Age-Specific Incidence and Prevalence: A Statistical Perspective
本文从统计角度将发病率视为强度（风险），患病率视为概率，基于Lexis图建立个体动态模型，并利用现代非参数连续时间生存分析方法处理横截面数据，为流行病学数据分析提供严谨框架。
In epidemiology incidence denotes the rate of occurrence of new cases (of disease), while prevalence is the frequency in the population (of diseased people). From a statistical point of view it is useful to understand incidence and prevalence in the parameter space, incidence as intensity (hazard) and prevalence as probability, and to relate observable quantities to these via a statistical model. In this paper such a framework is based on modelling each individual's dynamics in the Lexis diagram by a simple three‐state stochastic process in the age direction and recruiting individuals from a Poisson process in the time direction. The resulting distributions in the cross‐sectional population allow a rigorous discussion of the interplay between age‐specific incidence and prevalence as well as of the statistical analysis of epidemiological cross‐sectional data. For the latter, this paper focuses on methods from modern nonparametric continuous time survival analysis, including random censoring and truncation models and estimation under monotonicity constraints. The exposition is illustrated by examples, primarily from the author's epidemiological experience.