Regression Methods for Poisson Process Data
本文针对个体可经历重复事件的情形，基于泊松过程和比例强度假设，介绍了参数与半参数回归方法，包括模型拟合、评估及随机效应处理，并探讨了计数数据的泊松与混合泊松回归的核心作用。
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 specified up to a parameter θ, and close connections with the semiparametric methods due to Cox (e.g., Andersen and Gill 1982) are noted. Random effects are incorporated by representing λ xi (t) as λ0(t)exp(α i , + x i ′β), where the α i 's are iid random variables. Details are examined and an example is given for the case in which exp(α i ,) has a gamma distribution.