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I like the restricted mean survival time (and the difference in RMST between cohorts) in survival analyses. However, it does not really convey the effect of an exposure on rare outcomes. For instance, if a drug decreases the risk of mortality by 30% (in relative terms) but the vast majority of people in either cohort don't die, the RMST might be very small (e.g. 10 days on a 3 years follow-up) which could easily be misinterpreted as a meaningless effect.

Is there another statistics that is similar to RMST but better highlight drug effects on rare outcomes?

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Coefficients of semi-parametric (e.g., Cox proportional hazards, PH) or fully parametric (e.g., accelerated failure time, AFT) survival regression models are useful here.

In the PH context the coefficients evaluate the relative hazard of an event as a function of exposure (and other covariates). The Cox regression coefficient for exposure is the log of the hazard ratio between exposed and non-exposed. It doesn't matter whether the baseline hazard is high or low; it doesn't even enter the calculations. You get a direct comparison between exposed and non-exposed.

In the AFT context the coefficients evaluate the apparent "acceleration" of time to event as a function of exposure (and other covariates). That might be more in keeping with your emphasis on the time scale; you can say that exposure "speeds up" the time to event by a certain factor.

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