Missing at random: a stochastic process perspective

Contribution to the discussion of ‘Longitudinal data with dropout: Objectives, assumptions and a proposal’ by P. J. Diggle, D. Farewell and R. Henderson

D M Farewell, R M Daniel and S R Seaman

Biometrika, 2022, vol. 109, issue 1, 227-241

Abstract: SummaryWe 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.

Keywords: Missingness at random; Sigma algebra; Stochastic process (search for similar items in EconPapers)
Date: 2022
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