Analysis of Complex Survival and Longitudinal Data in Observational Study
Wu, Fan
2017
Abstract
This dissertation is motivated by several complex biomedical studies, where challenges arise from that 1) survival data from a prevalent cohort are subject to both left truncation and right censoring, and 2) longitudinal data on human subjects are sparse and unbalanced. For example, in the Renal Research Institute Chronic Kidney Disease (RRI-CKD) study and in the United Network for Organ Sharing (UNOS) kidney transplantation registry, recruited were patients with kidney diseases of which the onsets precede the enrollment, whereas in the Normative Aging Study (NAS), subjects' measurements were not collected at a common sequence of ages. There is an urgent necessity to develop robust and efficient methods to analyze such data which account for their observational nature. This dissertation, comprising of three projects, proposes a cohort of new statistical methods to address these challenges. In the first project, we consider efficiency improvement in the regression method with left-truncated survival data. When assumptions can be made on the truncation, conventional conditional approaches are inefficient, whereas methods assuming parametric truncation distributions are pruned to misspecification. We propose a pairwise likelihood augmented Cox estimator assuming only independence between the underlying truncation and covariates, yet leave the truncation form unspecified. We eliminate the truncation distribution using a pairwise likelihood argument, and construct a composite likelihood for the parameters of interest only. Simulation studies showed a substantial efficiency gain of the proposed method, especially for the regression coefficients. In the second project, the PLAC estimator is extended to incorporate extraneous time-dependent covariates to study the association between time to death and treatment among patients with end-stage renal disease. The transplantation registry violates of the independence between the underlying truncation and covariates. However, the pairwise likelihood can be modified to accommodate such types of dependence, so that the resulting estimator is still consistent, asymptotically normal and more efficient than the conditional approach estimator, as long as there is heterogeneity in the covariates before enrollment. In the third project, we identify homogeneous subgroups within unbalanced longitudinal data. Most clustering methods require pre-specified number of clusters and suffer from locally optimal solutions. An extension of the clustering using fusion penalty to longitudinal data is proposed. Alternative formulation using mixed effect model with quadratic penalty on the random effects is considered to achieve more stable estimates. Simulations show the proposed method has robust performance under various magnitudes of within-cluster heterogeneity and random error. It performs better than the existing methods when the observations are sparse.Subjects
Left Truncation Composite Likelihoods Cluster Analysis Chronic Kidney Disease Kidney Transplantation Normative Aging Study
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