Search

In clinical studies of survival, additional endpoints on patients may be collected over the course of the study that give additional insight into a treatment's effect. We propose three methods to analyze right censored survival data in the presence of multiple outcomes. In order to make limited parametric assumptions on the data-generating mechanisms, the methods are based on Wilcoxon-type rank statistics. Each method is applied to a recent clinical trial of Ceftriaxone in patients with amyotrophic lateral sclerosis. In chapter 1, we modify the Gehan-Wilcoxon test for survival to account for auxiliary information on intermediate disease states (e.g. progression) that subjects may pass through before failure. We use multi-state modeling to compute expected ranks for each subject conditional on their last observed disease states and censoring time, and these ranks form the basis of our test statistic. Simulations demonstrate that the proposed test can improve power over the log-rank and generalized Wilcoxon tests in some settings while maintaining the nominal type 1 error rate. In chapter 2, we propose an estimator for an accelerated failure time model based on the test statistic proposed in chapter 1. We use the statistic as an estimating equation for a parameter that accelerates the time to each subsequent disease state. The estimator incorporates the intermediate states in a manner relevant to the survival outcome, yielding interpretable treatment and covariate effects that consider the entire trajectory of the patient. Simulations demonstrate that the estimator is unbiased, and that the proposed standard error estimator is near the empirical value. In chapter 3, we aim to assess the treatment effect globally across any types of multiple endpoints. The test we propose is based on a simple scoring mechanism applied to each pair of subjects for each endpoint. The scores for each pair of subjects are then reduced to a summary score, and a rank-sum test is applied to the summary scores. This can be seen as a generalization of several other global rank tests in the literature. Additionally, for certain statistics we describe optimal weighting schemes with respect to statistical power, and provide a method of selecting outcome weights adaptively., Biostatistics

The rapid technological development of high-throughput genomics has given rise to complex high-dimensional microarray datasets. One strategy for reducing the dimensionality of microarray experiments is to carry out a cluster analysis to find groups of genes with similar expression patterns. Though cluster analysis has been studied extensively, the clinical context in which the analysis is performed is usually considered separately if at all. However, allowing clinical outcomes to inform the clustering of microarray data has the potential to identify gene clusters that are more useful for describing the clinical course of disease. The aim of this dissertation is to utilize outcome information to drive the clustering of gene expression data. In Chapter 1, we propose a joint clustering model that assumes a relationship between gene clusters and a continuous patient outcome. Gene expression is modeled using cluster specific random effects such that genes in the same cluster are correlated. A linear combination of these random effects is then used to describe the continuous clinical outcome. We implement a Markov chain Monte Carlo algorithm to iteratively sample the unknown parameters and determine the cluster pattern. Chapter 2 extends this model to binary and failure time outcomes. Our strategy is to augment the data with a latent continuous representation of the outcome and specify that the risk of the event depends on the latent variable. Once the latent variable is sampled, we relate it to gene expression via cluster specific random effects and apply the methods developed in Chapter 1. The setting of clustering longitudinal microarrays using binary and survival outcomes is considered in Chapter 3. We propose a model that incorporates a random intercept and slope to describe the gene expression time trajectory. As before, a continuous latent variable that is linearly related to the random effects is introduced into the model and a Markov chain Monte Carlo algorithm is used for sampling. These methods are applied to microarray data from trauma patients in the Inflammation and Host Response to Injury research project. The resulting partitions are visualized using heat maps that depict the frequency with which genes cluster together.