Average Hazard as Harmonic Mean

A new measure was recently developed in the context of survival analysis that can be interpreted as a weighted arithmetic mean of the hazards with the survival function as the weight. However, when the average hazard is desired, it is more appropriate to use the harmonic mean rather than the arithmetic mean. Therefore, in this article, we derive the average hazard as a harmonic mean version of the expectation for hazards and show it to be equal to the previous weighted arithmetic mean. Furthermore, we demonstrate that the average hazard should be estimated using only the times at which the event is observed, while previous studies have allowed estimating the average hazard even when the truncation time is set to a time at which the event is not observed.