Stratified Analysis and Classical Methods for Controlling Confounding

This chapter introduces fundamental statistical techniques for evaluating exposure–outcome associations while accounting for potential confounding variables in epidemiological research. The chapter begins with constructing and interpreting 2 × 2 contingency tables, which provide the foundation for calculating three key measures of association: the Risk Ratio (RR), Odds Ratio (OR), and Risk Difference (RD). Students learn how these measures quantify the relative and absolute differences in health outcomes between exposed and unexposed groups, including the interpretation of confidence intervals and statistical uncertainty. The material also explains how the appropriate measure depends on the epidemiological study design and the availability of information about disease risk. Through worked examples and R programming, students practice calculating and interpreting these measures using health data, developing the statistical skills needed to evaluate exposure–disease relationships.

The second major focus is stratified analysis and the Mantel–Haenszel method for controlling confounding. Students learn how to divide a study population into relatively homogeneous subgroups according to a potential confounder, such as age, and estimate exposure–outcome associations separately within each stratum. By comparing stratum-specific estimates with the crude estimate, they can assess whether differences in the distribution of confounding variables distort the observed association. The chapter introduces the Mantel–Haenszel method to obtain pooled, adjusted estimates of the RR or OR across strata, together with confidence intervals and statistical tests. It also explains how to assess confounding in practice by comparing crude and adjusted estimates, emphasizing that the magnitude of the change is more informative than statistical significance alone. In addition, students explore effect modification, which occurs when the strength of an exposure–outcome association genuinely differs across subgroups. Using stratified estimates, graphical comparisons, and tests of homogeneity, they learn to distinguish confounding from effect modification and understand why heterogeneous effects may require separate reporting for different population groups.

The final component examines the limitations of classical stratification and how statistical models handle categorical and continuous confounders. Students explore how the measurement scale of a confounding variable influences its representation in an analytical model, including indicator variables for categorical confounders and continuous terms for numerical variables such as age. The chapter highlights the limitations of categorizing continuous variables, including information loss, reduced statistical power, and potentially distorted dose–response relationships. It introduces more flexible approaches, such as transformations and restricted cubic splines, and explains why generalized linear models (GLMs), including logistic regression, are useful when several confounders must be controlled simultaneously. Throughout the chapter, R programming supports contingency-table analysis, stratification, Mantel–Haenszel estimation, and graphical presentation of results. Overall, this material equips Statistics students to quantify epidemiological associations, identify and control confounding, detect effect modification, and recognize when more advanced multivariable methods are needed to produce reliable, interpretable health data analyses.