Immune-selection stability is a neglected property of the causal risk ratio

Risk ratios are one of the most commonly used effect measures in epidemiology. Yet their properties and transportability across different populations remain debated. In this article, we show that the causal risk ratio is stable to selection based on immune status. For example, the causal risk ratio remains unchanged when individuals who cannot experience the outcome regardless of the assigned treatment, are excluded from a study. We call this property "immune-selection stability" (ISS). The ISS can help researchers justify the transportability of the risk ratio, based on explicit arguments about the data generating mechanism. An isomorphic property holds for survival ratios when selecting individuals based on doomed status. Despite extensive debates on the properties of risk ratios, the ISS has received little attention. We highlight its practical relevance and discuss implications for interpreting, comparing, and transporting estimates across populations.