Abstracts

This dissertation is motivated by several complex biomedical studies, wherechallenges arise from that 1) survival data from a prevalent cohort are subjectto both left truncation and right censoring, and 2) longitudinal data on humansubjects are sparse and unbalanced. For example, in the Renal Research InstituteChronic Kidney Disease (RRI-CKD) study and in the United Network for OrganSharing (UNOS) kidney transplantation registry, recruited were patients withkidney diseases of which the onsets precede the enrollment, whereas in theNormative Aging Study (NAS), subjects' measurements were not collected ata common sequence of ages. There is an urgent necessity to develop robust andefficient methods to analyze such data which account for their observationalnature. This dissertation, comprising of three projects, proposes a cohort ofnew statistical methods to address these challenges.In the first project, we consider efficiency improvement in the regressionmethod with left-truncated survival data. When assumptions can be made on thetruncation, conventional conditional approaches are inefficient, whereas methodsassuming parametric truncation distributions are pruned to misspecification. Wepropose a pairwise likelihood augmented Cox estimator assuming only independencebetween the underlying truncation and covariates, yet leave the truncation formunspecified. We eliminate the truncation distribution using a pairwiselikelihood argument, and construct a composite likelihood for the parameters ofinterest only. Simulation studies showed a substantial efficiency gain of theproposed method, especially for the regression coefficients. In the second project, the PLAC estimator is extended to incorporate extraneoustime-dependent covariates to study the association between time to death andtreatment among patients with end-stage renal disease. The transplantationregistry violates of the independence between the underlying truncation andcovariates. However, the pairwise likelihood can be modified to accommodatesuch types of dependence, so that the resulting estimator is still consistent,asymptotically normal and more efficient than the conditional approachestimator, as long as there is heterogeneity in the covariates beforeenrollment. In the third project, we identify homogeneous subgroups within unbalancedlongitudinal data. Most clustering methods require pre-specified number ofclusters and suffer from locally optimal solutions. An extension of theclustering using fusion penalty to longitudinal data is proposed. Alternativeformulation using mixed effect model with quadratic penalty on the randomeffects is considered to achieve more stable estimates. Simulations show theproposed method has robust performance under various magnitudes ofwithin-cluster heterogeneity and random error. It performs better than theexisting methods when the observations are sparse.Advisors/Committee Members: Kim, Sehee (committee member), Li, Yi (committee member), Park, Sung Kyun (committee member), Wiggins, Roger C (committee member), Zhang, Min (committee member).