Missing at random: a stochastic process perspective.
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Peer-reviewed
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Authors
Farewell, DM
Daniel, RM
Seaman, SR
Abstract
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.
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Keywords
Missingness at random, Sigma algebra, Stochastic process
Journal Title
Biometrika
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Journal ISSN
0006-3444
1464-3510
1464-3510
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Publisher
Oxford University Press (OUP)
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All rights reserved