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 MICE, generating five imputed data sets.
“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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<b>mice</b>: Multivariate Imputation by Chained Equations in<i>R</i>
Buuren, S. V., & Groothuis-Oudshoorn, K. (2011) · Journal of Statistical Software · doi:10.18637/jss.v045.i03 · Cited by 13,870 · see citing works
“Schafer (1997) developed various JM techniques for imputation under the multivariate normal, the log-linear, and the general location model.”
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White, I. R., Royston, P., & Wood, A. M. (2011) · Statistics in Medicine · doi:10.1002/sim.4067 · Cited by 9,792 · see citing works
“Instead, as data analysts, we want to be confident that a repeat analysis of the same data would produce essentially the same results [13, 36].”
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“This is partly because statistical methods that can tackle problems arising from missing data have, until recently, not been readily accessible to medical researchers. However, multiple imputation—a relatively flexible, general purpose approach to dealing with missing data—is now available in standard statistical soft…”
BackgroundSelf-citationThwaites, G. (2010) · PLoS ONE · doi:10.1371/journal.pone.0014170 · Cited by 2,905
Multiple imputation of discrete and continuous data by fully conditional specification
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MethodMultiple Imputation of Missing Values: Update
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“Patrick Royston Cancer Group MRC Clinical Trials Unit 222 Euston Road London NW1 2DA UK 1 Introduction Royston (2004) introduced mvis, an implementation for Stata of MICE, a method of multiple multivariate imputation of missing values under missing-at-random (MAR) assumptions. In a second article, Royston (2005) descr…”
InfluentialSelf-citation4. Regression with Missing Ys: An Improved Strategy for Analyzing Multiply Imputed Data
von Hippel, P. T. (2007) · Sociological Methodology · doi:10.1111/j.1467-9531.2007.00180.x · Cited by 1,495 · see citing works
“ing, and imputation was tricky because Y was a categorical variable, with four possible values. Although there does exist software for imputing multicategory variables (e.g., Raghunathan et al. 2002; Royston 2004), initially it was more convenient to use imputation software that assumed normality (the MI procedure in…”
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Multiple Imputation by Chained Equations (MICE): Implementation in <i>Stata</i>
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“As described by Royston (2005b), to satisfy the normality assumption for a continuous variable, a transformation toward normality may be effective.”
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“Royston [18] created a version of MICE in Stata.”
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“Our missing data analysis procedures used missing at random (MAR) assumptions. We used the MICE (multivariate imputation by chained equations) method of multiple multivariate imputation in STATA.”
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“We used the Cox proportional hazards model in the derivation dataset to estimate the coefficients associated with each potential risk factor for the first ever recorded diagnosis of cardiovascular disease for men and women separately. A priori we specified the variables we intended to include in the model on the basis…”
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“Before imputing the missing values, the skewed variables wcc and t_mt were transformed to an approximate Normal distribution using the lnskew0 program in Stata, which replaces a variable X with log(±X−k) where k and the sign are chosen so that log(±X−k) has zero skewness.”
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“We used an imputation technique (Royston, 2004) to predict whether a student would be in need of developmental instruction in math based on their 12th grade test scores.”
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“At the scale level we did multiple imputation by using the MICE (multivariate imputation by chained equations) method (Allison, 2002; Royston, 2004; Van Buuren, Boshuizen, & Knook, 1999).”
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“An alternative for FCS is to impute values using prediction matching (12, 24), under which the missing value is replaced by the nonmissing value for the case whose predictive mean is closest to that of the case with the missing value.”
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“Multiple imputation (10 cycles) was used for missing information on obesity, dietary, or lifestyle indicators in the final models of hypovitaminosis D (29).”
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“Using Stata 10, we employ multiple imputation to account for variables with missing data and we estimate our models using OLS regression techniques.(37) The control variable with the most missing values (10%) was ACT score.”
What Improves with Increased Missing Data Imputations?
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“First, Royston (2004) and Schafer (1997a) reported conflicting conclusions on the importance of imputation variability on O h m .”
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“[28,29] discuss the impact of the number of imputations on the precision of the estimates and suggest ways of determining the required number of imputations by evaluating the sampling error of the multiple-imputation estimates.”
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“to combine parameter estimates across the five imputed data sets obtained by multiple imputation.(26)”
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“For the present study, we used multiple imputation by chained equations (i.e., MICE, Royston, 2004) to generate five complete data sets that combined observed and imputed values.”
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“Third, to ensure appropriate analysis, we utilized several econometric methods such as multiple imputation of missing values (King et al., 2001; Royston & Divison, 2004; Rubin, 1996), the Heckman correction model for solving the “sample selection bias” (Heckman, 1979), and the sensitivity analysis…”
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“Patrick Royston’s ICE (imputation using chained equations), implemented within Stata, provides support for categorical missing values (Royston 2005).”
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“1 Introduction Royston (2004) introduced mvis, an implementation for Stata of multiple imputation by chained equations (MICE), a method of multiple multivariate imputation of missing values under missing-at-random (MAR) assumptions. The name of the main command was changed to ice (imputation by chained equations) in R…”
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“…which was a cross-section of the U.S. pop- 6 If the measures of parents’ or children’s family characteristics are missing but the family meets all other criteria for selection into the sample, we use a regression imputation method developed by Royston (2004) to impute values for nonresponse.”
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“To address bias from missing data (assumed missing at random), 2 additional methods were performed: last observation carried forward and the multivariate imputation by chained equations method of multiple imputation in Stata (5 data sets were imputed and analyzed).(19,20) Finally, analyses for center effect and adjust…”
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Smith, G., Ben-Shlomo, Y., Beswick, A., Yarnell, J., Lightman, S., & Elwood, P. (2005) · Circulation · doi:10.1161/circulationaha.104.489088 · Cited by 348 · see citing works
The Continuum of Psychotic Symptoms in the General Population: A Cross-national Study
Nuevo, R., Chatterji, S., Verdes, E., Naidoo, N., Arango, C., & Ayuso-Mateos, J. L. (2012) · Schizophrenia Bulletin · doi:10.1093/schbul/sbq099 · Cited by 340 · see citing works
THE SEXUAL DOUBLE STANDARD AND ADOLESCENT PEER ACCEPTANCE
Kreager, D., & Staff, J. (2009) · Social psychology quarterly · doi:10.1177/019027250907200205 · Cited by 336 · see citing works
Rural-Nonrural Disparities in Postsecondary Educational Attainment Revisited
Byun, S.-Y., Meece, J., & Irvin, M. J. (2011) · The American Educational Research Journal · doi:10.3102/0002831211416344 · Cited by 328 · see citing works
“To address the nested nature of the NELS data (i.e., students were randomly selected within the sampled schools), we used the cluster option in Stata, which adjusts for the inflated standard errors resulting from the violation of the independent errors (Rogers, 1993).”
MethodInfluentialChildren's early approaches to learning and academic trajectories through fifth grade.
Li-Grining, C., Votruba-Drzal, E., Maldonado-Carreño, C., & Haas, K. (2010) · Developmental Psychology · doi:10.1037/a0020066 · Cited by 322 · see citing works
Coparenting and nonresident fathers’ involvement with young children after a nonmarital birth
Carlson, M., Mclanahan, S., & Brooks-Gunn, J. (2008) · Demography · doi:10.1353/dem.0.0007 · Cited by 322 · see citing works
“We use Stata 9.2 SE with the ice (imputation by chained equations) command developed by Patrick Royston (Royston 2004).”
MethodInfluentialLate mortality after sepsis: propensity matched cohort study
Prescott, H., Osterholzer, J., Langa, K., Angus, D., & Iwashyna, T. (2016) · British medical journal · doi:10.1136/bmj.i2375 · Cited by 320 · see citing works
Long working hours and sleep disturbances: the Whitehall II prospective cohort study
Virtanen, M., Ferrie, J. E., Gimeno, D., Vahtera, J., Elovainio, M., Singh-Manoux, A., Marmot, M. G., & Kivimäki, M. (2009) · SLEEP · doi:10.1093/sleep/32.6.737 · Cited by 316 · see citing works
“The estimates are obtained by averaging across the results from each of these 20 datasets using Rubin’s rules.(34) The procedure takes account of uncertainty in the imputation as well as uncertainty due to random variation, as undertaken in all multivariable analyses.”
MethodStaging Exchange Partner Choices: When Do Status and Reputation Matter?
Jensen, M., & Roy, A. (2008) · Academy of Management Journal · doi:10.5465/amj.2008.32625985 · Cited by 316 · see citing works
“We used Royston's (2004) implementation for Stata of the MICE method of multiple imputation (Buuren, Boshuizen, & Knook, 1999; Little & Rubin, 1987).”
A Prospective Study of Frailty in Nephrology-Referred Patients With CKD
Roshanravan, B., Khatri, M., Robinson-Cohen, C., Levin, G. P., Patel, K., de Boer, I. D., Seliger, S., Ruzinski, J., Himmelfarb, J., & Kestenbaum, B. (2012) · American Journal of Kidney Diseases · doi:10.1053/j.ajkd.2012.05.017 · Cited by 315 · see citing works
“Current smoking 99 63 (19) 53 (19) 10 (22)”
Lawlor, D., Benfield, L., Logue, J., Tilling, K., Howe, L., Fraser, A., Cherry, L., Watt, P., Ness, A., Smith, G. D., et al. (2010) · British medical journal · doi:10.1136/bmj.c6224 · Cited by 315 · see citing works
“To increase efficiency and minimise selection bias we used multivariate multiple imputation to impute missing variables for participants considered to be eligible (that is, those attending one or other of the 9-10 or 11-12 year assessment and also the 15-16 year assessment), including all exposures, covariables, outco…”
MethodWolfe, F., & Marmor, M. (2010) · Arthritis care & research · doi:10.1002/acr.20133 · Cited by 314 · see citing works
“The MI method used was imputation with chained equations, with bootstrap sampling of the non-missing observations (10).”
MethodImpact speed and a pedestrian's risk of severe injury or death.
Tefft, B. C. (2013) · Accident Analysis and Prevention · doi:10.1016/j.aap.2012.07.022 · Cited by 309 · see citing works
Effects of High School Course-Taking on Secondary and Postsecondary Success
Long, M. C., Conger, D., & Iatarola, P. (2012) · American Educational Research Journal · doi:10.3102/0002831211431952 · Cited by 305 · see citing works
“To improve efficiency and to avoid sampling bias, we impute the missing values using multiple imputation by chained equations (Royston, 2004; Rubin, 1987) creating five multiply imputed data sets.”
MethodDearing, E., Mccartney, K., & Taylor, B. A. (2009) · Child Development · doi:10.1111/j.1467-8624.2009.01336.x · Cited by 304 · see citing works
“Specifically, we used MI by chained equations (i.e., MICE; Royston, 2004), computing five complete data sets that combined observed and imputed values.”
MethodButterworth, P., Rodgers, B., & Windsor, T. D. (2009) · Social Science & Medicine · doi:10.1016/j.socscimed.2009.05.008 · Cited by 303 · see citing works
“The multiple imputation procedure ICE available in Stata 9.0 was used to impute missing data using the multiple imputation by chained equations procedure (Royston, 2004).”
MethodInfluentialFerraro, K., Schafer, M. H., & Wilkinson, L. (2015) · American Sociological Review · doi:10.1177/0003122415619617 · Cited by 303 · see citing works
Do Payments for Environmental Services Affect Forest Cover? A Farm-Level Evaluation from Costa Rica
Arriagada, R., Ferraro, P. J., Sills, E., Pattanayak, S., & Cordero-Sancho, S. (2012) · Land Economics · doi:10.3368/le.88.2.382 · Cited by 303 · see citing works
IQ and non-clinical psychotic symptoms in 12-year-olds: results from the ALSPAC birth cohort
Horwood, J., Salvi, G., Thomas, K., Duffy, L., Gunnell, D., Hollis, C., Lewis, G., Menezes, P., Thompson, A., Wolke, D., et al. (2008) · The British journal of psychiatry : the journal of mental science · doi:10.1192/bjp.bp.108.051904 · Cited by 300 · see citing works
Gestational Diabetes Mellitus: Clinical Predictors and Long-Term Risk of Developing Type 2 Diabetes
Lee, A. J., Hiscock, R., Wein, P., Walker, S., & Permezel, M. (2007) · Diabetes Care · doi:10.2337/dc06-1816 · Cited by 300 · see citing works
“The multiple imputation technique used the imputation by chained equations method (16) to create 20 imputed datasets, from which parameter point and variance estimates (adjusted using Rubin’s rules) were computed.”
MethodIncluding all individuals is not enough: lessons for intention-to-treat analysis
White, I., Carpenter, J., & Horton, N. (2012) · Clinical Trials · doi:10.1177/1740774512450098 · Cited by 299 · see citing works
“MI is implemented by the multivariate imputation by chained equations (MICE) algorithm [28,61,62].”
MethodCheadle, J. E. (2008) · Sociology of Education · doi:10.1177/003804070808100101 · Cited by 296 · see citing works
Multiple Imputation of Missing Values: Further Update of Ice, with an Emphasis on Interval Censoring
Royston, P. (2007) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x0800700401 · Cited by 295 · see citing works
“Royston (2004) introduced mvis, an implementation for Stata of MICE, a method of multiple multivariate imputation of missing values under missing-at-random (MAR) assumptions.”
Self-citation
- 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 › Computer Science › Artificial Intelligence › 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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