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Multiple Imputation of Missing Values
Open accessAbstract
Following the seminal publications of Rubin about thirty years ago, statisticians have become increasingly aware of the inadequacy of “complete-case” analysis of datasets with missing observations. In medicine, for example, observations may be missing in a sporadic way for different covariates, and a complete-case analysis may omit as many as half of the available cases. Hotdeck imputation was implemented in Stata in 1999 by Mander and Clayton. However, this technique may perform poorly when many rows of data have at least one missing value. This article describes an implementation for Stata of the MICE method of multiple multivariate imputation described by van Buuren, Boshuizen, and Knook (1999). MICE stands for multivariate imputation by chained equations. The basic idea of data analysis with multiple imputation is to create a small number (e.g., 5–10) of copies of the data, each of which has the missing values suitably imputed, and analyze each complete dataset independently. Estimates of parameters of interest are averaged across the copies to give a single estimate. Standard errors are computed according to the “Rubin rules”, devised to allow for the between- and within-imputation components of variation in the parameter estimates. This article describes five ado-files. mvis creates multiple multivariate imputations. uvis imputes missing values for a single variable as a function of several covariates, each with complete data. micombine fits a wide variety of regression models to a multiply imputed dataset, combining the estimates using Rubin's rules, and supports survival analysis models (stcox and streg), categorical data models, generalized linear models, and more. Finally, misplit and mijoin are utilities to intercon-vert datasets created by mvis and by the miset program from John Carlin and colleagues. The use of the routines is illustrated with an example of prognostic modeling in breast cancer.
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“Missing data were imputed through multiple imputation with Stata using the MICE (multivariate imputation by chained equations) module (Royston, 2004).Five imputed data sets were generated.”
From Culture and Identity‐Protective Cognition: Explaining the White‐Male Effect in Risk Perception (2007) · cites this paper as Royston, 2004
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Cites
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- 10.1177/1536867X0300300302 · DOI
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“Missing values in the data were multiply imputed using a chained equation algorithm implemented in the Stata ice program (Royston, 2004).”
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“Multiple imputation (10 cycles) was used for missing information on waist circumference or physical activity (n 238) (16).”
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“Our analyses are performed on the data in which missing values were replaced with the estimates from Stata 10 multiple imputation procedure known as “ICE” (Royston, 2004).”
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“To reduce the potential bias from item nonresponse, we used multiple imputation techniques available in Stata (Royston, 2004; StataCorp, 2009).”
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“We used ICE in Stata 10 (Royston 2004), taking all variables included in our analyses as predictors and generated ten imputated datasets, each of which replaced cases with missing information with plausible values based on their predictive distributions.”
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“Due to problems with item nonresponse (ranging from 1% to 16%), four independent variables used in this study were imputed using the multiple imputation by chained equations or ICE procedure, in conjunction with the Stata statistical package (Royston, 2004, 2005).”
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“ICE imputes missing values using an iterative regression switching procedure (Royston, 2004, 2005).”
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Predictors of suicidality across the life span: The Isle of Wight study
Pickles, A. R., Aglan, A., Collishaw, S., Messer, J., Rutter, M. L., & Maughan, B. (2009) · Psychological Medicine · doi:10.1017/s0033291709991905 · Cited by 178
“1999) as implemented in the ice procedure (Royston, 2004).”
MethodSchane, R., Walter, L., Dinno, A., Covinsky, K. E., & Woodruff, P. (2008) · Journal of general internal medicine · doi:10.1007/s11606-008-0749-z · Cited by 176
Lawlor, D., Wills, A., Fraser, A., Sayers, A., Fraser, W., & Tobias, J. (2013) · The Lancet · doi:10.1016/s0140-6736(12)62203-x · Cited by 175
Causal effects of retirement timing on subjective physical and emotional health.
Calvo, E., Sarkisian, N., & Tamborini, C. R. (2013) · The journals of gerontology. Series B, Psychological sciences and social sciences · doi:10.1093/geronb/gbs097 · Cited by 175
“To handle missing data, we performed a multiple imputation with chained equations (MICE; Royston 2004); our model estimates are based on 20 imputations.”
MethodLawlor, D., Smith, G., & Ebrahim, S. (2005) · Diabetologia · doi:10.1007/s00125-005-0040-3 · Cited by 175
“We used multiple multivariate imputation, using all other covariates, the outcome, the log of survival time and the censoring indicator, to impute a distribution of missing values for those variables with some missing data with switching regression [14].”
MethodLarkin, G., Copes, W., Nathanson, B., & Kaye, W. (2010) · Resuscitation · doi:10.1016/j.resuscitation.2009.11.021 · Cited by 174
Violence, Older Peers, and the Socialization of Adolescent Boys in Disadvantaged Neighborhoods
Harding, D. J. (2009) · American Sociological Review · doi:10.1177/000312240907400306 · Cited by 173
Social Capital and Health Inequality: Evidence from Taiwan
Song, L., & Lin, N. (2009) · Journal of Health and Social Behavior · doi:10.1177/002214650905000203 · Cited by 169
Gradual Retirement, Sense of Control, and Retirees' Happiness
Calvo, E., Haverstick, K., & Sass, S. A. (2008) · Research on Aging · doi:10.1177/0164027508324704 · Cited by 200
Glance, L. G., Wissler, R. N., Mukamel, D. B., Li, Y., Diachun, C. A. B., Salloum, R. M., Fleming, F. J., & Dick, A. W. (2010) · Anesthesiology · doi:10.1097/aln.0b013e3181eff32e · Cited by 185
Adolescent Loneliness and Health in Early Adulthood
Goosby, B. J., Bellatorre, A., Walsemann, K. M., & Cheadle, J. E. (2013) · Sociological Inquiry · doi:10.1111/soin.12018 · Cited by 231
“…with stress-related metabolic health conditions in early adulthood, including hypertension, high cholesterol, and obesity, as well as its effects on diagnosed depression and self-rated health, addressing the following hypotheses: H1—Loneliness is associated with poor mental and physical…”
The Latin American Left's Mandate: Free-Market Policies and Issue Voting in New Democracies
Baker, A., & Greene, K. F. (2011) · World Politics · doi:10.1017/s0043887110000286 · Cited by 197
Emergency Medical Service (EMS) systems in developed and developing countries.
Roudsari, B., Nathens, A., Arreola-Risa, C., Cameron, P., Civil, I., Grigoriou, G., Gruen, R., Koepsell, T., Lecky, F., Lefering, R., et al. (2007) · Injury · doi:10.1016/j.injury.2007.04.008 · Cited by 171
Suppiah, R., Judge, A., Batra, R., Flossmann, O., Harper, L., Höglund, P., Javaid, M., Jayne, D., Mukhtyar, C., Westman, K., et al. (2011) · Arthritis care & research · doi:10.1002/acr.20433 · Cited by 169
Yang, T., Shen, Y.-M., Zhu, M.-J., Liu, Y.-L., Deng, J.-W., Chen, Q., & See, L. (2015) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph13010072 · Cited by 167
“Missing values for observed indicators were imputed using expectation-maximization (EM) implementation of maximum likelihood [47,48].”
MethodDangerous Liaisons? Dating and Drinking Diffusion in Adolescent Peer Networks
Kreager, D. A., & Haynie, D. L. (2011) · American Sociological Review · doi:10.1177/0003122411416934 · Cited by 180
Happiness and ‘economic migration’: A comparison of Eastern European migrants and stayers
Bartram, D. (2013) · Migration Studies · doi:10.1093/migration/mnt006 · Cited by 166
Job Stress and Job Satisfaction: Home Care Workers in a Consumer‐Directed Model of Care
Delp, L., Wallace, S. P., Geiger-Brown, J. M., & Muntaner, C. (2010) · Health Services Research · doi:10.1111/j.1475-6773.2010.01112.x · Cited by 172
“Missing data were imputed using the multiple imputation method (Royston 2004, 2005).”
MethodRoberfroid, D., Huybregts, L., Lanou, H. B., Henry, M., Méda, N., Menten, J., & Kolsteren, P. (2008) · American Journal of Clinical Nutrition · doi:10.3945/ajcn.2008.26296 · Cited by 166
“To assess the robustness of the primary analyses to baseline imbalances between treatment groups and missing data, we repeated the analyses adjusting for maternal body mass index (BMI) and hemoglobin at baseline and using multiple imputation of missing data by the MICE system of chained equations (42).”
MethodStephens, P. R., Altizer, S., Smith, K. F., Aguirre, A. A., Brown, J. H., Budischak, S. A., Byers, J. E., Dallas, T., Davies, T. J., Drake, J. M., et al. (2016) · Ecology Letters · doi:10.1111/ele.12644 · Cited by 187
“Values for other kinds of missing data (e.g. host or parasite traits) can be imputed (Royston 2004; Little & Rubin 2014; Swenson 2014), or estimated via surrogate splits in classification and regression tree analyses (Feelders 1999; Hapfelmeier et al. 2012).”
Metadata
- Authors
- Royston, P.
- Affiliations
- MRC Clinical Trials Unit at UCL (GB)
- Corresponding author
- Royston, Patrick
- ORCID
- Royston, Patrick
- Venue
- The Stata Journal: Promoting communications on statistics and Stata
- Publisher
- SAGE Publications
- Published
- 2004-08
- Volume
- 4
- Issue
- 3
- Pages
- 227-241
- ISSN
- 1536-867X (ISSN-L)
- 1536-8734
- OpenAlex
- W2161375627
- Cited by
- 2,340
- References
- 0
- Citations by year
- 2026: 40 · 2025: 49 · 2024: 42 · 2023: 67 · 2022: 99 · 2021: 106 · 2020: 100 · 2019: 107 · 2018: 103 · 2017: 109 · 2016: 123 · 2015: 129 · 2014: 137 · 2013: 179 · 2012: 178
- FWCI
- 46.61
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Stata Journal Promoting communications on statistics and Stata (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- AgEcon Search (University of Minnesota, USA) (submittedVersion, cc-by-nc-nd)
- AgEcon Search (University of Minnesota, USA)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Data Analysis with R
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Keywords
- multiple imputation, chained equations, Stata ado file, missing data, complete case analysis, Rubin's rules, survival analysis, prognostic model, breast cancer
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