  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.
