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Abstract:
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VanderWeele and Robins derived counterfactual and empirical conditions for sufficient cause interaction between two binary exposures for a binary outcome (Biometrika 2008). Sufficient cause interaction can be shown present if there exists a subpopulation for whom the binary outcome occurs if both exposures are present, but will not occur if either of the two exposures is absent. We extend the sufficient cause framework from binary outcomes to ordinal and categorical outcomes. Novel empirical conditions, in the form of inequality constraints on the observed data distribution, are derived for detecting sufficient cause interaction for ordinal outcomes. These inequality constraints cannot be derived through first dichotomizing the ordinal or categorical outcome, then applying the earlier empirical conditions for binary outcomes. Inference to test the null hypothesis that there is no sufficient cause interaction using these novel inequality constraints is developed. Using the Stanford HIV drug resistance database, we discover mutations that mechanistically interact to confer resistance (none, partial, full) to particular HIV drugs.
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