This proposal requests funding for the development of new statistical methodologies for research in survival analysis. Survival time data arise in many clinical and medical studies of diseases. One of the primary variables is the time to some event such as recurrence of the disease or death. The time to event or survival time is right-censored if the event has not occurred before the end of the study period. Statistical analyses for these studies are required to include covariates that may vary with time. The study subjects may constitute a selection-biased or random truncation sample. Also, the survival times may be correlated as in the study of occurrences of multiple diseases or in studies where subjects are family members. The primary purpose of this proposal is to address these issues by developing methods of statistical inference based on extended linear modeling, and to do so in a manner that effectively balances the bias and variance of the estimates. The proposal has seven projects. The first project will conduct a theoretical investigation of the bootstrap method based on-the nonadaptive approach to the saturated HARE models. The second project considers the problem of estimating covariate effect function in proportional hazards modeling. The third project establish distributional properties and standard errors of estimates of the transition intensities for event history analysis. The fourth project develops an extended linear model in estimating the density. conditional density, regression and hazard regression functions for length-biased data. The fifth project considers a new approach to randomly truncated data. Methods of extended linear models are used to model the underlying density and conditional density functions. The sixth project considers a new approach to longitudinal data analysis using extended linear models. The seventh project considers a new approach to multivariate survival data analysis using extended linear models. The strengths and weaknesses of the proposed procedures will be critically examined by simulations and theoretical investigations. Software will be developed to analyze clinical data from cancer and cardiovascular studies. Distributional properties will be established and standard errors of the estimates of effects will be provided and will be used to lend support to the software development.
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