper suggests to avoid prole likelihood methods and use instead integrated likelihood for inference on highly stratied data with relatively small within-stratum sample sizes.