The average hazard (AH), recently introduced by Uno and Horiguchi, represents a novel summary metric of event time distributions, conceptualized as the general censoring-free average person-time incidence rate on a given time window, $[0,\tau].$ This metric is calculated as the ratio of the cumulative incidence probability at $\tau$ to the restricted mean survival time at $\tau$ and can be estimated through non-parametric methods. The AH's difference and ratio present viable alternatives to the traditional Cox's hazard ratio for quantifying the treatment effect on time-to-event outcomes in comparative clinical studies. While the methodology for evaluating the difference and ratio of AH in randomized clinical trials has been previously proposed, the application of the AH-based approach in general comparative effectiveness research (CER), where interventions are not randomly allocated, remains underdiscussed. This paper aims to introduce several approaches for applying the AH in general CER, thereby extending its utility beyond randomized trial settings to observational studies where treatment assignment is non-random.

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