Regression Methods for Poisson Process Data

Abstract

Abstract This article is directed toward situations where individuals can experience repeated events, and data on an individual consist of the number and occurrence times of events, along with concomitant variables. Methods of regression analysis are presented, based on Poisson process and proportional intensity assumptions. These include parametric and semi-parametric approaches to model fitting, model assessment, and the treatment of random effects. In addition, insight is gained as to the central role of Poisson and mixed Poisson regression analysis of counts in these methods, and as to the effects of unobserved heterogeneity on semi-parametric analyses. The methods in the article are based on the proportional intensity Poisson process model, for which an individual with given fixed covariate vector x has repeated events occur according to a nonhomogeneous Poisson process with intensity function λx(t) = λ0(t)exp(x′β). Estimation of β and the baseline intensity λ0(t) are considered when λ0(t) is specifi...