This is an R29 re- application in which the investigator intends to develop statistical methods to analyze multivariate survival data. Frailty concepts will be used to model the correlated survival data. Initially, methods will be developed in a bivariate context, but most will then be extended to the multivariate situation. Four methods are proposed for estimating co- variate effects each of which is expected to perform better than existing methods in terms of efficiency. Large sample theory will be developed and small sample statistical properties will be investigated. In addition, two methods have been proposed for estimating the association between survival times. These results will be extended to investigate the use of frailty models and crossover designs involving survival data. Another important objective of this proposal is to develop statistical models which are useful in genetic epidemiology. The applicant will focus on two issues: (1) she proposes new survival models for the analysis of MZ and DZ twin data to obtain interpretable parameters representing genetic and environmental effects; (2) the applicant also proposes new multivariate survival models that can handle different correlations among family members. She will extend the methods proposed in specific aim 1 to make inference on the parameters of these models and their statistical properties will be investigated; this is specific aim 2. A data set on cardiovascular disease from NHLBI will be used to assess the appropriateness of the models. These data are on a study of twins. The methods for assessing the frailty assumption for a given data set will also be evaluated in this study. This will be accomplished by proposing diagnostic plots and goodness-of-fit test statistics, as well as studying the performance of the preceding methods when the assumptions of frailty models are violated. Three data sets will be analyzed to show the use of the proposed methods and to yield a more complete understanding of the relative merits and limitations of the use of frailty models in practical applications.
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