Additive frailty model for recurrent events data with application to cancer data: Accepted - October 2024

Felipe  Rodrigues da Silva; Vera Tomazella; Cleide Mayra Menezes Lima; Saralees Nadarajah

Authors

Felipe Rodrigues da Silva Federal University of Piaui https://orcid.org/0000-0003-0017-9736
Vera Tomazella Federal University of São Carlos https://orcid.org/0000-0002-6780-2089
Cleide Mayra Menezes Lima Federal University of Piaui
Saralees Nadarajah University of Manchester https://orcid.org/0000-0002-0481-0372

Keywords:

additive hazard rate models, cancer data, frailty models, recurrent events

Abstract

Both the additive and proportional intensity models provide two principal frameworks for studying the association between risk factors and disease recurrences. When the events of interest are not terminal and can occur more than once for the same individual, we have the so-called recurrent events, these types of data appear in areas such as biomedicine, criminology and industrial reliability. In this paper, we study an additive intensity model with gamma frailty and propose an estimator for the individual frailties of patients. An advantage of the studied model is the possibility to jointly consider the heterogeneity among patients and to evaluate the dependence within recurrent events captured by the frailty variable. Such a distribution has theoretical arguments to model medical data and has been shown empirically to be a good option. We consider likelihood-based methods to estimate the model parameters, and also investigate large-sample properties of the estimators. In order to illustrate our methodology, we consider two data sets including one from an experimental animal carcinogenesis study.