Unifying relative and absolute risk: a general family of continuous risk indices for binary outcomes

This paper proposes a unified mathematical framework for binary outcome measures through the introduction of the General Risk Index (GRI). While classical metrics such as the risk ratio (RR), odds ratio (OR), and risk difference (RD) are often treated as distinct entities, we demonstrate that they belong to a single family of indices defined by the relative weighting of concordant and discordant pairs. By parameterizing these weights, we show that the GRI consistently preserves the direction of the treatment effect while providing a continuous spectrum of risk assessment. We apply this framework to data from a randomized trial of closed-loop insulin delivery systems, illustrating how the choice of index—and the subsequent weighting of concordant outcomes—can significantly influence the perceived magnitude of clinical impact. The GRI provides researchers with a versatile tool for comparing classical indices and selecting the optimal measure based on specific clinical and statistical requirements.