Quantile Regression with Multivariate Failure Time Data

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In medical studies and other areas of research, researchers often seek methods for understanding and modeling how multiple variables of interest (e.g., age, gender, diagnosis) depend on each other - quantile regression is one of these methods. In this proposed research, we plan to extend some most recent developments in this area to model multivariate event times (e.g. disease occurrence times of twins or closely related persons). There are different definitions of multivariate quantile in the literature, all with advantages and drawbacks. We are going to work on both analytical and geometric definitions, with an emphasis on the halfspace depth, ellipsoids and projections. We are going to define quantile contours through random imputation for the censored observations. Then we conduct two-sample test of multivariate failure times. We are going to develop estimation methods of the multivariate failure time quantile regression model parameters and investigate the asymptotics of the estimators. Efficient computation approaches will be investigated, especially for the two-sample test. Successful completion of the proposed research will advance the theory of quantile regression and widen the application of the methods in relevant areas.