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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“Multiple imputation (MI) (Rubin 1978, 1987a–2004, 1996; Schafer 1997; Little and Rubin 2002; van Buuren 2012; Carpenter and Kenward 2013) has become a standard Fan Li is Assistant Professor, Department of Statistical Science, Duke University, Durham, NC 27708 (E-mail: fli@stat.duke.edu).”
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Background
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“The random coefficient analysis from Equation 1 served as the true population model for the 5 Carpenter and Kenward (2013, p. 220) attribute the idea of including cluster means as predictors to a personal communication from Ian White. simulations.”
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“For simplicity, suppose that all the categorical covariates are binary (see Carpenter and Kenward (2013) for general case).”
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“Hence we adopted a similar strategy to that recommended by Carpenter and Kenward (2013) and, for each modelled outcome variable, we apply multiple imputation to handle any item missingness for those cases who had complete observations on the outcome and the key explanatory variable (school type).”
Method
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“The general MI procedure for obtaining estimates of β X and β Z is (Carpenter and Kenward, 2013, p. 39): A model p(X|T, D, Z; α X ) is specified for p(X|T, D, Z), the distribution of X given T, D and Z. α X is a vector of regression coefficients and, in the case of a linear regression, the residual…”
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Method
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Missing covariates in competing risks analysis
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“An increasingly popular approach for handling missing data is to use multiple imputation (MI), usually under the MAR assumption (Carpenter and Kenward, 2013).”
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“In short, MI (Rubin 1987; Schafer 1997; Little & Rubin 2002; Molenberghs & Kenward 2007; van Buuren 2012; Carpenter & Kenward 2013) consists of three steps.”
Background
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BackgroundMethod
Missing continuous outcomes under covariate dependent missingness in cluster randomised trials
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“In MI, missing values are imputed several times to produce several different complete-data estimates of the parameters, and the results are then combined/ pooled into single point estimates plus standard error (Carpenter & Kenward, 2013; Little & Rubin, 2002; Van Buuren, 2012).”
Method
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Missing data: Issues, concepts, methods
Pham, T. M., Pandis, N., & White, I. R. (2024) · Seminars in Orthodontics · doi:10.1053/j.sodo.2024.01.007 · Cited by 30
“4 In our example above, if probing depth at time point 6 was more likely to be missing for younger participants with low probing depth at baseline, then including age and baseline probing depth in the analysis will make the MAR assumption more plausible.”
Background
Methodological approaches in analysing observational data: A practical example on how to address clustering and selection bias
Trutschel, D., Palm, R., Holle, B., & Simon, M. (2017) · International Journal of Nursing Studies · doi:10.1016/j.ijnurstu.2017.06.017 · Cited by 26
Multiple imputation using linked proxy outcome data resulted in important bias reduction and efficiency gains: a simulation study
Cornish, R., Macleod, J., Carpenter, J. R., & Tilling, K. M. (2017) · Emerging Themes in Epidemiology · doi:10.1186/s12982-017-0068-0 · Cited by 23
Self-citation
Iterative Multiple Imputation: A Framework to Determine the Number of Imputed Datasets
Nassiri, V., Molenberghs, G., Verbeke, G. N., & Barbosa‐Breda, J. (2018) · The American Statistician · doi:10.1080/00031305.2018.1543615 · Cited by 23
Handling missing data in modelling quality of clinician-prescribed routine care: Sensitivity analysis of departure from missing at random assumption
Gachau, S., Quartagno, M., Njagi, E. N., Onyango, N. O., English, M., & Ayieko, P. (2020) · Statistical Methods in Medical Research · doi:10.1177/0962280220918279 · Cited by 30
Prediction of arithmetic competence: role of cognitive abilities, socioeconomic variables and the perception of the teacher in Early Childhood Education
Pazeto, T. D. C. B., Dias, N. M., Gomes, C. M. A., & Seabra, A. G. (2020) · Estudos de Psicologia (Natal) · doi:10.22491/1678-4669.20190024 · Cited by 25
Can Computing Be Diversified on “Principles” Alone? Exploring the Role of AP Computer Science Courses in Students’ Major and Career Intentions
Sax, L. J., Newhouse, K. N. S., Goode, J., Nakajima, T. M., Skorodinsky, M., & Sendowski, M. (2022) · ACM Transactions on Computing Education · doi:10.1145/3479431 · Cited by 25
Controlled multiple imputation methods for sensitivity analyses in longitudinal clinical trials with dropout and protocol deviation
Kenward, M. G. (2015) · Clinical Investigation · doi:10.4155/cli.14.132 · Cited by 25
Self-citation
Nested case–control studies: should one break the matching?
Borgan, Ø., & Keogh, R. H. (2015) · Lifetime Data Analysis · doi:10.1007/s10985-015-9319-y · Cited by 25
“MI is now awidely used approach to handlingmissing data and is familiar to many researchers; see e.g. Carpenter and Kenward (2013) for a review.”
BackgroundMethod
Multiple imputation and analysis for high‐dimensional incomplete proteomics data
Yin, X., Levy, D. A., Willinger, C. M., Adourian, A. S., & Larson, M. G. (2015) · Statistics in Medicine · doi:10.1002/sim.6800 · Cited by 24
Combining Analysis Results from Multiply Imputed Categorical Data
Ratitch, B. (2013) · Cited by 25
Handling attrition and non-response in longitudinal data with an application to a study of Australian youth
Cumming, J., & Goldstein, H. (2016) · Longitudinal and Life Course Studies · doi:10.14301/llcs.v7i1.342 · Cited by 25
A solid majority remit following evidence-based OCD treatments: a 3-year naturalistic outcome study in pediatric OCD
Melin, K., Skarphéðinsson, G., Skärsäter, I., Haugland, B. S. M., & Ivarsson, T. (2018) · European Child & Adolescent Psychiatry · doi:10.1007/s00787-018-1137-9 · Cited by 25
A Bayesian framework for health economic evaluation in studies with missing data
Mason, A. J., Gomes, M., Grieve, R., & Carpenter, J. R. (2018) · Health Economics · doi:10.1002/hec.3793 · Cited by 24
“2018;1–14. wileyonlinelibrary.com/journal/hec 1 Broadly speaking, the MAR assumption can be expressed in two ways (Carpenter & Kenward, 2013, Ch. 1).”
BackgroundSelf-citation
Group cognitive rehabilitation to reduce the psychological impact of multiple sclerosis on quality of life: the CRAMMS RCT
Lincoln, N. B., Bradshaw, L. E., Constantinescu, C. S., Day, F., Drummond, A. E., Fitzsimmons, D. F., Harris, S. R. S., Montgomery, A. A., & das Nair, R. (2020) · Health Technology Assessment · doi:10.3310/hta24040 · Cited by 24
Comparison of the Working Alliance in Blended Cognitive Behavioral Therapy and Treatment as Usual for Depression in Europe: Secondary Data Analysis of the E-COMPARED Randomized Controlled Trial
(2024) · doi:10.2196/47515 · Cited by 24
Bayesian models for cost-effectiveness analysis in the presence of structural zero costs
Baio, G. (2013) · Statistics in Medicine · doi:10.1002/sim.6074 · Cited by 22
Is there an association between commonly employed biomarkers of liver fibrosis and liver stiffness in the general population?
Foschi, F., Domenicali, M., Giacomoni, P., Dall'aglio, A., Conti, F., Borghi, A., Bevilacqua, V., Napoli, L., Mirici, F., Cucchetti, A., et al. (2020) · Annals of Hepatology · doi:10.1016/j.aohep.2020.04.003 · Cited by 21
A multilevel Bayesian framework for predicting municipal waste generation rates
Cubillos, M., Wulff, J. N., & Wøhlk, S. (2021) · Waste Management · doi:10.1016/j.wasman.2021.04.011 · Cited by 24
A Hybrid Imputation Method for Multi-Pattern Missing Data: A Case Study on Type II Diabetes Diagnosis
Nadimi-Shahraki, M. H., Mohammadi, S., Zamani, H., Gandomi, M., & Gandomi, A. H. (2021) · Electronics · doi:10.3390/electronics10243167 · Cited by 24
A Review of Causal Inference for External Comparator Arm Studies
Rippin, G., Ballarini, N. M., Sanz, H., Largent, J. A., Quinten, C., & Pignatti, F. (2022) · Drug Safety · doi:10.1007/s40264-022-01206-y · Cited by 25
Sex dependent risk factors for mortality after myocardial infarction: individual patient data meta-analysis
van Loo, H. M., van den Heuvel, E. R., Schoevers, R. A., Anselmino, M., Carney, R. M., Denollet, J., Doyle, F., Freedland, K. E., Grace, S. L., Hosseini, S. H., et al. (2014) · BMC Medicine · doi:10.1186/s12916-014-0242-y · Cited by 24
Relative efficiency of joint-model and full-conditional-specification multiple imputation when conditional models are compatible: The general location model
Seaman, S. R., & Hughes, R. A. (2016) · Statistical Methods in Medical Research · doi:10.1177/0962280216665872 · Cited by 24
Exploring the complex associations over time among albendazole treatment, cyst evolution, and seizure outcomes in neurocysticercosis
Carpio, A., Chang, M., Zhang, H., et al. (2019) · Epilepsia · doi:10.1111/epi.16302 · Cited by 24
Multiple Imputation for Longitudinal Data: A Tutorial
Wijesuriya, R., Moreno‐Betancur, M., Carlin, J. B., White, I. R., Quartagno, M., & Lee, K. J. (2025) · Statistics in Medicine · doi:10.1002/sim.10274 · Cited by 29
Productive activities, mental health and quality of life in disability: exploring the role enhancement and the role strain hypotheses
for the SwiSCI Study Group, Fekete, C., Siegrist, J., Post, M. W. M., & Brinkhof, M. W. G. (2019) · BMC Psychology · doi:10.1186/s40359-018-0276-6 · Cited by 23
“Missing values in potential confounders were accounted for using multiple imputation (MI) by chained equations (MICE), imputing categorical, ordinal and linear variables in one model [48, 49].”
Method
Analysis of Interactions and Nonlinear Effects with Missing Data: A Factored Regression Modeling Approach Using Maximum Likelihood Estimation
Lüdtke, O., Robitzsch, A., & West, S. G. (2019) · Multivariate Behavioral Research · doi:10.1080/00273171.2019.1640104 · Cited by 22
“One central advantage of the Bayesian estimation approach is that it can be used to implement a multiple imputation strategy that separates the missing data treatment (i.e., imputation phase) from the analysis of the model of interest (i.e., analysis phase; see Carpenter & Kenward, 2013).”
BackgroundMethodResult

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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Multiple Imputation and its Application

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