Abstract The methodological objective of the present study is to extend Rothman’s additive interaction framework from two factors to three or more factors considered simultaneously, while preserving its original causal interpretation and operational simplicity. we propose a generalized Synergy Index ( S p ) that retains the additive logic of Rothman’s original formulation while extending it to an arbitrary number of dichotomous factors. For the analysis we used a database of a previous work in which the synergistic factor was calculated for each couples of two factors (alcohol, tobacco smoke and other risk factors) for age-related macular degeneration. The proposed three-factor S p is sensitive to the underlying structure of the risk factors considered. When a strong susceptibility component such as family history is included, the combined exposure exhibits clear super-additive behavior ( S p = 1.783). Conversely, when hypercholesterolemia replaces family history, the joint effect remains substantial but does not exceed additivity ( S p = 0.756). The generalized multi-factor Synergy Index represents a valuable conceptual and analytical tool for investigating higher-order interactions. It is particularly well suited for the study of complex diseases, where multiple exposures co-occur and interact. It enables the identification of exposure constellations characterized by true superadditivity, with potential implications for etiological research, risk stratification, and targeted prevention strategies.
Torre et al. (Fri,) studied this question.
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