A general dynamical statistical model with causal interpretation

• 成果类型: Article
• 署名作者: Commenges, Daniel; Gegout-Petit, Anne
• 署名单位: Institut National de la Sante et de la Recherche Medicale (Inserm); Universite de Bordeaux; Institut National de la Sante et de la Recherche Medicale (Inserm); Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Bordeaux
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2009.00703.x
• 发表日期: 2009
• 页码: 719-736
• 关键词: Graphical models; instrumental variables; longitudinal data; MARKOV-PROCESSES; inference; time; INDEPENDENCE; likelihood; infection; BIAS

摘要

We develop a general dynamical model as a framework for causal interpretation. We first state a criterion of local independence in terms of measurability of processes that are involved in the Doob-Meyer decomposition of stochastic processes; then we define direct and indirect influence. We propose a definition of causal influence using the concepts of a 'physical system'. This framework makes it possible to link descriptive and explicative statistical models, and encompasses quantitative processes and events. One of the features of the paper is the clear distinction between the model for the system and the model for the observation. We give a dynamical representation of a conventional joint model for human immunodeficiency virus load and CD4 cell counts. We show its inadequacy to capture causal influences whereas in contrast known mechanisms of infection by the human immunodeficiency virus can be expressed directly through a system of differential equations.