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SIMULATION STUDY FOR MISSPECIFICATIONS ON A FRAILTY MODEL

Summary Nielsen, G.G.; Gill, R.D.; Andersen, P.K.; Sorensen, T.I.A. (1992) propose a consistent and asymptotically normal estimator for the variance of the frailty distribution under gamma assumption. A simulation study shows that this estimator is asymptotically biased for log-normal and absolute value of normal frailty distributions. In the last two decades there was a big leap in terms of survival analysis methodology. This type of analysis has been applied not only in the traditional areas of biology and engineering, but also in demography, social sciences and economy. One of the biggest problems in survival analysis is related to the presence of populational heterogeneity. A very well-known method of analysis is the method of partial likelihood based on the Cox’s proportional hazard model (Cox, 1972). In this model it is assumed that the heterogeneity can be measured through the observable covariates and they were all included in the model. It is a semi-parametric model since it considers the hazard function to be unknown but models covariate variables through a regression model. However, it is possible that there are factors that are influencing the variable of interest and cannot be measured. This unobserved covariable can lead to very different conclusions, biased estimators and reduced efficiency of the model (Heckman and Singer, 1982; Vaupel and Yashin; 1985; Trussel and Rodrigues, 1990). Several analysis in epidemiology and prognostic studies require the inclusion of non-observable covariates. For example, studies about incidence of colon cancer can depend on familiar variable or genetic factors, also it can depend on environment factors shared by elements of the same family or living in a close