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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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“Additionally, this study imputed any missing values for at least one of the covariates (required for approximately 17 percent of our sample) by using switching regression, an iterative multivariable regression technique of multiple imputations by chained equations (Royston, 2004) implemented in Stata 11.”
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MethodDelays From First Medical Contact to Antibiotic Administration for Sepsis*
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Lawlor, D., Macdonald-Wallis, C., Fraser, A., Nelson, S., Hingorani, A., Smith, G. D., Sattar, N., & Deanfield, J. (2011) · European Heart Journal · doi:10.1093/eurheartj/ehr300 · Cited by 151
“78 Offspring apolipoprotein A1 (mg/dL) 136 (20) [3369] 135 (19) [689] 136 (17) [88] 0.”
Physical Activity and Change in Estimated GFR among Persons with CKD
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Parity and breastfeeding are protective against breast cancer in Nigerian women
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MethodLepper, P. M., Ott, S. R., Nüesch, E., von Eynatten, M., Schumann, C., Pletz, M. W., Mealing, N. M., Welte, T., Bauer, T. T., Suttorp, N., et al. (2012) · BMJ · doi:10.1136/bmj.e3397 · Cited by 152
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MethodHuybregts, L., Roberfroid, D., Lanou, H. B., Menten, J., Méda, N., Camp, J. V., & Kolsteren, P. (2009) · American Journal of Clinical Nutrition · doi:10.3945/ajcn.2009.28253 · Cited by 147
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El Morr, C., Ritvo, P., Ahmad, F., Moineddin, R., & MVC Team (2020) · JMIR Mental Health · doi:10.2196/18595 · Cited by 145
“Missing data in the intervention group are also a limitation, but we mitigated the missing data by multiple imputation, a robust high-quality imputation method [66,67].”
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“Multiple imputation was implemented by employing the user-written “ice” (imputation by chained equations) program, which was run on Stata version 10 SE (Royston, 2004, 2005a, 2005b).”
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Lee, C.-J., Gray, S., & Lewis, N. (2010) · Patient Education and Counseling · doi:10.1016/j.pec.2010.09.004 · Cited by 144
“Multiple imputation was used to address missing data following procedures recommended by Allison [36] using STATA 10 and the ICE program [37].”
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“At the scale level we did multiple imputation using the MICE method of multivariate imputation (Allison, 2002; Royston, 2004; Van Buuren, Boshuizen, & Knook, 1999).”
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Zammit, S., Odd, D., Horwood, J., Thompson, A., Thomas, K., Menezes, P., Gunnell, D., Hollis, C., Wolke, D., Lewis, G., et al. (2009) · Psychological Medicine · doi:10.1017/s0033291708005126 · Cited by 142
“2001; Royston, 2004).”
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“We used the user-written ice command in Stata to impute missing values of the covariates for the adjusted OLS analysis [45, 46].”
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“We chose to do this by stratifying the imputation model by gender (Royston 2005), though this could also have been accomplished by including the interaction when specifying custom prediction equations (see mi impute chained).”
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“Nonetheless, to address potential bias resulting from item-missing data, we used multiple imputation — the statistical package Stata (the ICE procedure) (”
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“To investigate possible bias due to missing data, we used multiple multivariate imputation to impute values in any covariates with missing values (Royston, 2004).”
MethodMcnamara, T., & Gonzales, E. (2011) · The journals of gerontology. Series B, Psychological sciences and social sciences · doi:10.1093/geronb/gbr055 · Cited by 137
“Imputed data sets were created through data augmentation (Acock, 2005), using chained equations as implemented in Stata (Royston, 2004).”
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“Beginner 594 (25) 178 (16) 163 (30) 5631 (33) 544 (2.”
InfluentialCulture and Identity‐Protective Cognition: Explaining the White‐Male Effect in Risk Perception
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“Missing data were imputed through multiple imputation with Stata using the MICE (multivariate imputation by chained equations) module (Royston, 2004).”
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Pollitt, R. A., Kaufman, J. S., Rose, K. M., Roux, A. V. D., Zeng, D., & HEISS, G. M. (2008) · Journal of Epidemiology & Community Health · doi:10.1136/jech.2006.054106 · Cited by 134
Exposure to statins and risk of common cancers: a series of nested case-control studies
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“As body mass index, smoking status and Townsend deprivation score may be important confounders and have a certain amount of missing data, we used multiple imputation for the missing values[35,36].”
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“To ensure that patients with missing values were not excluded from the multivariable analysis, we used the technique of multiple imputation as described by Royston.28,29 Missing values were imputed 10 times using switching regression to create 10 complete datasets that were each independently analyzed.”
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“Missing information was imputed using the multivariate imputation by chained equation method [38].”
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Ramírez, A., Freres, D. R., Martinez, L. S., Lewis, N., Bourgoin, A., Kelly, B., Lee, C.-J., Nagler, R. H., Schwartz, J., & Hornik, R. C. (2013) · Journal of health communication · doi:10.1080/10810730.2012.743632 · Cited by 130
“We used the ICE module (Royston, 2005) to conduct multiple imputations; consistent with Rubin and others’ recommendations, five imputed data sets were generated.”
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“Missing data at the individual scale level for children who actively participated in the study were handled using imputation with the MICE method of multivariate imputation (Royston, 2004).”
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“Missing values have been imputed using multiple imputation (Royston, 2004).”
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Kohtamäki, M., Kraus, S., Mäkelä, M. M., & Rönkkö, M. (2012) · International Journal of Entrepreneurial Behaviour & Research · doi:10.1108/13552551211204201 · Cited by 125
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“According to Royston (2004), there is no firm rule available to determine the proportion of missing observations at which multiple imputation is no longer reliable.”
BackgroundInfluentialBereznicki, H. G. K., Clark, G. M., Youssef, G. J., Fried, P. J., Jannati, A., Davies, C. B., Gomes‐Osman, J., Stamm, J. M., Chung, S. W., Bowe, S. J., et al. (2020) · Brain stimulation · doi:10.1016/j.brs.2020.07.018 · Cited by 167
Breastfeeding and risk of overweight and obesity at nine-years of age.
McCrory, C., & Layte, R. (2012) · Social Science & Medicine (1967) · doi:10.1016/j.socscimed.2012.02.048 · Cited by 128
“Consequently, missing values on household income were imputed using the Multiple Imputation UVIS programs implemented in STATA by Royston (2004). Thus, the effective case base for the analyses that follow was 7798.”
MethodPsychiatric Disorders in Extremely Preterm Children: Longitudinal Finding at Age 11 Years in the EPI
Johnson, S., Hollis, C., Kochhar, P., Hennessy, E., Wolke, D., & Marlow, N. (2010) · Journal of the American Academy of Child & Adolescent Psychiatry · doi:10.1016/j.jaac.2010.02.002 · Cited by 128
Racial and gender identity among Black adolescent males: an intersectionality perspective.
Rogers, L. E., Scott, M., & Way, N. (2015) · Child Development · doi:10.1111/cdev.12303 · Cited by 127
“Specifically, we primarily used a series of “chained regressions” in which variables are imputed in order from least to most missing (Royston, 2004; van Buuren, 2012).”
MethodOldehinkel, A. J., Ormel, J., Bosch, N. M., Bouma, E., van Roon, A. M., Rosmalen, J. G. M., & Riese, H. (2010) · Psychophysiology · doi:10.1111/j.1469-8986.2010.01118.x · Cited by 126
Gardner, M., Roth, J. L., & Jeanne Brooks-gunn, B. (2009) · Developmental Psychology · doi:10.1037/a0014063 · Cited by 109
“We used the Multivariate Imputation by Chained Equations program (Royston, 2004) in STATA 8.0 to perform multiple imputation; this program uses nonmissing data from specified variables to generate predicted scores for missing values.”
MethodInfluentialYoung Adult Outcomes and the Life-Course Penalties of Parental Incarceration
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International comparison of prehospital trauma care systems
Roudsari, B. S., Nathens, A. B., Cameron, P. A., Civil, I. D., Gruen, R. L., Koepsell, T. D., Lecky, F. E., Lefering, R. L., Liberman, M., Mock, C., et al. (2007) · Injury · doi:10.1016/j.injury.2007.03.028 · Cited by 121
“We used the ICE command written by Royston for STATA (STATA Corporation, College Station, Texas) in order to implement the multiple imputation process.(34,35) Each imputed dataset was analysed separately.”
MethodInformational Lobbying in the European Union: The Effect of Organisational Characteristics
Klüver, H. (2012) · West European Politics · doi:10.1080/01402382.2012.665737 · Cited by 125
“Multiple imputation should however be avoided for variables that have 50 per cent or more missing values, which is the case for all explanatory variables in the model (Royston 2004 : 240).”
Hippisley‐Cox, J., & Coupland, C. A. C. (2011) · British Journal of General Practice · doi:10.3399/bjgp11x606627 · Cited by 92
Haskins, A. R., & Jacobsen, W. C. (2017) · American Sociological Review · doi:10.1177/0003122417709294 · Cited by 124
Sikora, J., Evans, M., & Kelley, J. (2019) · Social Science Research · doi:10.1016/j.ssresearch.2018.10.003 · Cited by 123
“To maximise the use of available information we imputed the missing data on independent variables separately in each society (see Supplementary materials Appendix Table 1), utilising chained equations and generating 10 imputed datasets to match the number of plausible values (Royston, 2004).”
MethodHippisley-Cox, J., & Coupland, C. (2013) · BMJ Open · doi:10.1136/bmjopen-2013-003482 · Cited by 123
“Our final model was fitted based on five multiply imputed datasets using Rubin’s rules to combine estimates and standard errors to allow for the uncertainty due to imputing missing data.(20) We took the logarithm of HR for each variable from the final model and used these as weights for the risk equations.”
MethodGimsing, P., Carlson, K. E., Turesson, I., Fayers, P. M., Waage, A., Vangsted, A. J., Mylin, A. K., Gluud, C. N., Juliusson, G., Gregersen, H., et al. (2010) · The Lancet Oncology · doi:10.1016/s1470-2045(10)70198-4 · Cited by 117
Roettger, M., Swisher, R. R., Kuhl, D. C., & Chávez, J. M. (2010) · Addiction · doi:10.1111/j.1360-0443.2010.03110.x · Cited by 122
“The STATA ‘ice’ procedure was used to estimate missing values, assuming that the data were missing at random [38,39].”
Sleep characteristics and cardiovascular events in a large Swedish cohort
Westerlund, A., Bellocco, R., Sundström, J., Adami, H., Åkerstedt, T., & Lagerros, Y. T. (2013) · European Journal of Epidemiology · doi:10.1007/s10654-013-9802-2 · Cited by 129
“To assess the influence of missing values on the observed estimates, under the assumption of missing completely at random, we carried out multiple imputation by chained equations [22, 23].”
MethodFlaherty, J., & Brown, R. B. (2010) · American Journal of Sociology · doi:10.1086/653600 · Cited by 120
Decomposing the Components of Friendship and Friends' Influence on Adolescent Drinking and Smoking
Fujimoto, K., & Valente, T. W. (2012) · Journal of Adolescent Health · doi:10.1016/j.jadohealth.2011.11.013 · Cited by 117
Veenstra, R., Lindenberg, S., Tinga, F., & Ormel, J. (2010) · International Journal of Behavioral Development · doi:10.1177/0165025409347987 · Cited by 118
“At the scale level we performed multiple imputation using the MICE method of multivariate imputation (Allison, 2002; Royston, 2004).”
MethodMuscle strength in youth and cardiovascular risk in young adulthood (the European Youth Heart Study)
Grøntved, A., Ried‐Larsen, M., Møller, N. C., Kristensen, P. L., Froberg, K., Brage, S., & Andersen, L. B. (2013) · British Journal of Sports Medicine · doi:10.1136/bjsports-2012-091907 · Cited by 125
Xu, J., & Hampden‐Thompson, G. (2012) · Comparative Education Review · doi:10.1086/661289 · Cited by 116
Votruba‐Drzal, E., Coley, R. L., Maldonado‐Carreño, C., Li-Grining, C. P., & Chase-Lansdale, P. L. (2010) · Child Development · doi:10.1111/j.1467-8624.2010.01485.x · Cited by 127
Pujades-Rodriguez, M., Balkan, S., Arnould, L., Brinkhof, M., & Calmy, A. (2010) · Journal of the American Medical Association (JAMA) · doi:10.1001/jama.2010.980 · Cited by 118
Web-based collaborative care for type 1 diabetes: a pilot randomized trial
McCarrier, K. P., Ralston, J. D., Hirsch, I. B., Lewis, G., Martin, D. P., Zimmerman, F. J., & Goldberg, H. I. (2009) · Diabetes Technology & Therapeutics · doi:10.1089/dia.2008.0063 · Cited by 117
“Because a complete case approach excluding these individuals could potentially bias the analyses in the presence of differential drop-out between groups, primary analyses of both A1C and DES outcomes were performed with multiple imputation of missing values using the ‘‘ICE’’ procedure in Stata.20,21 Sensitivity analys…”
MethodLong-term consequences of youth volunteering: Voluntary versus involuntary service
Kim, J., & Morgül, K. (2017) · Social Science Research · doi:10.1016/j.ssresearch.2017.05.002 · Cited by 117
Scholarly Culture and Academic Performance in 42 Nations
Evans, M., Kelley, J., & Sikora, J. (2014) · Social Forces · doi:10.1093/sf/sou030 · Cited by 117
Depleting Capital?: Race, Wealth and Informal Financial Assistance
O'Brien, R. L. (2012) · Social Forces · doi:10.1093/sf/sos132 · Cited by 117
Explaining Race, Poverty, and Gender Disparities in Advanced Course-Taking.
Conger, D., Long, M., & Iatarola, P. (2009) · Journal of Policy Analysis and Management · doi:10.1002/pam.20455 · Cited by 117
Evaluation of software for multiple imputation of semi-continuous data
Yu, L.-M., Burton, A., & Rivero-Arias, O. (2007) · Statistical Methods in Medical Research · doi:10.1177/0962280206074464 · Cited by 117
Using built environment characteristics to predict walking for exercise
Lovasi, G., Moudon, A., Pearson, A., Hurvitz, P., Larson, E. B., Siscovick, D., Berke, E. M., Lumley, T., & Psaty, B. (2008) · International Journal of Health Geographics · doi:10.1186/1476-072x-7-10 · Cited by 116
“For adjusted models, missing values for income (10 percent) and education (less than one percent) were estimated through multiple imputation [58].”
MethodLobbying as a collective enterprise: winners and losers of policy formulation in the European Union
Klüver, H. (2012) · Journal of European Public Policy · doi:10.1080/13501763.2012.699661 · Cited by 119
“Multiple imputation should however be avoided for variables that have 50 per cent or more missing values (Royston 2004: 240).”
BackgroundThe Impact of Education on Inter-Group Attitudes: A Multiracial Analysis
Wodtke, G. (2012) · Social psychology quarterly · doi:10.1177/0190272511430234 · Cited by 114
Dispositional Optimism Protects Older Adults From Stroke: The Health and Retirement Study
Kim, E. S., Park, N., & Peterson, C. (2011) · Stroke · doi:10.1161/strokeaha.111.613448 · Cited by 114
Griffin, S. C., Barber, J., Manca, A., Sculpher, M., Thompson, S. G., Buxton, M. J., & Hemingway, H. (2007) · BMJ · doi:10.1136/bmj.39129.442164.55 · Cited by 107
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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