Cited by 913Statistical Methods and Bayesian InferenceAdvanced Causal Inference TechniquesStatistical Methods in Clinical Trials

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Multiple Imputation and its Application

Carpenter, James R., Kenward, Michael G.·2013·Wiley eBooks

DOI 10.1002/9781119942283

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Abstract

A practical guide to analysing partially observed data. Collecting, analysing and drawing inferences from data is central to research in the medical and social sciences. Unfortunately, it is rarely possible to collect all the intended data. The literature on inference from the resulting incomplete data is now huge, and continues to grow both as methods are developed for large and complex data structures, and as increasing computer power and suitable software enable researchers to apply these methods. This book focuses on a particular statistical method for analysing and drawing inferences from incomplete data, called Multiple Imputation (MI). MI is attractive because it is both practical and widely applicable. The authors aim is to clarify the issues raised by missing data, describing the rationale for MI, the relationship between the various imputation models and associated algorithms and its application to increasingly complex data structures. Multiple Imputation and its Application: Discusses the issues raised by the analysis of partially observed data, and the assumptions on which analyses rest. Presents a practical guide to the issues to consider when analysing incomplete data from both observational studies and randomized trials. Provides a detailed discussion of the practical use of MI with real-world examples drawn from medical and social statistics. Explores handling non-linear relationships and interactions with multiple imputation, survival analysis, multilevel multiple imputation, sensitivity analysis via multiple imputation, using non-response weights with multiple imputation and doubly robust multiple imputation. Multiple Imputation and its Application is aimed at quantitative researchers and students in the medical and social sciences with the aim of clarifying the issues raised by the analysis of incomplete data data, outlining the rationale for MI and describing how to consider and address the issues that arise in its application.

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Method
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“Missing items If the proportion of missing data exceeds 10%, missing outcome data will be imputed using multiple imputation methodology and the sensitivity of the missing at random assumption will be investigated [24].”
Background
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Li, C., Miles, T. P., Shen, Y., Bayakly, R. A., Ido, M., & Khan, M. M. (2023) · BMC Medical Research Methodology · doi:10.1186/s12874-023-01917-5 · Cited by 9
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BackgroundMethod
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“…publisher’s web-site 1 Introduction Missing data is a ubiquitous problem in clinical and epidemiological research and there is a huge amount of literature on the statistical consequences and how to deal with it (e.g., Molenberghs and Kenward, 2007; Sterne et al., 2009; Carpenter and Kenward, 2013).”
Background
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“Further details about multiple imputation can be found in Carpenter and Kenward (2013).”
BackgroundMethod
Imputation Methods Outperform Missing-Indicator for Data Missing Completely at Random
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Method
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Method
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Missing Data
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“As for single ratio imputation and multiple imputation, see de Waal et al. (2011), Hu et al. (2001), King et al. (2001), Carpenter & Kenward (2013), Honaker & King (2010), Honaker et al. (2011), Little & Rubin (2002).”
Background
The side effects of service changes: exploring the longitudinal impact of participation in a randomised controlled trial (DOORWAYS) on staff perceptions of barriers to change
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Unsettling Experiences: Factors That Discourage International Students From Desiring Research and Teaching Careers
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“Although it is not feasible to test whether the dataset is MAR (missing at random) and MNAR (missing not at random), the multiple imputation allows a less-biased estimation than alternative methods, such as list-wise deletion (Carpenter & Kenward, 2013; van Buuren, 2018).”
Method
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“…implies properness in the sense that the variance estimator derived from ‘Rubin’s rule’ is consistent, as the number of completed data sets tends to infinity (a more substantive discussion of the theoretical context of congeniality can be found in Nielsen, 2003 and Carpenter & Kenward, 2013).”
Background
Flexible, Free Software for Multilevel Multiple Imputation: A Review of Blimp and jomo
Hayes, T. (2019) · Journal of Educational and Behavioral Statistics · doi:10.3102/1076998619858624 · Cited by 7
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“We conducted multiple imputation using the Blimp software Version 2.2.2 (Keller & Enders, 2020), which utilizes a fully conditional specification (i.e., imputation using chained equations; Carpenter & Kenward, 2013) and probit regression for imputing ordinal variables (Enders et al., 2018).”
MethodInfluential
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Pattern‐Mixture Model
Kenward, M. G. (2016) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat07848 · Cited by 7
Self-citation
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Paul, E., Kounali, D., Kwong, A. S. F., Major‐Smith, D., Costantini, I., Lawlor, D. A., Sayal, K. S., Bould, H., Timpson, N. J., Northstone, K., et al. (2020) · SSRN Electronic Journal · doi:10.1101/2021.05.11.21257040 · Cited by 7
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Snefjella, B., & Blank, I. (2020) · PsyArXiv (OSF Preprints) · doi:10.31234/osf.io/y2gav · Cited by 8
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Rose, P. M., Sabatés, R., Delprato, M., & Alcott, B. (2022) · Comparative Education Review · doi:10.1086/721849 · Cited by 6
“Therefore, we adjust the estimation of program effects for the fact that we apply multiple imputation methods (Carpenter and Kenward 2012).”
Method
A Comprehensive Guideline for Hybrid Modeling of Engineered Microbial Processes
Cheng, Z., Xia, W., Zhu, J.-J., Cao, J., Ren, Z. J., & Yuan, H. (2025) · Water Research · doi:10.1016/j.watres.2025.124559 · Cited by 6
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Gómez‐Rubio, V., Cameletti, M., & Blangiardo, M. (2019) · UPCommons institutional repository (Universitat Politècnica de Catalunya) · doi:10.48550/arxiv.1912.10981 · Cited by 11
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Levy, R., & Enders, C. K. (2021) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918.2021.1921799 · Cited by 6
“…another advantage of the multivariate approach is that it readily accommodates discrete variables by assuming an underlying normal latent variable distribution (Chib and Greenberg 1998; Goldstein et al. 2009; Carpenter and Kenward 2013; Enders, Keller, and Levy 2018; Enders, Du, and Keller 2020).”
BackgroundMethod
Multiple imputation regression discontinuity designs: Alternative to regression discontinuity designs to estimate the local average treatment effect at the cutoff
Takahashi, M. (2021) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918.2021.1960374 · Cited by 6
“For a more detailed account on multiple imputation, see Rubin (1987), King et al. (2001), Allison (2002, pp. 27 – 50), Enders (2010, pp. 164 – 253), and Carpenter and Kenward (2013).”
Background
Effect of Financial Incentives for Process, Outcomes, or Both on Cholesterol Level Change
Reese, P. P., Barankay, I., Putt, M., Russell, L. B., Yan, J., Zhu, J., Huang, Q. E., Loewenstein, G. F., Andersen, R. L., Testa, H., et al. (2021) · JAMA Network Open · doi:10.1001/jamanetworkopen.2021.21908 · Cited by 6
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A sequential, multiple assignment randomized trial comparing web-based education to mobile video interpreter access for improving provider interpreter use in primary care clinics: the mVOCAL hybrid type 3 study protocol
Lion, K. C., Zhou, C., Fishman, P. A., Senturia, K., Cole, A., Sherr, K., Opel, D. J., Stout, J. W., Hazim, C., Warren, L., et al. (2023) · Implementation Science · doi:10.1186/s13012-023-01263-6 · Cited by 8
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Schoenen, S., Verbeeck, J., Koletzko, L., Brambilla, I., Kuchenbuch, M., Dirani, M., Zimmermann, G., Dette, H., Hilgers, R.-D., Molenberghs, G., et al. (2024) · Orphanet Journal of Rare Diseases · doi:10.1186/s13023-024-03103-2 · Cited by 6
School and education
Oswell, D. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9781139033312.010 · Cited by 6
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Self-citation
Multiple imputation of unordered categorical missing data: A comparison of the multivariate normal imputation and multiple imputation by chained equations
Karangwa, I., Kotze, D., & Blignaut, R. J. (2016) · Brazilian Journal of Probability and Statistics · doi:10.1214/15-bjps292 · Cited by 6
Bayesian Models for Weighted Data with Missing Values: A Bootstrap Approach
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“In such cases the procedures suggested by Carpenter and Kenward (2013), chapter 11, based on weighted multiple imputation can be used and further work extending these is currently being pursued.”
MethodSelf-citation
Fast two-stage estimator for clustered count data with overdispersion
Flórez, A. J., Molenberghs, G., Verbeke, G. N., Kenward, M. G., Mamouris, P., & Vaes, B. (2019) · Journal of Statistical Computation and Simulation · doi:10.1080/00949655.2019.1630411 · Cited by 6
Self-citation
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Visual Imputation Analytics for Missing Time-Series Data in Bayesian Network
Yeon, H., Son, H., & Jang, Y. (2020) · IEEE International Conference on Big Data and Smart Computing (BigComp) · doi:10.1109/bigcomp48618.2020.00-57 · Cited by 6
Multiple Imputation in Multilevel Models. A Revision of the Current Software and Usage Examples for Researchers
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“(6) Fully Conditional Specification: Unlike JM, FCS draws missing value from univariate distribution conditioned to other model variables (see, for example, Carpenter & Kenward, 2013; Hughes et al., 2014).”
BackgroundMethodInfluential
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Improved methods for estimating fraction of missing information in multiple imputation
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“Multiple imputation (MI) becomes the most popular approach to accounting for missing data (Carpenter & Kenward, 2013, Dohoo, 2015, Rezvan, Lee, & Simpson, 2015, Rubin, 1987, Van Buuren, 2012).”
Method
Analyzing patient‐reported outcome data when completion differs between arms in open‐label trials: an application of principal stratification
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“However, data cannot be definitively confirmed as MAR or MCAR, rather than missing not at random (MNAR).(31) The MI analysis assumes that missing outcome variables can be imputed using observed covariates, resulting in an estimand that is different from”
Background
Updating Poverty Estimates in the Absence of Regular and Comparable Consumption Data: Methods and Illustration with Reference to a Middle-Income CountryPreprint
Dang, H.-A. H., Lanjouw, P., & Serajuddin, U. (2015) · SSRN Electronic Journal · doi:10.2139/ssrn.2624531 · Cited by 6
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Silverwood, R. J., Goodman, A. T., & Ploubidis, G. B. (2022) · Longitudinal and Life Course Studies · doi:10.1332/175795921x16428748347208 · Cited by 6
Employment wages and diseases of despair in early adulthood: Links through subjective socioeconomic status and cumulative stressor exposure
Dupéré, V., Beauregard, N., Pelletier‐Dumas, M., Racine, É., & Tardif‐Grenier, K. (2024) · SSM - Mental Health · doi:10.1016/j.ssmmh.2024.100324 · Cited by 6
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Productivity zoning and petrophysical assessment in the Munich metropolitan area for hydro-geothermal utilization using multivariate methods
Schölderle, F., Pfrang, D., Ernst, V., et al. (2025) · Geothermal Energy · doi:10.1186/s40517-025-00342-9 · Cited by 5
“This suggests that the imputation adequately reflects the underlying distribution (Carpenter and Kenward 2013).”
Estimating peer density effects on oral health for community-based older adults
Chakraborty, B., Widener, M. J., Salehabadi, S. M., et al. (2017) · BMC Oral Health · doi:10.1186/s12903-017-0456-4 · Cited by 5
Transformation All the Way Down? European Union Integration and the Professional Socialization of Municipal Health Officials in Serbia
Fagan, A., & Sircar, I. (2019) · JCMS Journal of Common Market Studies · doi:10.1111/jcms.12952 · Cited by 5
Multisystemic therapy compared with management as usual for adolescents at risk of offending: the START II RCT
Fonagy, P., Butler, S., Cottrell, D. J., Scott, S., Pilling, S., Eisler, I., Fuggle, P., Kraam, A., Byford, S., Wason, J. M. S., et al. (2020) · Health Services and Delivery Research · doi:10.3310/hsdr08230 · Cited by 5
Difficult temperament and social maladjustment in childhood: The mediating role of family environment
Lozano, E. A., Conesa, M. D. G., & Fernández-Vilar, M. Á. (2020) · Anales de Psicología · doi:10.6018/analesps.414241 · Cited by 6
Missing data, part 3. How to explore missing data
Pham, T. M., Pandis, N., & White, I. R. (2022) · American Journal of Orthodontics and Dentofacial Orthopedics · doi:10.1016/j.ajodo.2022.05.002 · Cited by 5
Internationalizing International Students’ Experiences: Analysis of Intercultural Dispositions for International Students who Engage in Study Abroad and Internationalization at Home
Katsumoto, S. (2023) · Journal of Studies in International Education · doi:10.1177/10283153231178128 · Cited by 5
“The results from this multiple imputation process are less biased compared to listwise deletion or alternative approaches (for more information, see Carpenter & Kenward, 2013; van Buuren, 2018).”
Method
Sharing Pattern Submodels for Prediction with Missing Values
Stempfle, L., Panahi, A., & Johansson, F. (2023) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v37i8.26179 · Cited by 5
How to mitigate selection bias in COVID-19 surveys: evidence from five national cohorts
Narayanan, M. K., Dodgeon, B., Katsoulis, M., Ploubidis, G. B., & Silverwood, R. J. (2024) · European Journal of Epidemiology · doi:10.1007/s10654-024-01164-y · Cited by 5
A multicentre randomized controlled trial on trans-generational attention deficit/hyperactivity disorder (ADHD) in mothers and children (AIMAC): an exploratory analysis of predictors and moderators of treatment outcome
Jaite, C., van Noort, B. M., Vloet, T. D., Graf, E., Kappel, V., Geissler, J. M., Warnke, A., Jacob, C., Groß‐Lesch, S., Hennighausen, K., et al. (2018) · Zeitschrift für Kinder- und Jugendpsychiatrie und Psychotherapie · doi:10.1024/1422-4917/a000602 · Cited by 5
Imputing Missing Values in EEG with Multivariate Autoregressive Models
Kanemura, A., Cheng, Y., Kaneko, T., et al. (2018) · doi:10.1109/embc.2018.8512790 · Cited by 5
Implementing online interventions in ICare: A biostatistical perspective
Görlich, D., & Faldum, A. (2019) · Internet Interventions · doi:10.1016/j.invent.2018.12.004 · Cited by 5
Randomised controlled trial with economic and process evaluations of domiciliary welfare rights advice for socioeconomically disadvantaged older people recruited via primary health care (the Do-Well study)
Haighton, C., Moffatt, S. M., Howel, D., Steer, M., Becker, F., Bryant, A., Lawson, S., McColl, E., Vale, L. D., Milne, E. M. G., et al. (2019) · Public Health Research · doi:10.3310/phr07030 · Cited by 5
Leveraging Auxiliary Information on Marginal Distributions in Nonignorable Models for Item and Unit Nonresponse
Akande, O., Madson, G., Hillygus, D. S., & Reiter, J. P. (2021) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/rssa.12635 · Cited by 5
“…throughout this article, one also could use approximately independent draws from the posterior samples to perform multiple imputation (MI) (Carpenter & Kenward, 2013; Reiter & Raghunathan, 2007; Rubin, 1987; Schafer, 1997), which can be appealing for data dissemination (Alanya et al.,…”
Method
Safety and efficacy of belimumab after B cell depletion therapy in systemic LUPUS erythematosus (BEAT-LUPUS) trial: statistical analysis plan
Muller, P. Y., Chowdhury, K., Gordon, C., et al. (2020) · Trials · doi:10.1186/s13063-020-04391-2 · Cited by 5
Multiple imputation and selection of ordinal level 2 predictors in multilevel models: An analysis of the relationship between student ratings and teacher practices and attitudes
Grilli, L., Marino, M. F., Paccagnella, O., & Rampichini, C. (2020) · Statistical Modelling · doi:10.1177/1471082x20949710 · Cited by 5
“Several strategies may be adopted to summarize level 1 variables: if all the variables are normal, the sample cluster mean is the optimal choice (Carpenter and Kenward, 2013).”
Background
Relationship between changing malaria burden and low birth weight in sub-Saharan Africa: A difference-in-differences study via a pair-of-pairs approach
Heng, S., O’Meara, W. P., Simmons, R., & Small, D. S. (2021) · eLife · doi:10.7554/elife.65133 · Cited by 6
Why Do Small Firms Implement Web Sales? The Italian Olive Oil Case
Polenzani, B., Riganelli, C., & Marchini, A. (2021) · Journal of International Food & Agribusiness Marketing · doi:10.1080/08974438.2021.2012547 · Cited by 5
A Scoping Review of Item-Level Missing Data in Within-Trial Cost-Effectiveness Analysis
Ling, X.-X., Gabrio, A., Mason, A. J., & Baio, G. (2022) · Value in Health · doi:10.1016/j.jval.2022.02.009 · Cited by 5
General and feasible tests with multiply-imputed datasets
Chan, K. W. (2022) · The Annals of Statistics · doi:10.1214/21-aos2132 · Cited by 7

Authors: Carpenter, J. R., & Kenward, M. G.
ORCID: Carpenter, James R.
Venue: Wiley eBooks
Publisher: Wiley
Published: 2012-12-18
DOI: 10.1002/9781119942283
OpenAlex: W1500944114
Cited by: 913
References: 0
Citations by year: 2026: 13 · 2025: 37 · 2024: 53 · 2023: 65 · 2022: 81 · 2021: 101 · 2020: 94 · 2019: 90 · 2018: 93 · 2017: 85 · 2016: 85 · 2015: 54 · 2014: 44 · 2013: 14 · 2012: 3
FWCI: 9.44
Type: book
Language: en
Open access: closed
Licence: doi.wiley.com/10.1002/tdm_license_1.1 (tdm)
Locations: Wiley eBooks (publishedVersion)
CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
LSHTM Research Online (London School of Hygiene and Tropical Medicine) (submittedVersion)
Wiley eBooks
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: multiple imputation, missing data, incomplete data analysis, imputation models, observational studies, nonlinear relationship, survival analysis, sensitivity analysis, medical statistics, social statistics

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