Causal analysis of absolute and relative risk reductions

Any new medical innovation must first prove its benefits with reliable evidence from clinical trials. Evidence is frequently expressed using two metrics, summarizing treatment benefits based on either absolute risk reductions (ARRs) or relative risk reductions (RRRs). While both metrics are derived from the same data (e.g., observed frequencies of a disease in a treatment and control group), they implement conceptually and causally distinct ideas. Here, we analyze these risk reductions measures from a causal modeling perspective, revealing an isomorphic relationship to central measure of causal strength and causal Bayesian networks. First, we show that ARR is equivalent to the Delta P metric, while RRR is equivalent to the causal power metric, thus clarifying the implicit causal assumptions. Second, we show how this formal equivalence establishes a relationship with causal Bayesian networks theory, offering a basis for incorporating risk reduction metrics into a computational causal modeling framework. Drawing on these analyses, we demonstrate that under dynamically varying baseline risks, ARRs are inadequate when generalizing treatment effects to novel contexts. Specifically, the inherent assumption of a linear parameterization of the underlying causal graph leads to incorrect conclusions when generalizing to baseline risks differing from those from which the original effect was obtained. For instance, generalizing the effect of a vaccine to new contexts with different baseline risks (e.g., from one population to another). Our analyses highlight the shared principles underlying risk reduction metrics and measures of causal strength, emphasizing the potential for explicating causal structure and inference in epidemiological research.