Date on Master's Thesis/Doctoral Dissertation

8-2010

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Bioinformatics and Biostatistics

Committee Chair

Datta, Somnath

Author's Keywords

Censoring; Informative cluster size; Re-weighting principle; U-statistic; AFT model; Waiting time

Subject

Survival analysis (Biometry); Statistics--Methodology

Abstract

In this dissertation research, we aim to solve problems of two types of survival data, clustered survival data with potentially informative cluster size and sojourn time data. The methods for these two types of data are different. However, both data have right censored observations, and we use reweighting approaches to deal with the censoring issue. In the first part of the dissertation research, we consider marginal AFT models for correlated survival data with potentially informative cluster size. Informative cluster size means that the size of the correlated groups may be predictive of their survival characteristics. Two competing proposals, cluster-weighted AFT (CWAFT) marginal model and non-cluster-weighted AFT (NCW AFT) marginal model, are investigated. Simulation and theoretical results show that the CW AFT approach produces unbiased parameter estimation, but that the NCWAFT model does not when the cluster size is informative. We use probability-probability plots to investigate statistical properties of confidence intervals and adopt Wald tests to examine power properties for the CW AFT model. To illustrate our analysis, we apply the CWAFT model to a dental study data set. In the second part of the dissertation research, we consider the problem of comparing sojourn time distributions of a transient state in a general multi state system in two samples (groups) when the transition times are right censored. Under this setup, the censoring induced on the weight times is complex since both the state entry and exit are subjected to right censoring. Using the reweighting principle, a two sample MannWhitney type U-statistic is constructed that compares only the uncensored state sojourn times from the two distributions. A second Mann-Whitney type statistic is also constructed using a different reweighting that allows for comparison when one of the two sojourn times is either uncensored or singly censored. While both statistics are asymptotically unbiased and reduce to the standard Mann-Whitney statistic when there is no censoring, the second statistic has smaller variance since it effectively uses larger pairs of samples. Asymptotic normality of these statistics are established. A test of comparing the equality of sojourn time distributions in two independent samples is constructed by symmetrizing the pair specific Mann-Whitney type statistics mentioned above. The testing methodology is illustrated using a kidney disease patients data set.

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