Abstract: The sufficient cause model is extended from binary to categorical and ordinal outcomes to formalize the concept of sufficient cause interaction and synergism in this setting. This extension allows us to derive counterfactual and empirical conditions for detecting the presence of sufficient cause interactions for ordinal and categorical outcomes. Some of these conditions are entirely novel in that they cannot be derived from the sufficient cause model for binary outcomes. These empirical conditions enable researchers to determine whether two exposures display synergism for an ordinal or a categorical outcome. Likelihood ratio tests that use these derived empirical conditions are developed to infer sufficient cause interaction for ordinal and categorical outcomes. Lastly, we apply these likelihood ratio tests to detect sufficient cause interaction between two major resistance mutations in the development of HIV drug resistance to Etravirine.

Key words and phrases: Interaction, ordinal outcome, sufficient cause.