Modeling and visualizing two-way contingency tables using compositional data analysis: A case-study on individual...

Two-way contingency tables arise in many fields, such as in medical studies, where the relation between two discrete random variables or responses is to be assessed. We propose to analyze and visualize a sample of 2 × 2 tables in the context of single-subject repeated measurements design by means of compositional data (CoDa) methods. First, we propose to visualize the tables in a quaternary diagram. Second, we show how to represent these tables by means of logratios indicating the relationship between the two variables as well as their strength and direction of dependency. Finally, we describe a technique to model those tables with a simplicial regression model. Data from a real-world study of self-prediction of migraine attack onset is used to illustrate this methodology. For each individual, the 2 × 2 table of their migraine expectation vs next day migraine occurrence is computed, generating a sample of tables. Then we visualize and interpret the prediction ability of individuals both in the simplex and in terms of logratios of components. Finally, we model the self-prediction ability with respect to demographic variables, days tracked and disease characteristics. Our application demonstrates that CoDa can be a useful tool for visualizing, modeling, and interpreting the components of 2 × 2 tables.