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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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“5, as in [36].”
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“The technique of multiple imputations by chained questions (Royston 2004) in Stata (StataCorp 2011) was used for all items included in the imputation model.”
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“Sensitivity analysis were performed imputing missing values on the outcomes and covariates (n = 140–450) using chained equations (“mi impute chained” in STATA) including all other covariates (respective outcome at baseline, age, gender, pubertal status, school type) and random effects (indicators for school class and…”
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“Missing data were imputed using the Imputation by Chained Equations (ICE) algorithm implemented in Stata (see Royston, 2004, 2005a, 2005b), with a small number of out of range values truncated to the minimum or maximum possible value for the variable based on the existing data.”
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“Um die Unsicherheit aufgrund fehlender Werte zu berücksichtigen, wurden mithilfe des Stata Programms ICE (Royston 2004) für jeden fehlenden Wert fünf plausible Werte erzeugt, die in den anschließenden Analysen nach dem von 14 Rubin (1987) vorgeschlagenen Verfahren kombiniert wurden.”
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“Recent developments in statistical software allow some automation of the multiple imputation process; for example, ICE in STATA (StataCorp, College Station, TX, USA) [16, 17] or MICE in R [18, 19].”
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Cooney, T., & Dykstra, P. (2011) · Ageing & Society · doi:10.1017/s0144686x10001339 · Cited by 51
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“The final model was confirmed using multiple imputation techniques (Royston 2004).”
MethodState High School Exit Examinations and NAEP Long-Term Trends in Reading and Mathematics, 1971-2004
Grodsky, E., Warren, J. R., & Kalogrides, D. (2009) · doi:10.1177/0895904808320678 · Cited by 51
“For the sake of simplicity we have not indexed the plausible values; we estimated models across plausible values and adjusted standard errors accordingly following Royston (2004) and using the “ice” procedure he wrote for Stata.”
MethodWatt, H., Carson, C., Lawlor, D., Patel, R., & Ebrahim, S. (2009) · American Journal of Public Health · doi:10.2105/ajph.2007.129288 · Cited by 51
Ma, J., Grogan-Kaylor, A., & Lee, S. J. (2018) · Child Abuse & Neglect · doi:10.1016/j.chiabu.2017.10.013 · Cited by 51
Pokropek, A., Marks, G. N., & Borgonovi, F. (2021) · Journal of Educational Psychology · doi:10.1037/edu0000687 · Cited by 63
“tions by chained equations” (Royston, 2004), which also accommodates PISA’s rotational design (OECD, 2012).”
BackgroundMethodFairness without Imputation: A Decision Tree Approach for Fair Prediction with Missing Values
Jeong, H., Wang, H., & Calmon, F. (2021) · AAAI Conference on Artificial Intelligence · doi:10.48550/arxiv.2109.10431 · Cited by 50
“Methods that handle missing values have a long history in statistics (Little and Rubin 2019; Schafer and Graham 2002; Buuren and Groothuis-Oudshoorn 2010; Royston 2004; Molenberghs and Kenward 2007; Stekhoven and Bühlmann 2012; Tang and Ishwaran 2017).”
InfluentialCardiac and Stress Biomarkers and Chronic Kidney Disease Progression: the CRIC study
Bansal, N., Zelnick, L. R., Shlipak, M., Anderson, A. H., Christenson, R., Deo, R., Defilippi, C., Feldman, H., Lash, J., He, J., et al. (2019) · Clinical Chemistry · doi:10.1373/clinchem.2019.305797 · Cited by 50
Sparse Convolutional Denoising Autoencoders for Genotype Imputation
Chen, J., & Shi, X. M. (2019) · Genes · doi:10.3390/genes10090652 · Cited by 49
“Prediction-model-based imputation methods [26,29] create a predictive model to estimate values that will substitute missing data in a machine learning fashion.”
MethodThe impact of multidimensional disadvantage over childhood on developmental outcomes in Australia.
Goldfeld, S., O'Connor, M., Chong, S., Gray, S., O’Connor, E., Woolfenden, S., Redmond, G., Williams, K. J., Mensah, F., Kvalsvig, A., et al. (2018) · International Journal of Epidemiology · doi:10.1093/ije/dyy087 · Cited by 50
Wan, E. Y. F., Fung, C. S. C., Yu, E. Y. T., Chin, W. Y., Fong, D., Chan, A. K. C., & Lam, C. L. K. (2017) · Journal of the American Heart Association · doi:10.1161/jaha.117.006400 · Cited by 60
“Multiple imputation was adopted to deal with missing data for all baseline covariates other than ABC.(21) This approach can effectively reduce unnecessary biases,(21,22) raise the power of the analysis, and produce more reliable and applicable models.”
MethodGrøntved, A., Koivula, R., Johansson, I., Wennberg, P., Østergaard, L., Hallmans, G., Renström, F., & Franks, P. (2016) · Journal of the American Heart Association : Cardiovascular and Cerebrovascular Disease · doi:10.1161/jaha.116.004413 · Cited by 50
“To evaluate the possibility of selection bias due to missing data, we carried out multiple imputation analyses according to Royston 15 by comparing estimates of associations in the sample with complete data on covariates and outcome (n = 19 751 – 23 732) with the full sample (n = 32 728) with…”
MethodStanley, L. R., & Swaim, R. (2015) · Drug and Alcohol Dependence · doi:10.1016/j.drugalcdep.2015.08.009 · Cited by 50
“A uthor M anuscript A uthor M anuscript A uthor M anuscript A uthor M anuscript 10.0 (Royston, 2004, 2005, 2007).”
BackgroundInfluentialWork Hours, Schedules, and Insufficient Sleep Among Mothers and Their Young Children
Kalil, A., Dunifon, R., Crosby, D. A., & Su, J. H. (2014) · Journal of Marriage and Family · doi:10.1111/jomf.12142 · Cited by 50
“Missing data were multiply imputed by chained equations using the ice commands for Stata, which facilitates statistically valid inference when data are missing at random (Royston, 2004; Rubin, 1987).”
MethodVenue-based affiliation networks and HIV risk-taking behavior among male sex workers
Fujimoto, K., Williams, M. L., & Ross, M. (2013) · Sexually Transmitted Diseases · doi:10.1097/olq.0b013e31829186e5 · Cited by 50
Impact of health‐care accessibility and social deprivation on diabetes related foot disease
Leese, G., Feng, Z.-Q., Leese, R., Dibben, C., & Emslie-Smith, A. (2013) · Diabetic Medicine · doi:10.1111/dme.12108 · Cited by 50
Alcohol peer influence of participating in organized school activities: A network approach.
Fujimoto, K., & Valente, T. W. (2012) · Health Psychology · doi:10.1037/a0029466 · Cited by 51
“Our study used multiple imputation via switching regression, an iterative multivariable regression technique by chained equations (Royston, 2004) implemented in Stata 11 to address the missing values of any covariates (17% of the sample).”
MethodBécares, L., Nazroo, J., Albor, C., Chandola, T., & Stafford, M. (2012) · Social Science & Medicine (1967) · doi:10.1016/j.socscimed.2011.11.007 · Cited by 50
Knudsen, H. K., & Studts, J. (2010) · Journal of Substance Abuse Treatment · doi:10.1016/j.jsat.2009.12.002 · Cited by 50
“The “micombine” command was then used during model estimation in order to produce a single set of results based on pooling the estimates from the analyses of each of the five imputed datasets (Barnard & Rubin, 1999; Royston, 2004, 2005a, 2005b).”
MethodSchool-based alcohol education: results of a cluster-randomized controlled trial.
Morgenstern, M., Wiborg, G., Isensee, B., & Hanewinkel, R. (2009) · Addiction · doi:10.1111/j.1360-0443.2008.02471.x · Cited by 50
Ben-Shlomo, Y., Naqvi, H., & Baker, I. (2007) · Heart · doi:10.1136/hrt.2007.119412 · Cited by 50
“we also examined whether the results differed by gender and tested for an ethnicity–gender interaction. The main analyses were performed only on those with complete data on ethnicity, but we also undertook a sensitivity analysis by imputing missing values. We used multiple imputation by chained equations and created f…”
MethodOsler, M., Andersen, A., Laursen, B., & Lawlor, D. (2007) · International Journal of Epidemiology · doi:10.1093/ije/dyl261 · Cited by 50
Purdy, S., Griffin, T., Salisbury, C., & Sharp, D. (2011) · Public Health · doi:10.1016/j.puhe.2010.07.006 · Cited by 50
“The main analysis was repeated using multiple imputation of the missing data (10 iterations) to examine the effect of exclusion of the 102 practices.(21) To assess the possible impact of admissions to Welsh and Scottish hospitals from practices in border areas, the analysis was repeated excluding the 393 practices wit…”
MethodEconomic growth, government policies, and forest transition in China
Wang, J.-Y., Xin, L.-J., & Wang, Y. (2019) · Regional Environmental Change · doi:10.1007/s10113-018-1450-3 · Cited by 49
Naicker, K., Øverland, S. N., Johnson, J. A., Manuel, D. G., Skogen, J. C., Sivertsen, B., & Colman, I. (2017) · Psychoneuroendocrinology · doi:10.1016/j.psyneuen.2017.07.002 · Cited by 53
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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