LIMITATIONS OF LOGISTIC REGRESSIONS TO ESTIMATE MEASURES OF ASSOCIATION FOR BINARY HEALTH OUTCOMES. A HANDS-ON STUDY WITH TWO EPIDEMIOLOGICAL EXAMPLES - Guedes, Lara Pinheiro (2023)
Introduction: In medical literature, the logistic regression is frequently used to estimate measures of association between an exposure, a health determinant or an intervention, and a binary outcome. How-ever, when the outcome is frequent (>10%), model estimates for relative risks and prevalence ratios might be biased, with potential impact on medical decision and policymaking. Despite the availability of several alternatives, many studies still rely on logistic regression models, and a consensus on this matter is yet to be reached. We aimed to compare the estimation and goodness-of-fit of logistic, log-binomial and robust Poisson regression models, in cross-sectional studies involving frequent binary outcomes. Methodology: Two cross-sectional studies with distinct characteristics and on different topics were con-ducted to estimate measures of association between an exposure and a frequent binary outcome. Study 1 was a nationally-representative study on the impact of air pollution on mental health. Study 2 was a local study on immigrants' access to urgent health care services. Odds ratios (OR) were obtained through logistic regression models, while prevalence ratios (PR) were obtained through log-binomial and robust Poisson regression models. Confidence intervals (CI), their ranges, and standard-errors (SE) were also computed, along with models’ relative goodness-of-fit through Akaike Information Criterion (AIC), when applicable. Results: In Study 1, the OR (95%IC) was 1.015 (0.970-1.063), while the PR (95%CI) obtained through the robust Poisson mode was 1.012 (0.979-1.045). The log-binomial regression model did not converge in this study. In Study 2, the OR (95%CI) was 1.584 (1.026-2.446), the PR (95%CI) for the log-binomial model was 1.217 (0.978-1.515), and 1.130 (1.013-1.261) for the robust Poisson model. The 95%CI, their ranges, and the SE of the OR were higher than those of the PR, in both studies. However, in Study 2, the AIC value was lower for the logistic regression model, followed by the log-binomial regression and the robust Poisson regression (1.345, 1.350, and 1.656, respectively). Discussion and conclusions: In the two presented examples, OR overestimated PR, with wider 95%CI and higher EPs. The extent of overestimation was greater as the outcome under study became more prevalent, in line with previous studies. Employing logistic regression models by default might lead to misinterpretations, especially by less experienced researchers. Robust Poisson models are viable alternatives to logistic regression models, in cross-sectional studies with frequent binary outcomes, avoiding the non-convergence issues of log-binomial models. Nonetheless, in Study 2, the logistic re-gression was the model with the best fit, which illustrates the need to consider multiple criteria, rather than just one, when selecting the most appropriate statistical model for each study. This dissertation highlights the need for statistical guidelines to support the selection of the most appropriate models and to facilitate the correct reporting, interpretation, and communication of scientific results.