On the relationship of sufficient component cause models with potential outcome (counterfactual) models

The sufficient-component cause (SSC) model provides a useful, concise method to conceptualize and organize ideas concerning biologic effects and interactions of multiple factors. Another type of model, the potential outcome or counterfactual models, has also proved useful in epidemiology, providing insights into definitions of effects, exchangeability and confounding, and selection bias. Prior work has shown important links between these two types of models. Here, we show additional connections between the two types of models. We first review basic concepts for both the SSC model and the potential outcome models. We then indicate additional similarities between them, and derive a quantitative link. Our results show that the SSC model actually corresponds to a unique response pattern in a particular potential outcome model. Recognition of the links between the two models should allow greater insight into use of each model, and allow the strengths of both models to be used jointly.