Cited by 198Statistical Methods and Bayesian InferenceAdvanced Causal Inference TechniquesStatistical Methods in Clinical Trials

Missing data: A statistical framework for practice

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Carpenter, James R., Smuk, Melanie·2021·Biometrical Journal

Abstract

Missing data are ubiquitous in medical research, yet there is still uncertainty over when restricting to the complete records is likely to be acceptable, when more complex methods (e.g. maximum likelihood, multiple imputation and Bayesian methods) should be used, how they relate to each other and the role of sensitivity analysis. This article seeks to address both applied practitioners and researchers interested in a more formal explanation of some of the results. For practitioners, the framework, illustrative examples and code should equip them with a practical approach to address the issues raised by missing data (particularly using multiple imputation), alongside an overview of how the various approaches in the literature relate. In particular, we describe how multiple imputation can be readily used for sensitivity analyses, which are still infrequently performed. For those interested in more formal derivations, we give outline arguments for key results, use simple examples to show how methods relate, and references for full details. The ideas are illustrated with a cohort study, a multi‐centre case control study and a randomised clinical trial.

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  • MI assumes data are missing at random (MAR), but missingness in loneliness and anxiety/depression was likely due to participants experiencing these conditions, making MI unreliable.

    “MI assumes data are missing at random (MAR), but missingness in loneliness and anxiety/depression was likely due to participants experiencing these conditions, making MI unreliable [111].”

    From The prospective association of adolescent loneliness and low resilience with anxiety and depression in young adulthood: The HUNT study (2025) · cites this paper as [111]

    The Multiple imputation section (page unavailable) says standard MI draws missing values from a distribution estimated under MAR. The Beyond Mar: Sensitivity Analysis section (page unavailable) also describes MI approaches for departures from MAR. The paper does not assess loneliness or anxiety/depression missingness, or establish that MI was unreliable for those variables. (LLM, conf=0.88)

    Experimental — accuracy not yet measured
  • Weighting does not fully remove bias when missingness relates to the outcome.

    “Weighting does not fully remove bias when missingness relates to the outcome [111].”

    From The prospective association of adolescent loneliness and low resilience with anxiety and depression in young adulthood: The HUNT study (2025) · cites this paper as [111]

    The Inverse probability weighting section says weighting will not always eliminate bias, which supports the concern in the claim. But it also gives an example where weighting eliminates bias even though missingness depends on the data value; the claim overstates a possibility as an invariable result. (LLM, conf=0.88)

    Experimental — accuracy not yet measured

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1 of the 94 references couldn’t be matched to a known paper.

Research works printed but not linked: 5

  1. Carpenter JR Kenward MG Development of methods and critique of ad-hoc methods Molenberghs G Fitzmaurice G Kenward MG Tsiatis A Verbeke G Handbook of missing data methodology 2015b 23 46 CRC press
  2. Carpenter JR Kenward MG Vansteelandt S A comparison of multiple imputation and inverse probability weighting for analyses with missing data Journal of the Royal Statistical Society, Series A (Statistics in Society) 2006 169 571 584
  3. Cro S Carpenter JR Kenward MG Information anchored sensitivity analysis Journal of the Royal Statistical Society: Series A (Statistics in Society) 2019 182 2 623 645 30828138 PMC6378615
  4. Kennickel AB Imputation of the 1989 survey of consumer finances Proceedings of the Section on Survey Research Methods, 1990 1991
  5. Mason AJ Gomes M Grieve R Ulug P Powell JT CarpenterC JR Rejoinder to commentary on ‘Development of a practical approach to expert elicitation for randomised controlled trials with missing health outcomes: Application to the IMPROVE Trial’ Clinical Trials 2017b 14 372 373 28675302 PMC5648050

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Authors
Carpenter, J. R., & Smuk, M.
Affiliations
London School of Hygiene & Tropical Medicine (GB)
Corresponding author
Carpenter, James R.
Venue
Biometrical Journal
Publisher
Wiley
Published
2021-02-24
Volume
63
Issue
5
Pages
915-947
ISSN
  • 0323-3847 (ISSN-L)
  • 1521-4036
OpenAlex
W3130968222
Cited by
198
References
94
Citations by year
2026: 38 · 2025: 54 · 2024: 36 · 2023: 32 · 2022: 31 · 2021: 7
FWCI
4.92
Type
journal article
Language
en
Open access
Locations
  • Biometrical Journal (publishedVersion, cc-by-nc)
  • PubMed (publishedVersion)
  • PubMed Central (acceptedVersion, cc-by-nc)
  • LSHTM Research Online (London School of Hygiene and Tropical Medicine) (acceptedVersion)
Funders
Medical Research Council (MC_UU_12023/21, MC_UU_12023/29, MC_UU_00004/07)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
Keywords
missing data, multiple imputation, sensitivity analysis, maximum likelihood estimation, Bayesian analysis, missing data mechanisms, cohort studies, case-control study, randomized controlled trials
MeSH terms
Bayes Theorem, Data Interpretation, Statistical, Humans, Cohort Studies, Case-Control Studies, Uncertainty

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