Some Problems in Statistical Analysis of Clinical data: From Missing Data to Non-Inferiority Trial

In this dissertation, we present three separate yet related methodology works that focus on solving certain statistical problems one may encounter when analyzing clinical data, especially data with time-to-event endpoints from oncology trials. Restricted mean survival time (RMST) is defined as the expectation of a time-to-event random variable restricted to a time point of clinical interest. The RMST function is intuitive to interpret and robust against the proportional hazards (PH) assumption compared to the hazard ratio (HR) measure. We develop nonparametric Bayesian approaches to model RMST functions as a mixture of kernel RMST functions with time-independent mixture weights by assigning dependent stick-breaking process priors that incorporate covariates dependence. In recent years, the use of RMST difference as a treatment effect measure in non-inferiority (NI) trials has gained many interests. Many historical NI trials conducted using the HR measure can be reanalyzed under a RMST measure with a proper tool that converts the original NI margin measured in HR to one measured in RMST difference or ratio. We propose a NI margin conversion method, which relies on Kaplan-Meier (KM) estimators and the meta-analysis framework, to help achieve the reanalysis goal. Though there is an extensive literature on testing for the missing completely at random (MCAR) assumption, there is no existing approach for testing the MCAR assumption for incomplete multivariate data with both quantitative and categorical components subject to be missing, which are common in oncology studies. We develop a test for incomplete multivariate mixed-type data with variables measured in both quantitative and categorical scales, which are commonly observed in oncology trials.