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Missing data: our view of the state of the art
Abstract
Statistical procedures for missing data have vastly improved, yet misconception and unsound practice still abound. The authors frame the missing-data problem, review methods, offer advice, and raise issues that remain unresolved. They clear up common misunderstandings regarding the missing at random (MAR) concept. They summarize the evidence against older procedures and, with few exceptions, discourage their use. They present, in both technical and practical language, 2 general approaches that come highly recommended: maximum likelihood (ML) and Bayesian multiple imputation (MI). Newer developments are discussed, including some for dealing with missing data that are not MAR. Although not yet in the mainstream, these procedures may eventually extend the ML and MI methods that currently represent the state of the art.
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“In line with the intention to treat, principle maximum likelihood estimation, an approach that uses information from all available observations, was used to estimate parameters and provides unbiased estimates and standard errors in the presence of incomplete data [35], under the assumption that data are missing at random (MAR).”
From Baseline Pro-Inflammatory Cytokine Levels Moderate Psychological Inflexibility in Behavioral Treatment for Chronic Pain (2022) · cites this paper as [35]
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“MI is viewed as a conservative approach for analyzing incomplete data sets, as it takes into account uncertainty due to missing information (Schafer and Graham, 2002).”
From Learning how to recover from stress: Results from an internet-based randomized controlled pilot trial (2023) · cites this paper as Schafer and Graham, 2002
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“we incorporated the methods for replacing missing data at the item level as described by Schafer and Graham (2002) for our psychological measures.”
From Postponement of elective cardiac surgery: A prospective observational analysis of anxiety, depression, social support and clinical complications. (2023) · cites this paper as Schafer and Graham (2002)
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“Missingness patterns are categorised by the literature into either not missing at random (NMAR), missing at random (MAR) or missing completely at random (MCAR)227,228.”
From The METRIC-framework for assessing data quality for trustworthy AI in medicine: A systematic review (2024) · cites this paper as [228]
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In the citing paper
“randomization to FC is associated with a variety of positive child and family outcomes, including increased connections to community resources, higher-quality home environments and parenting during infancy, reduced postpartum mental health symptoms, and a 37% reduction in child emergency medical care use through 24 months of age.10,11”
From Effect of a Universal Postpartum Nurse Home Visiting Program on Child Maltreatment and Emergency Medical Care at 5 Years of Age: A Randomized Clinical Trial (2021) · cites this paper as [11]
Experimental — accuracy not yet measured
In the citing paper
“Multiple imputation was employed to estimate missing data (93), using the Markov Chain Monte Carlo procedure (94) in SPSS software. The percentages of missing data ranged from 0–11.1%, well within the recommended ranges for imputation procedures.”
From Disorganized attachment in infancy predicts greater amygdala volume in adulthood (2016) · cites this paper as [93]
In the citing paper
“Missing data were at an acceptable level (missing value percentage = 13%, with 120 of 226 cases missing values) to use the multiple imputation approach [32] and thus this approach was pursued.”
From Measuring Experiential Avoidance: Evidence toward Multidimensional Predictors of Trauma Sequelae (2017) · cites this paper as [32]
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“Missing data will be handled using multiple imputations (MI).”
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Citations
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Metadata
- Authors
- Schafer, J. L., & Graham, J. W.
- Affiliations
- Pennsylvania State University (US)
- Venue
- Psychological Methods
- Published
- 2002
- Volume
- 7
- Issue
- 2
- Pages
- 147-177
- ISSN
- 1082-989X (ISSN-L)
- 1939-1463
- OpenAlex
- W2156267802
- Semantic Scholar
- f867e56d3a8ac2bbef6bfe5c74ee80ab43239718
- Cited by
- 11,638
- References
- 107
- Citations by year
- 2026: 438 · 2025: 485 · 2024: 449 · 2023: 466 · 2022: 510 · 2021: 635 · 2020: 621 · 2019: 655 · 2018: 614 · 2017: 697 · 2016: 693 · 2015: 712 · 2014: 701 · 2013: 686 · 2012: 604
- FWCI
- 113.09
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Psychological Methods (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Institute on Drug Abuse (P50DA010075, 1-P50-DA10075)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Keywords
- missing data, missing at random, maximum likelihood estimation, missing data mechanisms, statistical practice, survey data analysis
- MeSH terms
- Humans, Models, Theoretical, Research, Software, Databases as Topic
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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.
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