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Academic Seminar at HEI - 5th Annual Janice Pogue Lectureship - Janet Wittes: Once in Love with Hazard Ratios
In the old days, we used Kaplan-Meier curves (1958) to summarize data from time-to-event trials. We might have tacked on Greenwood-Yule methods (1920) to report estimated differences in survival probabilities at specific times. Unfortunately, we had no way of characterizing the curves in their entirety. Mantel’s log-rank test (1966) was a method for assigning a p-value to the curve, but we still did could not summarize in one number the difference between the two curves. (Some disciplines used medians, but they were poor summaries of the entire curve.) Cox’s proportional hazards model (1972) gave us the tool we were looking for: we could now calculate something called the hazard ratio (HR) which summarized in one number the effect of an experimental treatment relative to control over the entire period covered by the Kaplan-Meier curves. We had everything we needed – a visual representation of survival over time, a way of testing the difference in the curves at specific time, a method for assigning a p-value to assess the degree to which the difference between the curves was inconsistent with chance, and a summary statistic, the HR, to describe the magnitude of the difference between curves. We knew that the log-rank test was optimal when the curves had proportional hazards, but valid even when they did not. The Cox model, on the other hand, required proportional hazards, but if the hazards were not far from proportionality, the model was good enough to use. We invented sloppy language to describe what a HR was, suspecting that many non-statisticians would not understand the technical language of “hazard”. This talk addresses what a HR really is, how it applies in the case of non-proportional hazards, and asks whether we should be summarizing estimates from survival curves with other statistics – e.g., perhaps back to comparison of events at specific times or the increasingly popular restricted mean survival time.

Jun 27, 2022 04:00 PM in Eastern Time (US and Canada)

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