Review: a gentle introduction to imputation of missing values.
Open accessAbstract
In most situations, simple techniques for handling missing data (such as complete case analysis, overall mean imputation, and the missing-indicator method) produce biased results, whereas imputation techniques yield valid results without complicating the analysis once the imputations are carried out. Imputation techniques are based on the idea that any subject in a study sample can be replaced by a new randomly chosen subject from the same source population. Imputation of missing data on a variable is replacing that missing by a value that is drawn from an estimate of the distribution of this variable. In single imputation, only one estimate is used. In multiple imputation, various estimates are used, reflecting the uncertainty in the estimation of this distribution. Under the general conditions of so-called missing at random and missing completely at random, both single and multiple imputations result in unbiased estimates of study associations. But single imputation results in too small estimated standard errors, whereas multiple imputation results in correctly estimated standard errors and confidence intervals. In this article we explain why all this is the case, and use a simple simulation study to demonstrate our explanations. We also explain and illustrate why two frequently used methods to handle missing data, i.e., overall mean imputation and the missing-indicator method, almost always result in biased estimates.
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Missing values in clinical study data rarely occur completely at random.
“Missing values in clinical study data rarely occur completely at random.”
From Reporting and Methods in Clinical Prediction Research: A Systematic Review (2012) · cites this paper as [23]
The missing indicator method is known to lead to biased results in almost all observational studies.
“Even though this method is known to lead to biased results in almost all observational studies [13],[23],[60]–[62]”
From Reporting and Methods in Clinical Prediction Research: A Systematic Review (2012) · cites this paper as [23]
Exclusion of participants with missing values often leads to loss of statistical power and biased results.
“Exclusion of participants with missing values will therefore not only lead to loss of statistical power, but often also to biased results 10,12,13,23,24,57,58.”
From Reporting and Methods in Clinical Prediction Research: A Systematic Review (2012) · cites this paper as [23]
Commonly missing values are related to observed participant or disease characteristics.
“Commonly missing values are related to observed participant or disease characteristics.”
From Reporting and Methods in Clinical Prediction Research: A Systematic Review (2012) · cites this paper as [23]
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- Authors
- Donders, A. R. T., van der Heijden, G. J. M. G., Stijnen, T., & Moons, K. G. M.
- Affiliations
- Utrecht University (NL)
- Erasmus MC (NL)
- University Medical Center Utrecht (NL)
- Corresponding author
- Donders, A. Rogier T.
- Venue
- Journal of Clinical Epidemiology
- Publisher
- Elsevier BV
- Published
- 2006-10
- Volume
- 59
- Issue
- 10
- Pages
- 1087-1091
- ISSN
- 0895-4356 (ISSN-L)
- OpenAlex
- W2162772535
- Cited by
- 2,582
- References
- 18
- Citations by year
- 2026: 101 · 2025: 177 · 2024: 183 · 2023: 168 · 2022: 187 · 2021: 197 · 2020: 139 · 2019: 168 · 2018: 134 · 2017: 123 · 2016: 144 · 2015: 148 · 2014: 153 · 2013: 165 · 2012: 113
- FWCI
- 32.54
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Clinical Epidemiology (publishedVersion)
- PubMed (publishedVersion)
- EUR Research Repository (Erasmus University Rotterdam) (publishedVersion)
- EUR Research Repository (Erasmus University Rotterdam) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Keywords
- missing data, multiple imputation, single imputation, mean imputation, complete case analysis, missing at random, missing completely at random, bias, standard error estimation, simulation study
- MeSH terms
- Data Interpretation, Statistical, Humans, Research Design, Bias, Logistic Models
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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