Making sense of some odd ratios: A tutorial and improvements to present practices in reporting and visualizing quantities of interest for binary and count outcome models

Objective: Generalized linear models (GLMs) such as logistic and Poisson regression are among the most common statistical methods for modeling binary and count outcomes. Though single-coefficient tests (odds ratios, incidence rate ratios) are the most common way to test predictor-outcome relations in these models, they provide limited information on the magnitude and nature of relations with outcomes. We assert that this is largely because they do not describe direct relations with quantities of interest (QoIs) such as probabilities and counts. Shifting focus to QoIs makes several nuances of GLMs more apparent. Method: To bolster interpretability of these models, we provide a tutorial on logistic and Poisson regression and suggestions for enhancements to current reporting practices for predictor-outcome relations in GLMs. Results: We first highlight differences in interpretation between traditional linear models and GLMs, and describe common misconceptions of GLMs. In particular, we highlight that link functions A) introduce non-constant relations between predictors and outcomes and B) make predictor-QoI relations dependent on other covariates. Each of these properties causes interpretation of GLM coefficients to diverge from interpretations of linear models. Next, we argue for a more central focus on QoIs (probabilities and counts). Finally, we propose and provide graphics and tables, with sample R code, for enhancing presentation and interpretation of QoIs. Conclusions: By improving present practices in the reporting of predictor-outcomerelations in GLMs, we hope to maximize the amount of actionable information generated by statistical analyses and provide a tool for building a cumulative science of substance use disorders.Public Health Significance: We propose several enhancements to current reporting practices for statistical analyses of binary outcomes (e.g., psychiatric diagnoses) and count outcomes (e.g., number of alcoholic drinks consumed). We encourage researchers to interpret results in terms of quantities of interest (probabilities for binary models, counts for count models) and provide a tutorial and R code for implementing these analyses. Doing so can provide richer information about a statistical analysis, make study results easier for research consumers to understand, and facilitate comparison of results across studies.