Missing Data in Clinical Research: A Tutorial on Multiple Imputation
Open accessAbstract
Missing data is a common occurrence in clinical research. Missing data occurs when the value of the variables of interest are not measured or recorded for all subjects in the sample. Common approaches to addressing the presence of missing data include complete-case analyses, where subjects with missing data are excluded, and mean-value imputation, where missing values are replaced with the mean value of that variable in those subjects for whom it is not missing. However, in many settings, these approaches can lead to biased estimates of statistics (eg, of regression coefficients) and/or confidence intervals that are artificially narrow. Multiple imputation (MI) is a popular approach for addressing the presence of missing data. With MI, multiple plausible values of a given variable are imputed or filled in for each subject who has missing data for that variable. This results in the creation of multiple completed data sets. Identical statistical analyses are conducted in each of these complete data sets and the results are pooled across complete data sets. We provide an introduction to MI and discuss issues in its implementation, including developing the imputation model, how many imputed data sets to create, and addressing derived variables. We illustrate the application of MI through an analysis of data on patients hospitalised with heart failure. We focus on developing a model to estimate the probability of 1-year mortality in the presence of missing data. Statistical software code for conducting MI in R, SAS, and Stata are provided.
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Missing data were imputed using predictive mean matching (PMM).
“we imputed missing data using the predictive mean matching (PMM) method [57, 58] as simulation results showed that the PMM method worked well across a wide range of missing data situations [59].”
From The psychometric properties of the Vietnamese Version of the Five Facet Mindfulness Questionnaire (2022) · cites this paper as [58]
Multiple imputation is often recommended for participants with missing data, wherein missing outcomes or covariates are estimated using other variables.
“It is often recommended that participants with missing data be included in the analysis using multiple imputation, wherein the missing outcomes or covariates are estimated using other variables.432”
From SPIRIT 2025 explanation and elaboration: updated guideline for protocols of randomised trials (2025) · cites this paper as [432]
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“Multiple imputation [14, 15] Estimate the value to be interpolated, and add different noises to form multiple groups of optional interpolation values; select the most appropriate interpolation value according to a certain selection basis.”
BackgroundRoute of myomectomy and fertility: a prospective cohort study
Wise, L. A., Thomas, L. E., Anderson, S., Baird, D. D., Anchan, R. M., Terry, K. L., Marsh, E. E., Wegienka, G., Nicholson, W. K., Wallace, K. L., et al. (2022) · Fertility and Sterility · doi:10.1016/j.fertnstert.2022.01.013 · Cited by 27 · see citing works
Zhang, H., Duan, X., Rong, P., Dang, Y., Yan, M., Zhao, Y., Chen, F., Zhou, J., Chen, Y., Wang, D., et al. (2022) · Frontiers in Cardiovascular Medicine · doi:10.3389/fcvm.2022.966217 · Cited by 26 · see citing works
“Firstly, we imputed the missing values of covariates using multiple imputation with a predictive mean matching method (28).”
MethodChen, X., Chen, H., Nan, S., Kong, X., Duan, H., & Zhu, H. (2022) · JMIR Medical Informatics · doi:10.2196/38590 · Cited by 27 · see citing works
“However, its implementation is relatively complex, and it needs to involve the selection of an interpolation model and the number of interpolation data created [32].”
Yilma, M., Cogan, R., Shui, A., Neuhaus, J., Light, C., Braun, H., Mehta, N., & Hirose, R. (2023) · Hepatology Communications · doi:10.1097/hc9.0000000000000196 · Cited by 19 · see citing works
“[30] Yet in our study, our missing/unknown data did not meet the criteria for multiple imputation—missingness was associated with our outcome, suggesting these values were not missing at random.[31] Similarly, complete case analysis led to significantly different associations between the SES predictors and outcomes co…”
Habib, J. R., Kinny‐Köster, B., Javed, A. A., Zelga, P., Saadat, L. V., Kim, R. C., Gorris, M., Allegrini, V., Watanabe, S., Sharib, J. M., et al. (2024) · Journal of Clinical Oncology · doi:10.1200/jco.23.02313 · Cited by 26 · see citing works
“29 A sensitivity analysis multivariable Cox regression was performed in the AJCC N-stage cohorts to assess for a scaled bene fi t of adjuvant chemotherapy in worsening nodal stage and the survival impact of delayed adjuvant chemotherapy (>12 weeks after surgery) 30 was investigated using a log-rank…”
Brysbaert, M., & Debeer, D. (2025) · Journal of Cognition · doi:10.5334/joc.409 · Cited by 30 · see citing works
Kalantari, E., Gholami, H., Malakooti, H., Eftekhari, M., Saneei, P., Esfandiarpour, D., Moosavi, V., & Nafarzadegan, A. R. (2024) · Atmospheric Pollution Research · doi:10.1016/j.apr.2024.102063 · Cited by 25 · see citing works
Shen, L., Jin, Y., Pan, A., Wang, K., Ye, R., Lin, Y., Anwar, S., Xia, W., Zhou, M., & Guo, X. (2024) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2024.108561 · Cited by 25 · see citing works
Lee, S., Hwang, S. H., Park, S., Son, Y., Kim, S., Kim, H. J., Park, J., Jo, H., Lee, K., Oh, J., et al. (2025) · Circulation · doi:10.1161/circulationaha.125.073086 · Cited by 25 · see citing works
Nguyen, A., Khafagy, R. T. M., Gao, Y., Meerasa, A., Roshandel, D., Anvari, M., Lin, B., Cherney, D. Z. I., Farkouh, M. E., Shah, B. R., et al. (2023) · Diabetes · doi:10.2337/db22-0696 · Cited by 25 · see citing works
Selbæk‐Tungevåg, S., Selbæk, G., Strand, B. H., Myrstad, C., Livingston, G., Lydersen, S., Bergh, S., & Ernstsen, L. (2023) · Journal of Sleep Research · doi:10.1111/jsr.13820 · Cited by 25 · see citing works
“…to impute categorical variables and predictive mean matching, drawing values from the 10 closest subjects, to impute continuous variables (Austin et al., 2021 In additional analyses, we checked for interaction between ApoE and each of the insomnia variables (i.e. PID, DIS, DMS and EMA)…”
Mao, L., Cai, D., Chi, B., Xiao, T., Zou, A., Wang, Y., Chen, Q., Gu, Q., Wang, Q., Ji, Y., et al. (2023) · European Journal of Clinical Pharmacology · doi:10.1007/s00228-023-03495-3 · Cited by 26 · see citing works
“Finally, the complete dataset was put out [28, 29].”
BackgroundLyu, X., Liu, J., Gou, Y., Sun, S., Hao, J., & Cui, Y. (2024) · Open Research (University of Surrey) · doi:10.1002/viw.20240059 · Cited by 24 · see citing works
Survival prediction of heart failure patients using motion-based analysis method
Guo, S., Zhang, H., Gao, Y., Wang, H., Xu, L., Gao, Z., Guzzo, A., & Fortino, G. (2023) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2023.107547 · Cited by 24 · see citing works
Tong, R. M., Zhu, Z., & Ling, J. (2023) · Heliyon · doi:10.1016/j.heliyon.2023.e16068 · Cited by 24 · see citing works
田村, 典., & Okamura, K. (2023) · Sleep Health · doi:10.1016/j.sleh.2023.06.005 · Cited by 24 · see citing works
Cheng, H., Ling, Y., Li, Q., Li, X., Tang, Y., Guo, J., Li, J., Wang, Z., Ming, W., & Lyu, J. (2024) · CNS Neuroscience & Therapeutics · doi:10.1111/cns.14762 · Cited by 23 · see citing works
Zhao, M., Xiao, M., Zhang, H., Tan, Q., Ji, J., Cheng, Y., & Lu, F. Y. (2025) · Scientific Reports · doi:10.1038/s41598-025-86213-6 · Cited by 23 · see citing works
Network autonomic analysis of post-acute sequelae of COVID-19 and postural tachycardia syndrome
Novák, P., Giannetti, M. P., Weller, E., Hamilton, M. J., Mukerji, S. S., Alabsi, H. S., Systrom, D. M., Marciano, S. P., Felsenstein, D., Mullally, W. J., et al. (2022) · Neurological Sciences · doi:10.1007/s10072-022-06423-y · Cited by 23 · see citing works
“The preferred approach is to use multiple imputations which reduces the risk of biased estimates of resulting statistics [33].”
SART CORS IVF registry: looking to the past to shape future perspectives
Curchoe, C. L., Tarafdar, O., Aquilina, M. C., & Seifer, D. B. (2022) · Journal of Assisted Reproduction and Genetics · doi:10.1007/s10815-022-02634-6 · Cited by 23 · see citing works
“Imputation analysis is an acceptable method to overcome missing data by analyzing similar known data points and making informed extrapolations of the missing data based on an estimate of the distribution of the missing variable [10].”
MethodDEGAIN: Generative-Adversarial-Network-Based Missing Data Imputation
Shahbazian, R., & Trubitsyna, I. (2022) · Information · doi:10.3390/info13120575 · Cited by 23 · see citing works
“The missing data are categorized as follows [6]: • Missing completely at random (MCAR) : It means that the probability of missing data does not depend on any value of attributes.”
Zhong, Y., Sun, H. Y., Chen, H., Jing, W., Chen, W., & Ma, J. (2023) · Frontiers in Neurology · doi:10.3389/fneur.2023.1271391 · Cited by 22 · see citing works
Cingolani, L., & Morales, D. A. S. (2024) · Public Management Review · doi:10.1080/14719037.2024.2303609 · Cited by 23 · see citing works
“Other scholars have also highlighted the positive role of MICE in handling ‘endemic missing data points’ in educational research (Pampaka et al. 2016) as well as public health and clinical research (Austin et al. 2021).”
Alanazi, R., Bahari, G., Alzahrani, Z. A., Alhaidary, A., Alharbi, K. N., Albagawi, B. S., & Alanazi, N. H. (2023) · Healthcare · doi:10.3390/healthcare11243104 · Cited by 22 · see citing works
“Missing data (less than 5% per item) were handled using the mean-value imputation for continuous variables [23].”
MethodAzhari, H. E., Cherif, E. K., Halimi, R. E., Azzirgue, E. M., Larbi, Y. O., Coren, F., & Salmoun, F. (2024) · Sustainability · doi:10.3390/su16051951 · Cited by 22 · see citing works
Pu, Y., Xing, N., Wang, Y., Wang, H., Jiang, X., & Li, X. (2024) · BMC Cardiovascular Disorders · doi:10.1186/s12872-024-04450-5 · Cited by 21 · see citing works
“There were no variables in the dataset with more than 20% missing values, and all missing data were imputed using multiple imputation techniques [20].”
Artificial Intelligence in Veterinary Clinical Pathology—An Introduction and Review
Neal, S. V., Rudmann, D. G., & Corps, K. N. (2025) · Veterinary Clinical Pathology · doi:10.1111/vcp.70012 · Cited by 25 · see citing works
“Various imputation approaches are taken depending on the situation, ranging from replacing missing values with a measure of central tendency (mean/median/mode) to creating another ML model to predict the missing value [10, 12].”
Frailty and Duration of Maintenance Dialysis: A Japanese Nationwide Cross-Sectional Study
Yamamoto, S., Niihata, K., Toida, T., Abe, M., Hanafusa, N., & Kurita, N. (2024) · American Journal of Kidney Diseases · doi:10.1053/j.ajkd.2024.04.012 · Cited by 21 · see citing works
Donor Time to Death and Kidney Transplant Outcomes in the Setting of a 3-Hour Minimum Wait Policy
Tingle, S. J., Chung, N. D. H., Malik, A. K., Kourounis, G., Thompson, E. R., Glover, E. K., Mehew, J., Philip, J. L., Gardiner, D. D., Pettigrew, G. J., et al. (2024) · JAMA Network Open · doi:10.1001/jamanetworkopen.2024.43353 · Cited by 20 · see citing works
A novel model to optimize multiple imputation algorithm for missing data using evolution methods
Mohammed, Y. S., Abdelkader, H. M., Pławiak, P., & Hammad, M. A. (2022) · Biomedical Signal Processing and Control · doi:10.1016/j.bspc.2022.103661 · Cited by 19 · see citing works
Marsden, A., Hann, M., Barron, E., Ross, J., Valabhji, J., Murray, E., & Cotterill, S. (2023) · Preventive Medicine Reports · doi:10.1016/j.pmedr.2023.102161 · Cited by 19 · see citing works
“That is, the probability of a weight measure being missing, even after accounting for covariates, is dependent on the value of the missing weight (Austin et al., 2021).”
BackgroundPredictive models in emergency medicine and their missing data strategies: a systematic review
Arnaud, É., Elbattah, M., Ammirati, C., Dequen, G., & Ghazali, D. A. (2023) · npj Digital Medicine · doi:10.1038/s41746-023-00770-6 · Cited by 20 · see citing works
“However, Austin et al. 18 demonstrated that using MICE on clinical data is valuable — especially when the missing data mechanism is nonignorable.”
MethodPrediction model for cognitive frailty in older adults: A systematic review and critical appraisal
Huang, J., Zeng, X., Hu, M., Ning, H., Wu, S., Peng, R., & Feng, H. (2023) · Frontiers in Aging Neuroscience · doi:10.3389/fnagi.2023.1119194 · Cited by 20 · see citing works
Comparison of Imputation Strategies for Incomplete Longitudinal Data in Life-Course Epidemiology
Shaw, C. L., Wu, Y., Zimmerman, S. C., Hayes‐Larson, E., Belin, T. R., Power, M. C., Glymour, M. M., & Mayeda, E. R. (2023) · American Journal of Epidemiology · doi:10.1093/aje/kwad139 · Cited by 20 · see citing works
Tsiampalis, T., & Panagiotakos, D. B. (2023) · BMC Medical Research Methodology · doi:10.1186/s12874-023-02004-5 · Cited by 20 · see citing works
Frach, L., Barkhuizen, W., Allegrini, A. G., Ask, H., Hannigan, L. J., Corfield, E. C., Andreassen, O. A., Dudbridge, F., Ystrøm, E., Havdahl, A., et al. (2024) · Molecular Psychiatry · doi:10.1038/s41380-023-02383-7 · Cited by 20 · see citing works
“Multiple imputation of the phenotype data, which is more appropriate than listwise deletion when data is not missing completely at random [107, 108], did not considerably change our results, which suggests that our fi ndings hold robust despite some selective attrition.”
MethodWu, F., Chen, L., & Du, Y. (2024) · Clinical Rheumatology · doi:10.1007/s10067-024-06933-4 · Cited by 20 · see citing works
“If authors could not be reached, data imputation was performed based on the meaning of the data, such as using mean, median, and nearest-neighbor methods [23].”
Zhou, Y., Zhong, L., Zhong, Y., & Liao, Y. (2024) · BMC Infectious Diseases · doi:10.1186/s12879-024-10179-5 · Cited by 20 · see citing works
The association between sex hormones and bone mineral density in US females
Tian, X., & Zhang, B. (2025) · Scientific Reports · doi:10.1038/s41598-025-89985-z · Cited by 19 · see citing works
Rösel, I., Serna-Higuita, L. M., Sayah, F. A., Buchholz, M., Buchholz, I., Kohlmann, T., Martus, P., & Feng, Y. (2021) · Quality of Life Research · doi:10.1007/s11136-021-03037-3 · Cited by 18 · see citing works
“Excluding respondents with missing data from the analysis (complete cases: CC) is rarely adequate and only unbiased if data are MCAR [6, 8, 13].”
BackgroundMethodInfluentialTime-to-event modeling for hospital length of stay prediction for COVID-19 patients
Wen, Y., Rahman, M. F., Zhuang, Y., Pokojovy, M., Xu, H., McCaffrey, P., Vo, A. H., Walser, E., Moen, S. T., & Tseng, T.-L. (2022) · Machine Learning with Applications · doi:10.1016/j.mlwa.2022.100365 · Cited by 19 · see citing works
Huang, S., Guo, N., Duan, X., Zhou, Q., Zhang, Z., Luo, L., & Ge, L. (2022) · Experimental and Therapeutic Medicine · doi:10.3892/etm.2022.11735 · Cited by 19 · see citing works
“In this way, the multiple imputation allows the user to explicitly incorporate the uncertainty about the true value of imputed variables (16).”
BackgroundWatanabe, A., Katano, S., Yano, T., Nagaoka, R., Numazawa, R., Honma, S., Yamano, K., Fujisawa, Y., Ohori, K., Kouzu, H., et al. (2022) · Frontiers in Cardiovascular Medicine · doi:10.3389/fcvm.2022.1051570 · Cited by 19 · see citing works
A Machine Learning-Based Severity Prediction Tool for the Michigan Neuropathy Screening Instrument
Haque, F., Reaz, M. B. I., Chowdhury, M. E. H., Shapiai, M. I., Malik, R. A., Alhatou, M. I., Kobashi, S., Ara, I., Ali, S. H. M., Bakar, A. A. A., et al. (2023) · Diagnostics · doi:10.3390/diagnostics13020264 · Cited by 20 · see citing works
“In this study, missing data were calculated by the multiple imputations by chained equations (MICE) technique [37,38].”
MethodMcCaw, Z. R., Gao, J., Lin, X., & Gronsbell, J. L. (2024) · Nature Genetics · doi:10.1038/s41588-024-01793-9 · Cited by 19 · see citing works
Li, X., Tang, Y., Deng, X., Zhou, F., Huang, X., Bai, Z., Liang, X., Wang, Y., & Lyu, J. (2024) · Intensive and Critical Care Nursing · doi:10.1016/j.iccn.2024.103749 · Cited by 19 · see citing works
Domaradzki, J. (2023) · Nutrients · doi:10.3390/nu15030608 · Cited by 18 · see citing works
“In this study, the propensity for a data point to be missing was completely random, also known as missing completely at random (MCAR) [34,35].”
BackgroundMoazzam, Z., Alaimo, L., Endo, Y., Lima, H. A., Woldesenbet, S., Rueda, B. O., Yang, J., Ratti, F., Marques, H. P., Cauchy, F., et al. (2023) · Annals of Surgery · doi:10.1097/sla.0000000000006056 · Cited by 18 · see citing works
“18,19 Probabilities for SAR were estimated and compared using the Kaplan-Meier and log-rank method.”
MethodRosselló, X., Ramallal, R., Romaguera, D., Alonso‐Gómez, Á. M., Alonso, Á., Tojal‐Sierra, L., Fernández-Palomeque, C., Martínez‐González, M. Á., Uriarte, M. G., López, L., et al. (2023) · European Journal of Preventive Cardiology · doi:10.1093/eurjpc/zwad380 · Cited by 18 · see citing works
- Authors
- Austin, P. C., White, I. R., Lee, D. S., & van Buuren, S.
- Affiliations
- University of Toronto (CA)
- MRC Clinical Trials Unit at UCL (GB)
- University Health Network (CA)
- Corresponding author
- Austin, Peter C.
- Venue
- Canadian Journal of Cardiology
- Publisher
- Elsevier BV
- Published
- 2021-09
- Volume
- 37
- Issue
- 9
- Pages
- 1322-1331
- ISSN
- 0828-282X (ISSN-L)
- PMC
- PMC8499698
- OpenAlex
- W3109682927
- Cited by
- 1,006
- References
- 36
- Citations by year
- 2026: 191 · 2025: 306 · 2024: 264 · 2023: 150 · 2022: 82 · 2021: 13
- FWCI
- 10.00
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Canadian Journal of Cardiology (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- TNO Repository (submittedVersion)
- Utrecht University Repository (Utrecht University) (submittedVersion, other-oa)
- UCL Discovery (University College London) (submittedVersion)
- Funders
- Institute for Clinical Evaluative Sciences
- Canadian Institutes of Health Research (CRT43823, CTP79847)
- Ontario Ministry of Health and Long-Term Care
- Medical Research Council (MC_UU_12023/21)
- Chest Heart and Stroke Scotland
- Heart and Stroke Foundation of Canada
- 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 › Statistical Methods in Clinical Trials
- Keywords
- multiple imputation, missing data, clinical research, complete case analysis, mean imputation, imputation models, derived variables, heart failure, one-year mortality
- MeSH terms
- Clinical Trials as Topic, Data Interpretation, Statistical, Humans, Research Design
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