A regression method for modelling geometric rates

The occurrence of an event of interest over time is often summarized by the incidence rate, defined as the average number of events per person-time. This type of rate applies to events that may occur repeatedly over time on any given subject, such as infections, and Poisson regression represents a natural regression method for modelling the effect of covariates on it. However, for events that can occur only once, such as death, the geometric rate may be a better summary measure. The geometric rate has long been utilized in demography for studying the growth of populations and in finance to compute compound interest on capital. This type of rate, however, is virtually unknown to medical research. This may be partly a consequence of the lack of a regression method for it. This paper describes a regression method for modelling the effect of covariates on the geometric rate. The described method is based on applying quantile regression to a transform of the time-to-event variable. The proposed method is used to analyze mortality in a randomized clinical trial and in an observational epidemiological study.