Semiparametric Analysis For Auxiliary Data Problem And Multivariate Failure Times

This dissertation addresses three issues:the auxiliary data problem in the two-stage sample design, the auxiliary data problem in the multivariate failure times, and a class of general additive-multiplicative rates models for recurrent event times.It is of interest to exploit these auxiliary data to improve the efficiency of inferences. Firstly, we propose a two-stage outcome-auxiliary-dependent sampling design when outcome Y is continuous and there exists auxiliary variable W at the first stage. To be specific, outcome Y, auxiliary variable W for some expensive or hard-obtained X of interest, and other covariates Z are all observed for all subjects at the first stage. Then we select the sub-sample within each stratum defined by the partition of the domain of Y x W to ascertain the value of X at the second stage. The proposed estimator which maximizes an estimated likelihood function is shown to be consistent and asymptotically normal. We conduct simulation studies to evaluate the finite sample approximations and the efficiency gains of the proposed estimator. A data set from an environmental epidemiologic study is analyzed to illustrate the proposed method.Secondly, we consider the multivariate failure times regression analysis in which the primary covariate is assessed only in a validation set, but a continuous auxiliary covariate for it is available for all subjects in the study cohort. Under the framework of marginal proportional hazards model, we propose to estimate the induced relative risk function in the non-validation set through kernel smoothing method and then obtain an estimated pseudo-partial likelihood function. The proposed estimator which maximizes the estimated pseudo-partial likelihood is shown to be consistent and asymptot-ically normal. We also give an estimator of the marginal cumulative baseline hazard function. Simulation studies are conducted to examine the finite sample performances of our proposed estimator. The proposed method is il-lustrated by analyzing a heart disease data from the Study of Left Ventricular Dysfunction (SOLVD).Finally, a class of general additive-multiplicative rates models, which in-cludes the additive rates model and the multiplicative rates model as special cases, is considered to model the recurrent event times. An estimating equa- tion for the regression parameter is proposed and the resulting estimator is also shown to be consistent and asymptotically normal. Simulation studies are conducted to investigate the finite sample behaviors of the proposed es-timator. A simple model selective criterion based on the observed and the expected times of recurrent events is adopted to select the model within the class of rates models. A medical study of patients with cystic fibrosis suf-fered from recurrent pulmonary exacerbations is provided for illustration of the proposed method.