FLEXIBLE AND ROBUST METHODS BASED ON RANK AND CONCORDANCE FOR DATA WITH MULTIPLE OUTCOMES

Parametric models often require strong distributional assumptions about the data and are usually sensitive to outliers. When it comes to two or more outcomes, it is usually more diffcult to make correct distributional assumptions for each of the outcomes. Robust statistical methods, which are often insensitive to outliers and pose fewer assumptions about the distribution of the data, serve as desirable alternatives to the parametric methods. In this dissertation, we developed flexible and robust statistical methods to address problems encountered in the analyses of data with multiple outcomes. In the first article, we are interested in bivariate outcomes, with the complication of right-censoring. Robust quantile regression and quantile copula frameworks were adopted to quantify the conditional association between the bivariate outcomes in the presence of covariates. In the second article, we focus on situations where scientific interest centers on a global percentile outcome formed by multiple individual outcomes. A regression framework posing minimal model assumptions was developed to evaluate the relationship between covariates and the global percentile outcome. In the third article, we are interested in assessing the predictive accuracy of biomarkers in the presence of informative censoring, targeting the commonly used concordance measure of C-index. The dependence between the primary event outcome and the competing event was tackled by taking into account the information of longitudinal biomarker under the joint modeling framework