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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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BackgroundMethodWan, E., Fung, C., Fong, D., & Lam, C. (2016) · Journal of diabetes and its complications · doi:10.1016/j.jdiacomp.2016.05.024 · Cited by 49
Watkins, A. M., & Melde, C. (2016) · Criminal Justice and Behavior · doi:10.1177/0093854816631797 · Cited by 66
“The decision to use the psmatch2 program in Stata 10.0 was based upon personal preference and familiarity with postestimation procedures the author(s) utilized for model specification and diagnostics.”
InfluentialJacob, M., Klein, M., & Iannelli, C. (2015) · European Sociological Review · doi:10.1093/esr/jcv006 · Cited by 49
“To avoid an excessive reduction in the number of cases analysed, we imputed missing values by multiple imputation via ‘chained equations’ (Rubin, 1996) using STATA module ‘ice’ (Royston, 2005).”
MethodChild height, health and human capital: Evidence using genetic markers
von Hinke, S., Smith, G. D., Lawlor, D. A., Propper, C., & Windmeijer, F. (2012) · European Economic Review · doi:10.1016/j.euroecorev.2012.09.009 · Cited by 45
“We deal with missing values on other covariates by using multivariate imputation (Royston, 2004).”
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Serum HE4 Level is an Independent Prognostic Factor in Epithelial Ovarian Cancer
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“We fit a linear relationship based on a visual assessment that the associations were generally linear across the measured spectrum of 25-OHD concentrations and that fractional polynomial assessment indicated that nonlinear models did not fit the data statistically better than the linear form (19, 20).”
MethodDosage Effects on School Readiness: Evidence from a Randomized Classroom-Based Intervention
Zhai, F., Raver, C. C., Jones, S. M., Li-Grining, C. P., Pressler, E., & Gao, Q. (2010) · Social Service Review · doi:10.1086/657988 · Cited by 46
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Jones, R. N., Rudolph, J. L., Inouye, S. K., Yang, F. M., Fong, T. G., Milberg, W., Tommet, D., Metzger, E. D., Cupples, L. A., & Marcantonio, E. R. (2010) · Journal of Clinical and Experimental Neuropsychology · doi:10.1080/13803391003662728 · Cited by 51
“No tests, except category fluency and digit symbol substitution were normally distributed (p<.05) (D'Agostino, Belanger, & D'Agostino Jr, 1990;Royston, 2005) and thus, the decile transformation was justified.”
InfluentialLewis, N., Gray, S., Freres, D. R., & Hornik, R. (2009) · Health Communication · doi:10.1080/10410230903264030 · Cited by 49
“Analyses using ordinary least squares regression were performed with the Stata 10 survey module (Statacorp, 2007), with the ICE add-in package for multiple imputation of missing data by chained equations (Royston, 2005).”
Schuster, M., Chung, P., Elliott, M., Garfield, C., Vestal, K. D., & Klein, D. J. (2009) · American Journal of Public Health · doi:10.2105/ajph.2008.138313 · Cited by 49
Multiple Edit/Multiple Imputation for Multivariate Continuous Data
Ghosh-Dastidar, B., & Schafer, J. (2003) · doi:10.1198/016214503000000738 · Cited by 49
Alsaadon, H., Afroz, A., Karim, A., Habib, S., Alramadan, M. J., Billah, B., & Shetty, A. (2022) · BMC Public Health · doi:10.1186/s12889-022-12509-1 · Cited by 48
“Missing data were imputed five times using the chained equation method, creating five imputed samples [33, 34].”
MethodImputing missing values using cumulative linear regression
Mostafa, S. M. (2019) · CAAI Transactions on Intelligence Technology · doi:10.1049/trit.2019.0032 · Cited by 48
Cheliotis, M., Gkerekos, C., Lazakis, I., & Theotokatos, G. (2019) · Ocean Engineering · doi:10.1016/j.oceaneng.2019.106220 · Cited by 48
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Handling missing data in large healthcare dataset: A case study of unknown trauma outcomes
Mirkes, E. M., Coats, T., Levesley, J., & Gorban, A. N. (2016) · Comput. Biol. Medicine · doi:10.1016/j.compbiomed.2016.06.004 · Cited by 48
“The multiple imputation algorithms are implemented in the standard statistical software [33].”
MethodZuba, M., & Schneider, U. (2013) · Journal of Family and Economic Issues · doi:10.1007/s10834-012-9347-7 · Cited by 48
“Missing values were imputed using the STATA module ›mi ice‹, which implements multiple imputation using chained equations (Royston 2004).”
MethodMultiple Imputation of Missing Data: A Simulation Study on a Binary Response
Hardt, J., Herke, M., Brian, T., & Laubach, W. (2013) · Open Journal of Statistics · doi:10.4236/ojs.2013.35043 · Cited by 48
Henderson, M., Richards, M., Stansfeld, S., & Hotopf, M. (2012) · BMJ Open · doi:10.1136/bmjopen-2011-000777 · Cited by 48
In-hospital formula supplementation of breastfed babies: a population-based survey.
Biro, M., Sutherland, G., Yelland, J., Hardy, P., & Brown, S. (2011) · Birth · doi:10.1111/j.1523-536x.2011.00485.x · Cited by 48
Campbell, H., Gray, A., Harris, A., Briggs, A., & Taylor, M. (2010) · British Journal of Cancer · doi:10.1038/sj.bjc.6605863 · Cited by 48
“We performed MI in STATA (version 10; Stata Corp., College Station, TX, USA), imputing three values for each missing data point and in effect creating three separate data sets (Royston, 2004).”
MethodCombined effects of obesity and physical activity in predicting mortality among men
Orsini, N., Bellocco, R., Bottai, M., Pagano, M., Michaëlsson, K., & Wolk, A. (2008) · Journal of Internal Medicine · doi:10.1111/j.1365-2796.2008.01985.x · Cited by 48
A cautionary case study of approaches to the treatment of missing data
Paul, C., Mason, W., McCaffrey, D., & Fox, S. (2008) · Stat. Methods Appl. · doi:10.1007/s10260-007-0090-4 · Cited by 48
“The technique requires that the missing observations be imputed M times (Rubin 1996) indicates that M = 3 or M = 5 is often sufficient; Royston (2004) suggests the use of a larger M .”
MethodColarusso, L., Serafini, M., Lagerros, Y., Nyren, O., la Vecchia, C., Rossi, M., Ye, W., Tavani, A., Adami, H., Grotta, A., et al. (2017) · Nutrition (Burbank, Los Angeles County, Calif.) · doi:10.1016/j.nut.2016.07.009 · Cited by 48
Guiriguet, C., Muñoz-Ortiz, L., Burón, A., Rivero, I., Grau, J., Vela-Vallespín, C., Vilarrubí, M., Torres, M., Hernández, C., Méndez-Boo, L., et al. (2016) · British Journal of General Practice · doi:10.3399/bjgp16x685657 · Cited by 47
Remiro‐Azócar, A., Heath, A., & Baio, G. (2022) · Research Synthesis Methods · doi:10.1002/jrsm.1565 · Cited by 46
“This strategy is common in implementations of sequential conditional algorithms for parametric multiple imputation.(48,49) For instance, consider two baseline characteristics: age, which is a continuous variable, and the presence of a 722 REMIRO-AZÓCAR ET AL.”
MethodBergold, S., Wirthwein, L., & Steinmayr, R. (2020) · Gifted Child Quarterly · doi:10.1177/0016986220932533 · Cited by 78
“We chose the upper bound of the 95% confidence interval of the highest FMI and a coefficient of variation (CV) of .05, as recommended by Royston (2004).”
MethodCai, M., Loy, S., Tan, K., Godfrey, K., Gluckman, P., Chong, Y., Shek, L., Cheung, Y., Lek, N., Lee, Y. S., et al. (2018) · JAMA Network Open · doi:10.1001/jamanetworkopen.2018.5025 · Cited by 47
Re-thinking social exclusion in later life: a case for a new framework for measurement
MacLeod, C., Ross, A., Sacker, A., Netuveli, G., & Windle, G. (2017) · Ageing & Society · doi:10.1017/s0144686x17000794 · Cited by 47
“0 (Royston 2004; Royston 2005) to impute missing values for respondents who were missing a single item within a subscale.”
BackgroundAsiimwe, S. B., Kanyesigye, M., Bwana, B., Okello, S., & Muyindike, W. (2015) · BMC Infectious Diseases · doi:10.1186/s12879-016-1392-7 · Cited by 47
“We then multiply imputed missing predictor values, using variables with complete information (age, sex, OI/comorbidity diagnoses, dropout status, and follow-up time), as well as the available data from the variables with missing values [31].”
MethodAuld, A., Mbofana, F., Shiraishi, R. W., Alfredo, C., Sánchez, M., Ellerbrock, T., & Nelson, L. (2013) · PLoS ONE · doi:10.1371/journal.pone.0054665 · Cited by 47
“The ice [21–23] procedure in Stata was used to create 20 imputed datasets.”
MethodTulloch, A., Khondoker, M., Fearon, P., & David, A. (2012) · BMC Psychiatry · doi:10.1186/1471-244x-12-121 · Cited by 47
“After exploring missing data, we then used multiple imputation using chained equations [46,47] to impute the missing values.”
MethodMultipartnered Fertility and Depression among Fragile Families
Turney, K., & Carlson, M. (2011) · Journal of Marriage and Family · doi:10.1111/j.1741-3737.2011.00828.x · Cited by 47
“Few observations within the analytic sample are missing on the covariates, and we used the ice (imputation by chained equations) command in Stata 11.1 (Royston, 2004) to impute missing data on the covariates.”
BackgroundMethodInfluentialByford, S., Sharac, J., Lloyd-Evans, B., Gilburt, H., Osborn, D., Leese, M., Johnson, S., & Slade, M. (2010) · British Journal of Psychiatry · doi:10.1192/bjp.bp.110.081067 · Cited by 47
Russell, E. C., Charalambous, S., Pemba, L., Churchyard, G., Grant, A., & Fielding, K. (2010) · BMC Public Health · doi:10.1186/1471-2458-10-433 · Cited by 47
“using multiple imputation was examined, with 10 imputed datasets derived [13] and estimates combined on the basis of Rubin’s Rules [14].”
MethodWang, C. J., Elliott, M., Rogowski, J., Lim, N., Ratner, J. A., & Schuster, M. (2009) · Academic pediatrics · doi:10.1016/j.acap.2009.04.001 · Cited by 47
The Social Security Administration's youth transition demonstration projects
Rangarajan, A., Fraker, T., Honeycutt, T., Mamun, A., Martinez, J., O'Day, B., & Wittenburg, D. C. (2009) · Journal of Vocational Rehabilitation · doi:10.3233/jvr-2009-0463 · Cited by 47
Father Doesn’t Know Best? Parents’ Control of Money and Children’s Food Insecurity
Kenney, C. T. (2008) · Journal of Marriage and the Family · doi:10.1111/j.1741-3737.2008.00512.x · Cited by 47
Predicting Clinical Outcome After Surgical Treatment in Patients With Carpal Tunnel Syndrome.
Jansen, M. C., Evers, S., Slijper, H., Haas, K. D., Smit, X., Hovius, S., & Selles, R. (2018) · Journal of Hand Surgery-American Volume · doi:10.1016/j.jhsa.2018.05.017 · Cited by 46
Failing to estimate the costs of offshoring: A study on process performance
Larsen, M. (2016) · International Business Review · doi:10.1016/j.ibusrev.2015.05.008 · Cited by 46
“Although various methods exist to replace missing values (e.g., Royston, 2004), only actual responses are used in this study.”
MethodCan center-based childcare reduce the odds of early chronic absenteeism?
Gottfried, M. A. (2015) · Early Childhood Research Quarterly · doi:10.1016/j.ecresq.2015.04.002 · Cited by 48
Revisiting the political life-cycle model: later maturation and turnout decline among young adults
Smets, K. (2015) · European Political Science Review · doi:10.1017/s1755773914000460 · Cited by 46
Paediatric chronic illness and educational failure: the role of emotional and behavioural problems
Layte, R., & McCrory, C. (2013) · Social Psychiatry and Psychiatric Epidemiology · doi:10.1007/s00127-012-0609-3 · Cited by 46
Forns, J., Torrent, M., Garcia-Esteban, R., Cáceres, A., Gomila, M. P., Martínez, D., Morales, E., Júlvez, J., Grimalt, J., & Sunyer, J. (2012) · Environmental Research · doi:10.1016/j.envres.2012.04.007 · Cited by 46
“sets were generated and analyzed separately and the results were combined using the standard Rubin’s rules (Supplementary Table 1a) (Royston, 2004), assuming missing at random data (MAR).”
MethodAlcohol availability and youth homicide in the 91 largest US cities, 1984-2006.
Parker, R., Williams, K., McCaffree, K., Acensio, E. K., Browne, A., Strom, K., & Barrick, K. (2011) · Drug and Alcohol Review · doi:10.1111/j.1465-3362.2011.00336.x · Cited by 46
“1 using the iterative chain equation procedure [64,65].”
MethodJustifications of Inequality: The Normative Basis of Pay Differentials in 31 Nations*
Evans, M., Kelley, J., & Peoples, C. D. (2010) · Social Science Quarterly · doi:10.1111/j.1540-6237.2010.00738.x · Cited by 45
Paths to literacy and numeracy problems: evidence from two British birth cohorts
Richards, M., Power, C., & Sacker, A. (2008) · Journal of Epidemiology & Community Health · doi:10.1136/jech.2007.064923 · Cited by 39
“[11] Five replicates of the data were created, giving 95% efficiency.”
MethodGrowth and cognitive function of Indonesian children: zero‐inflated proportion models
Cheung, Y. (2006) · Statistics in Medicine · doi:10.1002/sim.2467 · Cited by 46
Chang, J. T., Hays, R., Shekelle, P., MacLean, C., Solomon, D., Reuben, D., Roth, C., Kamberg, C., Adams, J. S., Young, R. T., et al. (2006) · Annals of Internal Medicine · doi:10.7326/0003-4819-145-8-200610170-00020 · Cited by 46
“Five participants missed 1 of the 4 communication items; in each case, the score for the missing item was imputed by the chained equation method of multiple multivariate imputation (25) to compute a composite communication score.”
MethodChesney, E., Robson, D., Patel, R., Shetty, H., Richardson, S., Chang, C.-K., McGuire, P., & McNeill, A. (2021) · Schizophrenia Research · doi:10.1016/j.schres.2021.09.006 · Cited by 45
Qin, X.-D., Zhou, Y., Bloom, M. S., Qian, Z. (., Geiger, S. D., Vaughn, M. G., Chu, C., Li, Q.-Q., Yang, B.-Y., Hu, L.-W., et al. (2023) · Environmental Health Perspectives · doi:10.1289/ehp11377 · Cited by 45
“29 Inverse probability of sampling weights were applied to the subsequent analysis 30 to ensure that the study population was representative of the 5,202 participants in the cohort.”
MethodSaadatmand, S., Salimifard, K., Mohammadi, R., Kuiper, A., Marzban, M., & Farhadi, A. (2022) · Annals of Operations Research · doi:10.1007/s10479-022-04984-x · Cited by 45
“One of the common issues in medical data is the presence of missing values in independent variables (features), which if omitted, may cause a great reduction in sample size (Royston, 2004).”
BackgroundSocial Capital, carbon dependency, and public response to climate change in 22 European countries
Hao, F., Liu, X., & Michaels, J. L. (2020) · Environmental Science & Policy · doi:10.1016/j.envsci.2020.07.028 · Cited by 53
Suntheimer, N. M., & Wolf, S. (2019) · Journal of School Psychology · doi:10.1016/j.jsp.2019.11.005 · Cited by 55
Wan, E. Y. F., Yu, E. Y. T., Chin, W. Y., Fong, D., Choi, E. P. H., & Lam, C. L. K. (2019) · Hypertension · doi:10.1161/hypertensionaha.119.13123 · Cited by 53
“By increasing time period of BP measurements, as shown in Figures S2 and S3, can help to minimize the potential for bias, such as in the case of measurement error or short-term fluctuations in SBP.”
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Nengsih, T., Bertrand, F., Maumy-Bertrand, M., & Meyer, N. (2018) · Statistical Applications in Genetics and Molecular Biology · doi:10.1515/sagmb-2018-0059 · Cited by 45
Mueller, C., Keil, S. I., & Bauer, C. (2017) · Energy Policy · doi:10.1016/j.enpol.2017.09.023 · Cited by 45
Taylor, G. M. J., Taylor, A. E., Thomas, K. H., Jones, T., Martin, R. M., Munafo, M. R., Windmeijer, F., & Davies, N. M. (2017) · International Journal of Epidemiology · doi:10.1093/ije/dyx109 · Cited by 57
“The imputation procedure produced 20 imputed datasets, and the imputation model included all exposures and covariates.(30) We compared the effect estimates derived from the sensitivity analysis (missing outcome data1⁄4 imputed) with those derived from the main analysis (missing outcome data1⁄4 continuing smoker).”
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Patterns and Predictors of Coparenting after Unmarried Parents Part
Goldberg, J. S., & Carlson, M. (2015) · Journal of family psychology · doi:10.1037/fam0000078 · Cited by 45
A Decomposition Analysis of the Relationship Between Parental Income and Multiple Child Outcomes
Washbrook, E., Gregg, P., & Propper, C. (2014) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/rssa.12074 · Cited by 45
Guarino, C. M., Dieterle, S., Bargagliotti, A., & Mason, W. (2013) · Journal of Research on Educational Effectiveness · doi:10.1080/19345747.2012.706695 · Cited by 45
“To counter the loss of information stemming from item nonresponse, we used Royston’s (2004) Stata implementation of chained multiple imputation (Van Buuren, Boshuizen, & Knook, 1999) to impute missing values for all variables except student test scores. Forty imputed data sets were produced for each of three types of…”
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Sumi, W. C., Woodbridge, M. W., Javitz, H. S., Thornton, S. P., Wagner, M. M., Rouspil, K. M., Yu, J. W., Seeley, J. R., Walker, H. M., Golly, A. M., et al. (2012) · Journal of Emotional and Behavioral Disorders · doi:10.1177/1063426611429571 · Cited by 37
“…values were imputed using fully conditional specification models (i.e., logistic, polytomous, or linear regression) applied iteratively using Stata’s “ice” procedure (which implements multiple imputation by chained equations) (Royston, 2004; Van Buren, Brands, Groothuis-Oudshoorn, & Rubin, 2006).”
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Tan, W., Goldstein, R., Gerrard, P., Ryan, C., Niewczyk, P., Kowalske, K., Zafonte, R., & Schneider, J. (2012) · Journal of Burn Care & Research · doi:10.1097/bcr.0b013e318234d91a · Cited by 45
SOCIAL CAPITAL AND WORK AMONG RURAL-TO-URBAN MIGRANTS IN CHINA
Chang, K.-C., Wen, M., & Wang, G.-X. (2011) · Asian Population Studies · doi:10.1080/17441730.2011.608989 · Cited by 45
“Missing values in the independent variable were imputed using the multiple imputation method based on age, gender, marital status and education (Royston 2005).”
MethodRetinal Microvascular Signs and Functional Loss in Older Persons: The Cardiovascular Health Study
Kim, D., Newman, A., Hajjar, I., Strotmeyer, E., Klein, R., Newton, E., Sarnak, M., Burke, G., & Lipsitz, L. (2011) · Stroke · doi:10.1161/strokeaha.110.605261 · Cited by 45
Lynch, F. L., Dickerson, J. F., Clarke, G. N., Vitiello, B., Porta, G., Wagner, K. D., Emslie, G. J., Asarnow, J. R., Keller, M. B., Birmaher, B. B., et al. (2011) · Archives of General Psychiatry · doi:10.1001/archgenpsychiatry.2011.9 · Cited by 54
O’Reilly, G. M., Jolley, D. J., Cameron, P. A., & Gabbe, B. J. (2010) · Academic Emergency Medicine · doi:10.1111/j.1553-2712.2010.00887.x · Cited by 47
Family investments in low-income children’s achievement and socioemotional functioning.
Longo, F., Lombardi, C. M., & Dearing, E. (2017) · Developmental Psychology · doi:10.1037/dev0000366 · Cited by 48
“Missing data were handled using multiple imputation—20 data sets—by chained equations and final estimates were combined according to “Rubin’s Rules” in Stata 13 (Royston, 2004).”
MethodSmithers, L., Searle, A. K., Chittleborough, C., Scheil, W., Brinkman, S., & Lynch, J. (2015) · BJOG: an International Journal of Obstetrics and Gynaecology · doi:10.1111/1471-0528.13324 · Cited by 44
The Acute and Enduring Consequences of Exposure to Violence on Youth Mental Health and Aggression
Kirk, D. S., & Hardy, M. (2012) · Justice Quarterly · doi:10.1080/07418825.2012.737471 · Cited by 41
“To handle missing data from nonresponse, we use the ice command in Stata to implement the multiple imputation by chained equation algorithm to create five imputed data-sets (see Royston, 2004; van Buuren, Boshuizen, & Knook, 1999).”
MethodUsing full‐cohort data in nested case–control and case–cohort studies by multiple imputation
Keogh, R., & White, I. R. (2013) · Statistics in Medicine · doi:10.1002/sim.5818 · Cited by 44
“MI can also be applied in the case of non-monotone missingness in multiple exposures or covariates, and packages are available in commonly used statistical software, for example, ice [25] and mi in Stata, mice in R [26], and proc mi and proc mianalyze in SAS.”
MethodWilliams, D. M., Fraser, A., Fraser, W. D., Hyppönen, E., Smith, G. D., Deanfield, J. E., Hingorani, A. D., Sattar, N. A., & Lawlor, D. A. (2013) · Heart · doi:10.1136/heartjnl-2013-303678 · Cited by 45
“23 Twenty cycles of regression switching were used, and estimates of results were averaged across the 20 imputed datasets according to Rubin ’ s rules.”
MethodDale, C., Bowling, A., Adamson, J., Kuper, H., Amuzu, A., Ebrahim, S., Casas, J., & Nüesch, E. (2013) · Age and Ageing · doi:10.1093/ageing/aft029 · Cited by 44
“Missing data in baseline predictors were addressed using multiple imputation via chained equations (for details, see Supplementary data available in Age and Ageing online, Appendix Methods 3) [16, 17].”
MethodHíjar, M., Chandran, A., Pérez-Núñez, R., Lunnen, J. C., Rodríguez-Hernández, J. M., & Hyder, A. (2012) · Traffic Injury Prevention · doi:10.1080/15389588.2011.631065 · Cited by 44
“Multiple imputation of missing values 7 – 10 : Using the “uvis” module 11 in Stata 10.”
MethodInfluentialBirnie, K., Martin, R. M., Gallacher, J., Bayer, A. J., Gunnell, D., Ebrahim, S. B. J., & Ben‐Shlomo, Y. (2010) · Journal of Epidemiology & Community Health · doi:10.1136/jech.2009.103648 · Cited by 42
Yucel, D., & Fan, W. (2023) · Applied Research in Quality of Life · doi:10.1007/s11482-023-10164-1 · Cited by 43
“Given that the PROCESS macro requires complete data, we first use Stata’s ice command (Royston, 2005) to impute the missing cases.”
MethodJara-Palomares, L., Jiménez, D., Bikdeli, B., Muriel, A., Rali, P., Yamashita, Y., Morimoto, T., Kimura, T., Mao, R. L., Riera-Mestre, A., et al. (2020) · European Respiratory Journal · doi:10.1183/13993003.02336-2020 · Cited by 43
Gianetto, Q. G., Wieczorek, S., Couté, Y., & Bürger, T. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.05.29.122770 · Cited by 67
“Possibly, confidence intervals can be obtained by using the Rubin’s rules (Royston et al. (2004)).”
Fung, C., Wan, E., Chan, A. K. L., & Lam, C. (2017) · BMC Nephrology · doi:10.1186/s12882-017-0468-y · Cited by 43
“Data analysis Missing data was handled by multiple imputation [20].”
MethodChi, L.-H., Beilin, L., Burrows, S., Huang, R.-C., Oddy, W., Hands, B., & Mori, T. (2013) · European Journal of Preventive Cardiology · doi:10.1177/2047487312452966 · Cited by 43
Race/Ethnicity, Attitudes, and Living With Parents During Young Adulthood
Britton, M. L. (2013) · doi:10.1111/jomf.12042 · Cited by 43
The Impact of Higher Education on Police Officer Attitudes toward Abuse of Authority
Telep, C. W. (2011) · Journal of Criminal Justice Education · doi:10.1080/10511253.2010.519893 · Cited by 43
“To address this, a missing value multiple imputation technique in Stata was employed (Royston 2005). degree, and one for officers who attended some college prior to joining the police service, but had no degree.”
MethodDistrusting Democrats and Political Participation in New Democracies
Carlin, R. E. (2011) · Political Research Quarterly · doi:10.1177/1065912910370692 · Cited by 43
Epperson, M., Khan, M. R., El-Bassel, N., Wu, E., & Gilbert, L. (2011) · Aids and Behavior · doi:10.1007/s10461-009-9660-9 · Cited by 43
“To reduce the potential bias of missing data and differential attrition due to loss to follow-up in the longitudinal data, multiple imputation was employed using the MICE function in Stata 10 [31].”
MethodJeong, D. (2009) · Educational Evaluation and Policy Analysis · doi:10.3102/0162373709342466 · Cited by 43
“To approach the issue of sample attrition, I imputed all variables except AP test results by using a multiple imputation method—the socalled iterative multivariate imputation technique (Royston, 2004).”
MethodLawlor, D., Ronalds, G., Macintyre, S., Clark, H., & Leon, D. (2006) · American Journal of Public Health · doi:10.2105/ajph.2005.066290 · Cited by 43
Effects of Vitamin D2 Supplementation on Vitamin D3 Metabolism in Health and CKD.
Batacchi, Z., Robinson-Cohen, C., Hoofnagle, A., Isakova, T., Kestenbaum, B., Martin, K., Wolf, M., & de Boer, I. D. (2017) · American Society of Nephrology. Clinical Journal · doi:10.2215/cjn.00530117 · Cited by 42
“Missing values for covariates were multiply imputed (n=10) with chained equations, and the resulting analyses were combined using the rules of Rubin (16,17).”
MethodPsychological morbidity and return to work after injury: multicentre cohort study.
Kendrick, D., Dhiman, P., Kellezi, B., Coupland, C., Whitehead, J., Beckett, K., Christie, N., Sleney, J., Barnes, J., Joseph, S., et al. (2017) · The British journal of general practice : the journal of the Royal College of General Practitioners · doi:10.3399/bjgp17x691673 · Cited by 42
“Ten datasets were created and combined using Rubin’s rules.[36, 37]”
MethodCockayne, S., Rodgers, S., Green, L., Fairhurst, C., Adamson, J., Scantlebury, A., Corbacho, B., Hewitt, C. E., Hicks, K., Hull, R., et al. (2017) · Health Technology Assessment · doi:10.3310/hta21240 · Cited by 42
“Level 2, n (%) 290 (57) 286 (63) 287 (60) 256 (61) 77 (15) 73 (16) 90 (19) 78 (19) 232 (46) 223 (49) 243 (51) 218 (52) 343 (68) 315 (70) 334 (69) 285 (69) 128 (25) 126 (28) 155 (32) 122 (30)”
Evaluating the effects of governmental regulations on South Korean private cram schools
Choi, J., & Cho, R. (2016) · Asia Pacific Journal of Education · doi:10.1080/02188791.2015.1064356 · Cited by 42
“…in the estimation model, we used the ice (imputation by chained equations) command in Stata 11.2 to impute missing values on the covariates (Royston, 2004).9 However, imputation of missing values was not conducted for the dependent variables since imputing the dependent variable can lead…”
BackgroundMethodInfluentialWhitley, E., Benzeval, M., & Popham, F. (2016) · Journal of Aging and Health · doi:10.1177/0898264316665208 · Cited by 49
“In sensitivity analyses, we repeated analyses with missing values for SA and SEP variables imputed using chained equations (Royston, 2004, 2005a, 2005b), with 20 sets of imputations, and results were very similar to those presented here.”
MethodÜbergangslösungen beim Eintritt in die Schweizer Berufsbildung: Brückenschlag oder Sackgasse?
Sacchi, S., & Meyer, T. (2016) · Swiss Journal of Sociology · doi:10.1515/sjs-2016-0002 · Cited by 42
“9 Gestützt auf Rubin (1996, 480) entscheiden wir uns für 10 Replikationssamples (generiert mit ICE, vgl. Royston 2004; Royston 2007) und kombinieren die 10 Modellschätzungen dann anhand der “Rubin-Rules”.”
BackgroundLong-term virological outcome in children on antiretroviral therapy in the UK and Ireland
Duong, T., Judd, A., Collins, I., Doerholt, K., Lyall, H., Foster, C., Butler, K., Tookey, P., Shingadia, D., Menson, E., et al. (2014) · AIDS (London) · doi:10.1097/qad.0000000000000438 · Cited by 42
Canché, M. S. G. (2014) · doi:10.1353/jhe.2014.0026 · Cited by 42
Low-income women's employment experiences and their financial, personal, and family well-being.
Coley, R., & Lombardi, C. (2014) · Journal of family psychology · doi:10.1037/a0034998 · Cited by 42
Futier, E., Paugam‐Burtz, C., Constantin, J., Pereira, B., & Jaber, S. (2013) · Trials · doi:10.1186/1745-6215-14-341 · Cited by 35
“If the frequency of missing data is >5%, an additional analysis will be performed using the multiple imputation method (STATA command mi) [21].”
Method
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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