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Missing at random: a stochastic process perspective

Farewell, D. ORCID:, Daniel, R. ORCID: and Seaman, S. 2022. Missing at random: a stochastic process perspective. Biometrika 109 (1) , pp. 227-241. 10.1093/biomet/asab002

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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 extends easily to incorporate explanatory variables, to describe longitudinal data in continuous time, and to admit more general coarsening of observations.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Medicine
Publisher: Oxford University Press (OUP)
ISSN: 0006-3444
Funders: Wellcome Trust
Date of First Compliant Deposit: 28 January 2021
Date of Acceptance: 23 December 2020
Last Modified: 03 May 2023 14:34

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