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Estimation in semiparametric conditional shared frailty models with events before study entry. (English) Zbl 1429.62445

Summary: In semiparametric conditional shared frailty models, the non-parametric hazard functions in the same cluster (family) are multiplied by the same (unobserved) random frailties and the survival times conditional on frailties are independent. In this paper, we generalise the maximum likelihood and expectation-maximisation algorithm for semiparametric conditional shared gamma frailty models with events before study entry to accommodate other parametric forms of frailty distributions. In particular, we develop a SAS macro for the semiparametric conditional shared log-normal frailty model with events before study entry and demonstrate the non-standard small sample statistical properties of the frailty variance estimates by simulations. We also fit the semiparametric conditional shared gamma and log-normal frailty models with events before study entry to the subset of 3066 Busselton Health Study adult children with more than 25% of coronary heart disease (CHD) events before study entry out of all CHD events identified from hospital admissions, follow-up survey diagnosis or cause of death. Then the frailty variance estimates become larger and the \(p\)-values of the test of whether the frailty variance is equal to zero become smaller than the previous corresponding values of fitting these models with events before study entry treated as if they happened at the entry time.

MSC:

62N02 Estimation in survival analysis and censored data
62G05 Nonparametric estimation
62P10 Applications of statistics to biology and medical sciences; meta analysis
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