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Title: Survival models for highly clustered censored data: Accurate inference based on integrated likelihoods Authors:  Giuliana Cortese - University of Padua (Italy) [presenting]
Nicola Sartori - University of Padova (Italy)
Abstract: Clustering structures are frequently encountered in censored time-to-event-data. Often the main interest is not in the cluster-related parameters, which are then treated as nuisance. When inference is on a parameter of interest in presence of many nuisance parameters, standard likelihood methods perform very poorly and may lead to severe bias. This problem is particularly evident in survival models where the number of clusters is high compared to the within-cluster size. We consider clustered failure time data under independent censoring and propose inference based on integrated likelihoods. This approach provides very accurate inference in presence of many nuisance parameters or small sample sizes. The regression models of interest can be parametric or semiparametric survival models. We show some applications of the proposed method in different types of regression approaches. A data example about late-stage HIV-infected patients is used to compare the new approach with the existing alternatives, such as frailty models and stratified Cox's models. Simulation studies show that appropriately defined integrated likelihoods provide very accurate inferential results in all circumstances, such as for highly clustered data or heavy censoring, even in extreme settings where standard likelihood procedures lead to strongly misleading results. We show that the proposed method performs as well as the frailty model and it is superior when the frailty distribution is misspecified.