Regression Methods for Poisson Process Data
泊松过程数据的回归方法AI 解读 ↓
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泊松过程数据的回归方法
- 研究问题
- 个体可反复经历事件时，如何结合事件次数、发生时间和协变量进行回归，并处理未观测个体异质性对分析的影响？
- 方法与思路
- 作者基于泊松过程和比例强度设定，讨论参数与半参数拟合、模型评估和随机效应，并分析与泊松及混合泊松计数回归的联系。
- 材料陈述的贡献
- 摘要称，计数回归在这些方法中具有核心作用，未观测异质性会影响半参数分析；文中还讨论随机效应并给出特定分布的例子。
- 阅读关注点
- 核对比例强度与事件过程假设、计数和发生时间分别提供的信息，以及随机效应分布如何影响估计、模型评估和半参数方法。
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- 仅据 OpenAlex 索引摘要，稿件版本未注明，刊本差异未核验；随机效应公式有提取歧义，需查原 PDF，具体推断条件未详述。
原文摘要
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.