Poisson Rate Regression

Poisson rate regression is the standard generalized linear model for analyzing event rates and counts, such as the number of deaths, hospitalizations, or new cases observed over a span of person-time. It models the logarithm of the expected event rate as a linear function of covariates, using a Poisson likelihood and a log link, and accommodates differing amounts of exposure by including the log of person-time as an offset. Because coefficients enter on the log scale, their exponentials are incidence-rate ratios that quantify multiplicative effects on the rate. The rate formulation was crystallized in Frome's 1983 Biometrics paper, and the model sits within the broader count-data framework developed comprehensively by Cameron and Trivedi, who also detail its central practical concern: overdispersion, where the variance exceeds the Poisson assumption and standard errors must be corrected.