Weighing the Causal Pies in Case-Control Studies

Purpose: Epidemiologists are familiar with the concepts of Rothman's causal pies. Using real data the Hoffman study showed recently how to calculate the " proportion of diseased subjects who develop the disease due to classes of sufficient causes" (PDCs). The PDC is actually an attributable-fraction index. It may be specific to a particular risk factor profile but it does not correspond to any given class of causal pies. In this study, we show how to estimate the " causal-pie weights" (CPWs), so that each and every class of causal pies has one and only one CPW attached to it. Methods: To conform to Rothman's model, we apply a non-negative linear odds model to constrain all the odds ratios (ORs) to be equal to or greater than one, and the interactions between them to be additive or superadditive. Based on these constrained ORs, we calculate the population attributable fractions, and then the CPWs. We used a published case-control data to show the methodology. Results: The CPWs succinctly quantify the relative importance of different classes of causal pies. Conclusions: The proposed method helps to clarify the multi-factorial and complex interactive effects in disease causation. It also provides important information for designing an efficient public health intervention strategy.