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.
Highlights
The Cox proportional hazards model (Cox, 1972) is commonly used in the analysis of survival time data
In the present paper three different models are applied to the Swedish breast cancer data set
It is possible to estimate the correlation between the frailties of the twin partners, which is large in the correlated gamma frailty cure and the correlated log-normal frailty cure model
Summary
The Cox proportional hazards model (Cox, 1972) is commonly used in the analysis of survival time data. These models extend the understanding of time-to-event data by allowing for the formulation of more accurate and informative conclusions than previously made These conclusions would otherwise be unobtainable from an analysis that fails to account for a cured fraction in the population. Depending on the point of view, this paper deals with frailty models including a nonsusceptible (or cured) fraction in the study population. In this case, the distribution of the frailty is a combination of discrete and continuous distributions. Models from survival analysis typically assume that everyone has the same susceptibility to the disease and will eventually be effected if the follow-up is sufficiently long These models possibly do not accurately describe the disease risk factors. The paper concludes with a discussion of further applications, drawbacks and advantages of the models
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