Title: Multivariate Data Analysis with Applications to Cancer
Description: Multivariate data is common in a wide range of settings. As data structures become increasingly complex, additional statistical tools are required to perform proper analyses. In this dissertation we develop and evaluate methods for the analysis of multivariate data generated from cancer trials. In the first chapter we consider the analysis of clustered survival data that can arise from multicenter clinical trials. In particular, we review and compare marginal and conditional models numerically through simulations and discuss model selection techniques. A multicenter clinical trial of children with acute lymphoblastic leukemia is used to illustrate the findings. The second and third chapters both address the setting where multiple outcomes are collected when the outcome of interest cannot be measured directly. A head and neck cancer trial in which multiple outcomes were collected to measure dysphagia was the particular motivation for this part of the dissertation. Specifically, in the second chapter we propose a semiparametric latent variable transformation model that incorporates measurable outcomes of mixed types, including censored outcomes. This method extends traditional approaches by allowing the relationship between the measurable outcomes and latent variable to be unspecified, rendering more robust inference. Using this approach we can directly estimate the treatment (or other covariate) effect on the unobserved latent variable, enhancing interpretation. In the third chapter, the basic model from the second chapter is maintained, but additional parametric assumptions are made. This model still has the advantages of allowing for censored measurable outcomes and being able to estimate a treatment effect on the latent variable, but has the added advantage of good performance in a small data set. Together the methods proposed in the second and third chapters provide a comprehensive approach for the analysis of complex multiple outcomes data.