Semiparametric statistical methods for censored or missing data and their applications in survival analysis and other related areas

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In medicine, economics, social science, engineering and other fields, practitioners are often faced with problems of exploring the relationship between an outcome variable and a set of covariates for prediction purposes. The standard statistical methods are often not directly available to solve the problems due to censored and missing data. Censored and missing data arise in almost all scientific disciplines. For example, in a clinical trial, the investigators are interested in evaluating the effect of a treatment on survival in HIV-1 seropositive drug users, adjusted for other predictive covariates such as BMI (body mass index) and age. Some patients may be still alive when the study terminates and their survival times are censored. In another example, autopsy for some patients may not be carried out and the failure causes are unknown. In this situation, some values of censoring indicators are missing. In many cases, people just simply delete records for which any data are censored or missing, and conduct the so-called "complete-case analysis". Such an analysis can lead to severe biases and wrong conclusions. Moreover, there may be many covariates and it is difficult to select important ones. For instance, investigators need to select active genes to predict patients' survival in microarray analysis. There is a challenge of high dimensionality of the gene expression data. This proposal is to develop semiparametric models to address all the issues arising from the aforementioned real applications. Semiparametric models are the models that include both a parametric and nonparametric component. Such models allow flexible covariate effects; they play the role of dimension reduction and avoid the curse of dimensionality; estimators in such models are more robust and efficient than in traditional parametric models and pure nonparametric models. Therefore, it is challenging and rewarding to work on semiparametric models. The outcomes of the proposed research will make contributions to the development of statistical theory and help bring the benefits of prosperity to all Canadians. In addition, the research will contribute significantly to the training of highly qualified young Canadian professionals.