Missing at random: a stochastic process perspective

• 成果类型: Article
• 署名作者: Farewell, D. M.; Daniel, R. M.; Seaman, S. R.
• 署名单位: Cardiff University; MRC Biostatistics Unit; University of Cambridge
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asab002
• 发表日期: 2022
• 页码: 227241
• 关键词: ignorability; models

摘要

We offer a natural and extensible measure-theoretic treatment of missingness at random. Within the standard missing-data framework, we give a novel characterization of the observed data as a stopping-set sigma algebra. We demonstrate that the usual missingness-at-random conditions are equivalent to requiring particular stochastic processes to be adapted to a set-indexed filtration. These measurability conditions ensure the usual factorization of likelihood ratios. We illustrate how the theory can be extended easily to incorporate explanatory variables, to describe longitudinal data in continuous time, and to admit more general coarsening of observations.