Topics in Multivariate Survival Analysis and Counting Processes

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Multivariate survival analysis is a rapidly growing area with a wide range of applications in medicine, genetic epidemiology, econometrics, astronomy and other fields. The purpose of this project is to develop estimation methods in some semiparametric models arising in analyses of multivariate survival data.Two projects are discussed in this proposal. The first one deals with estimation in partial transformation models, specifically in partial Cox regression and partial accelerated failure time model. These models are useful in goodness-of-fit testing and analyses of multivariate models involving time measurements recorded on two or more time scales. For estimation purposes we shall use local polynomial fitting.The second project deals with multivariate frailty models. A common approach towards analysis of these models rests on nonparametric maximum likelihood estimation with the form of the estimates derived from the counting process definition of the frailty models. The latter often fails to apply to multivariate data since they can involve time measurements recorded on several time scales, or nonpredictable censoring and covariate processes. In this project we consider an ad hoc estimation method designed for analysis of clustered familial data with multivariate failure time processes recorded on age scale, The estimation method allows to incorporate left truncation and accommodate calendar time effects arising in analyses of familial data.The results of the first project can be applied to any dataset involving censored observations. Results of the second project will be applied towards analysis of datasets provided by the Australian Twin Registry and Demographic Data Base, Umea, Sweden.