The purpose of this grant application is to develop new statistical methodologies for analyzing multi-variate censored survival data, and to apply these methodologies to data from cardio vascular disease research. The proposal describes four projects. The first project deals with random clusters (i.e., the clusters are considered as a random sample from an underlying population of such clusters). A latent variable model is proposed for such data. A pseudo-likelihood approach is proposed for estimating the average effects of the main study variables. Asymptotic properties of the proposed statistical methods will be studied. Software will be developed. Data from the Studies of Left Ventricular Dysfunction (SOLVD) will be analyzed using the proposed method. The second project considers the problem of surrogate/missing covariates in survival data. A mean score method is proposed to deal with these surrogate/ missing covariates for univariate and multivariate survival data. Statistical properties of the proposed procedures will be studied. Software will be developed. The proposed methodologies will be applied to data from the Studies of Left Ventricular Dysfunction, the U.S.-U.S.S.R. Collaboration in Area 1 (Pathogenesis of Atherosclerosis), and the Family Heart Study. Comparisons with existing procedures will also be made. The third project concerns data with multiple levels of clustering. Marginal hazard models are proposed for analyzing such data. An estimating equation approach is proposed for estimating the marginal hazard ratio parameters. Asymptotic properties will be investigated. Software will be developed, and analysis of data from the Family Study of the Collaborative Lipid Research Clinics Program (LRC) and the Framingham Heart Study will be performed. The fourth project concerns an evaluation of the effect of a misspecified baseline hazard in the marginal hazard models for multivariate survival data. Bias and efficiency loss will be evaluated in both large and finite samples. Analysis of data from the Family Study of Collaborative Lipid Research Clinics Program (LRC) and the Framingham Heart Study will be performed. Finally, the strengths and weaknesses of the proposed methodologies will be critically examined via simulations and theoretical investigations.
