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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]

Author

Listed:
  • D M Farewell
  • R M Daniel
  • S R Seaman

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.

Suggested Citation

  • D M Farewell & R M Daniel & S R Seaman, 2022. "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. H," Biometrika, Biometrika Trust, vol. 109(1), pages 227-241.
    • Handle: RePEc:oup:biomet:v:109:y:2022:i:1:p:227-241.
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    References listed on IDEAS

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    1. Geert Molenberghs & Caroline Beunckens & Cristina Sotto & Michael G. Kenward, 2008. "Every missingness not at random model has a missingness at random counterpart with equal fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 371-388, April.
    2. D. M. Farewell & C. Huang & V. Didelez, 2017. "Ignorability for general longitudinal data," Biometrika, Biometrika Trust, vol. 104(2), pages 317-326.
    3. J. T. Chang & D. Pollard, 1997. "Conditioning as disintegration," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 51(3), pages 287-317, November.
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