Stratified Analysis and Classical Methods for Controlling Confounding Models (GLMs) as a Unified Language for Epidemiological Analysis

This chapter introduces statistical modeling as an extension of descriptive analysis and stratification for investigating relationships between exposures and health outcomes. The chapter explains why simple measures of association, such as the Risk Ratio (RR) and Odds Ratio (OR), may be insufficient when researchers must consider several potential confounders simultaneously. Regression modeling offers a more flexible approach, allowing researchers to adjust for multiple covariates while estimating exposure–outcome associations. Students are introduced to the three fundamental components of a Generalized Linear Model (GLM): the random component, which specifies the probability distribution of the outcome; the systematic component, which represents the linear predictor formed from explanatory variables and their coefficients; and the link function, which connects the expected outcome to the linear predictor. These components allow researchers to select an appropriate model according to the characteristics of the health data and the objectives of the epidemiological investigation.

The second major focus is applying and interpreting different regression models for different types of health outcomes. The chapter discusses linear regression for continuous outcomes, such as systolic blood pressure and cholesterol levels, including coefficient interpretation, ordinary least squares (OLS) estimation, and diagnostic assessment of assumptions such as linearity, independence, homoscedasticity, and residual normality. For binary outcomes, such as the presence or absence of hypertension, students learn about binomial models and logistic regression, in which exponentiated coefficients are interpreted as adjusted Odds Ratios. For count data and incidence rates, the chapter introduces Poisson regression, including the use of offset terms to account for population size or observation time and the interpretation of exponentiated coefficients as Incidence Rate Ratios (IRRs). It also discusses overdispersion and alternatives, such as negative binomial models, when a standard Poisson model's assumptions are not met. Examples involving smoking and lung disease, obesity and hypertension, and dengue cases illustrate how model selection and interpretation depend on the outcome's measurement scale and distribution.

The final component examines parameter estimation, model-based prediction, and covariate selection for causal inference versus prediction. Students learn the principles of maximum likelihood estimation (MLE), the role of likelihood and log-likelihood functions, and how model parameters are estimated and evaluated using standard errors, confidence intervals, hypothesis tests, and model-fit measures such as deviance and the Akaike Information Criterion (AIC). The chapter also explains how to transform regression coefficients into interpretable epidemiological measures and how fitted models can generate predicted probabilities or expected event rates, supported by R programming and graphical visualization. Finally, it distinguishes causal covariate selection, guided by Directed Acyclic Graphs (DAGs) to identify confounders and avoid inappropriate adjustment, from predictive variable selection using techniques such as LASSO and cross-validation to improve predictive performance. Overall, this chapter equips Statistics students with the conceptual and computational skills to select appropriate regression models, estimate and interpret epidemiological associations, assess model assumptions, and use health data to support evidence-based research and public health decisions.