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

The DOI matches its Crossref record; 93 of the 94 references it cites were found in a registry or an index.

Missing data: A statistical framework for practice

Open access
Carpenter, James R., Smuk, Melanie·2021·Biometrical Journal
DOI 10.1002/bimj.202000196PMC PMC7615108
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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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Figures

Figure 1 Complete records analysis of the bed-sharing study: adjusted odds ratio (AOR) showing how the risk of bed-sharing for sudden infant death changes with the baby’s age. Grey lines: risk when mother smokes; black lines: risk for non-smokers. Dashed lines: 95% confidence interval
Figure 1 Complete records analysis of the bed-sharing study: adjusted odds ratio (AOR) showing how the risk of bed-sharing for sudden infant death changes with the baby’s age. Grey lines: risk when mother smokes; black lines: risk for non-smokers. Dashed lines: 95% confidence intervalCC BY-NC · PubMed Central
Figure 2 Framework for addressing issues raised by missing data, when (i) the scientifically substantive model is a generalised linear model of dependent variable Yi on covariates Xi (i = 1,…, n) and (ii) we may also have auxiliary variables, Zi, which are associated with (Yi, Xi), but which are not in the substantive model
Figure 2 Framework for addressing issues raised by missing data, when (i) the scientifically substantive model is a generalised linear model of dependent variable Yi on covariates Xi (i = 1,…, n) and (ii) we may also have auxiliary variables, Zi, which are associated with (Yi, Xi), but which are not in the substantive modelCC BY-NC · PubMed Central
Figure 3 NCDS data: panels show how the probability of no qualifications age 23 varies with mother’s age at birth and social housing. In each panel, for children not in care and with a birth weight of 111 ounces, the upper lines are for children who were in social housing and the lower lines for those who were not. Each panel compares the complete records analysis (dashed lines) with those from IPW (top left, largely overlaps complete records); standard MI (top right, 100 imputations); MI separately by social housing, with auxiliary variables (bottom left, 100 imputations); and substantive model compatible MI with auxiliary variables (bottom right, 100 imputations)
Figure 3 NCDS data: panels show how the probability of no qualifications age 23 varies with mother’s age at birth and social housing. In each panel, for children not in care and with a birth weight of 111 ounces, the upper lines are for children who were in social housing and the lower lines for those who were not. Each panel compares the complete records analysis (dashed lines) with those from IPW (top left, largely overlaps complete records); standard MI (top right, 100 imputations); MI separately by social housing, with auxiliary variables (bottom left, 100 imputations); and substantive model compatible MI with auxiliary variables (bottom right, 100 imputations)CC BY-NC · PubMed Central
Figure 4 Adjusted odds ratio (AOR) for risk of bed-sharing. Left panel: after imputation of missing alcohol and drug data under MAR; right panel: sensitivity analysis. Both panels: solid lines show estimated adjusted odds with non-smoking (solid) and smoking (grey) mother; dashed lines: 95% confidence intervals
Figure 4 Adjusted odds ratio (AOR) for risk of bed-sharing. Left panel: after imputation of missing alcohol and drug data under MAR; right panel: sensitivity analysis. Both panels: solid lines show estimated adjusted odds with non-smoking (solid) and smoking (grey) mother; dashed lines: 95% confidence intervalsCC BY-NC · PubMed Central
Figure 5 NCDS analysis: Comparison of CR (dashed) and MI under MNAR (solid) lines; upper lines: in social housing; lower lines: not in social housing; 100 imputations
Figure 5 NCDS analysis: Comparison of CR (dashed) and MI under MNAR (solid) lines; upper lines: in social housing; lower lines: not in social housing; 100 imputationsCC BY-NC · PubMed Central
Figure 6 Schematic illustration of ‘δ-method’ controlled sensitivity analysis
Figure 6 Schematic illustration of ‘δ-method’ controlled sensitivity analysisCC BY-NC · PubMed Central

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Citations

Cites

Research works printed but not linked: 2

  1. Carpenter J. R., 2015, Handbook of missing data methodology, 23
  2. 10.1177/1740774517711442 · DOI

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Metadata

Authors
Carpenter, J. R., & Smuk, M.
Affiliations
London School of Hygiene & Tropical Medicine (GB)
Corresponding author
Carpenter, James R.
ORCID
Venue
Biometrical Journal
Publisher
Wiley
Published
2021-02-24
Volume
63
Issue
5
Pages
915-947
ISSN
  • 0323-3847 (ISSN-L)
  • 1521-4036
DOI
10.1002/bimj.202000196
PMC
PMC7615108
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
Licence
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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