Part 1: Modelling Clustered Data -- Methods for Analyzing Secondary Outcomes in Public Health Case Control Studies -- Controlling for Population Density Using Clustering and Data Weighting Techniques When Examining Social Health and Welfare Problems -- On the Inference of Partially Correlated Data with Applications to Public Health Issues -- Modeling Time-Dependent Covariates in Longitudinal Data Analyses -- Solving Probabilistic Discrete Event Systems with Moore-Penrose Generalized Inverse Matrix Method to Extract Longitudinal Characteristics from Cross-Sectional Survey Data -- Part II: Modelling Incomplete or Missing Data -- On the Effects of Structural Zeros in Regression Models -- Modeling Based on Progressively Type-I Interval Censored Sample -- Techniques for Analyzing Incomplete Data in Public Health Research -- A Continuous Latent Factor Model for Non-ignorable Missing Data -- Part III: Healthcare Research Models -- Health Surveillance -- Standardization and Decomposition Analysis: A Useful Analytical Method for Outcome Difference, Inequality and Disparity Studies -- Cusp Catastrophe Modeling in Medical and Health Research -- On Ranked Set Sampling Variation and its Applications to Public Health Research -- Weighted Multiple Testing Correction for Correlated Endpoints in Survival Data -- Meta-analytic Methods for Public Health Research.