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Modeling Composite Outcome and Jointly Modeling Its Components

 Xianbin Li, PhD Candidate, Johns Hopkins Department of Biostatistics

Composite outcomes defined by logical (Boolean) operations on mixed original outcomes arise often in biomedical research. For example, hypertension is often defined as a systolic blood pressure greater than or equal to 140 mmHg, a diastolic blood pressure greater than or equal to 90 mmHg, or the use of antihypertensive medication. When there are no missing values in the original outcomes, the estimation of the proportion of successes from a composite outcome is straightforward; however, when there are missing values in the original outcomes, the estimation is less clear and common estimators can be biased, even if the missingness is completely at random. Motivated from the study of hypertension, we propose estimators of prevalence, methods of joint regression modeling of continuous and binary outcomes, and conduct a fully Bayesian longitudinal analyses of these outcomes. This dissertation comprises
three distinct papers. In the first paper, the logically defined outcome (composite outcome) is defined and four estimators of the prevalence are proposed and compared. The maximum likelihood estimator, using all available data, is shown to be consistent and efficient while the naive estimator is arbitrarily biased. In the second paper, we jointly model two continuous outcomes and one binary outcome using shared random effects (intercept) models with a probit model for the binary outcome and propose the use of the propensity score as a way to balance confounding variables in order to obtain the proportion of successes of the composite outcome associated with covariates. In the third paper, Bayesian joint modeling of longitudinal continuous and binary outcomes is proposed to analyze a novel hypertension data set and Markov chain Monte Carlo algorithms are used to sample from the posterior distributions of parameters. The proposed statistical methods for composite outcome and its components in this dissertation perform reasonably well and can be used in many epidemiologic studies and clinical trials with continuous and binary outcomes.

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