The Modelling of a Cure Fraction in Bivariate Time-to-Event Data

Abstract

Three correlated frailty models are used to analyze bivariate timeto- event data by assuming gamma, log-normal and compound Poisson distributed frailty. All approaches allow to deal with right censored lifetime data and account for heterogeneity as well as for a non-susceptible (cure) fraction in the study population. In the gamma and compound Poisson model traditional ML estimation methods are used, whereas in the log-normal model MCMC methods are applied. Breast cancer incidence data of Swedish twin pairs illustrate the practical relevance of the models, which are used to estimate the size of the susceptible fraction and the correlation between the frailties of the twin partners. We discuss future directions of development of the methods and additional thoughts concerning their advantages and use.