Statistical Methods for Multi-State Analysis of Incomplete Longitudinal Data

Statistics (Biostatistics)

Chen, Baojiang

University of Waterloo

关键词: Statistics (Biostatistics);   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/4041/1/thesis.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Analyses of longitudinal categorical data are typically based onsemiparametric models in which covariate effects are expressed onmarginal probabilities and estimation is carried out based ongeneralized estimating equations (GEE). Methods based on GEE aremotivated in part by the lack of tractable models for clusteredcategorical data. However such marginal methods may not yield fullyefficient estimates, nor consistent estimates when missing data arepresent. In the first part of the thesis I develop a Markov modelfor the analysis of longitudinal categorical data which facilitatesmodeling marginal and conditional structures. A likelihoodformulation is employed for inference, so the resulting estimatorsenjoy properties such as optimal efficiency and consistency, andremain consistent when data are missing at random. Simulationstudies demonstrate that the proposed method performs well under avariety of situations. Application to data from a smoking preventionstudy illustrates the utility of the model and interpretation ofcovariate effects.Incomplete data often arise in many areas of research in practice. This phenomenon iscommon in longitudinal data on disease history of subjects.Progressive models provide a convenient framework for characterizingdisease processes which arise, for example, when the staterepresents the degree of the irreversible damage incurred by thesubject. Problems arise if the mechanism leading to the missing datais related to the response process. A naive analysis might lead tobiased results and invalid inferences. The second part of thisthesis begins with an investigation of progressive multi-statemodels for longitudinal studies with incomplete observations.Maximum likelihood estimation is carried out based on an EMalgorithm, and variance estimation is provided using Louis method.In general, the maximum likelihood estimates are valid when themissing data mechanism is missing completely at random or missing atrandom. Here we provide likelihood based method in that theparameters are identifiable no matter what the missing datamechanism. Simulation studies demonstrate that the proposed methodworks well under a variety of situations.In practice, we often face data with missing values in both theresponse and the covariates, and sometimes there is some associationbetween the missingness of the response and the covariate. Theproper analysis of this type of data requires taking thiscorrelation into consideration. The impact of attrition inlongitudinal studies depends on the correlation between the missingresponse and missing covariate. Ignoring such correlation can biasthe statistical inference. We have studied the proper method thatincorporates the association between the missingness of the responseand missing covariate through the use of inverse probabilityweighted generalized estimating equations. The simulationillustrates that the proposed method yields a consistent estimator,while the method that ignores the association yields an inconsistentestimator.Many analyses for longitudinal incomplete data focus on studying theimpact of covariates on the mean responses. However, littleattention has been directed to address the impact of missingcovariates on the association parameters in clustered longitudinalstudies. The last part of this thesis mainly addresses this problem.Weighted first and second order estimating equations are constructedto obtain consistent estimates of mean and association parameters.