Estimation in semiparametric conditional shared frailty models with events before study entry

• Published in: Computational statistics & data analysis 2004-04, Vol.45 (3), p.621-637
• Main Author: Vu, Hien T.V.
• Format: Article
• Language: English
• Subjects: Applications; Busselton health study; Conditional shared frailty models; Events before study entry; Exact sciences and technology; Gamma frailties; Hybrid ML–EM; Log-normal frailties; Mathematics; MLE; Multivariate analysis; Non-parametric hazards; Nonparametric inference; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Reliability, life testing, quality control; Sciences and techniques of general use; Statistics
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/S0167-9473(02)00368-7

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.