Cited by 2,340Statistical Methods and Bayesian InferenceData Analysis with RAdvanced Causal Inference Techniques

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Multiple Imputation of Missing Values

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Royston, Patrick·2004·The Stata Journal: Promoting communications on statistics and Stata

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Abstract

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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Multiple Imputation for Nonresponse in Surveys
Rubin, D. B. (1987) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316696 · Cited by 20,701
A leisurely look at the bootstrap, the jackknife, and cross-validation
Efron, B., & Gong, G. (1983) · The American Statistician · doi:10.1080/00031305.1983.10483087 · Cited by 3,229

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10.1177/1536867X0300300302 · DOI
10.1016/S0895-4356(02)00539-5 · DOI
Mander A., 1999, Stata Technical Bulletin, 51, 32
10.1093/biomet/63.3.581 · DOI · Paper page
10.1111/1467-985X.00122 · DOI
10.1002/(SICI)1097-0258(19990330)18:6<681::AID-SIM71>3.0.CO;2-R · DOI · Paper page

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Cavassan, N. R. V., Camargo, C., de Pontes, L. G., Barraviera, B., Ferreira, R. S., Miot, H., Abbade, L. P., & dos Santos, L. D. (2019) · Journal of Proteomics · doi:10.1016/j.jprot.2018.09.009 · Cited by 31
Seeing Is Believing: Task-Exposure Specificity and the Development of Mathematics Self-Efficacy Evaluations
Borgonovi, F., & Pokropek, A. (2019) · Journal of Educational Psychology · doi:10.1037/edu0000280 · Cited by 31
“All our analyses take into account missing values (both planned by design and due to item nonresponse) through Stata’s imputations by chained equations (ICE) procedure (Royston, 2004).”
Method
Effect of Achieved Systolic Blood Pressure on Cardiovascular Outcomes in Patients With Type 2 Diabetes: A Population-Based Retrospective Cohort Study
Wan, E. Y. F., Yu, E. Y. T., Chin, W. Y., Fung, C. S. C., Fong, D., Choi, E. P. H., Chan, A. K. C., & Lam, C. L. K. (2018) · Diabetes Care · doi:10.2337/dc17-2443 · Cited by 30
“Data Analysis All missing data, except BP, in the study werehandledbythetechniqueofmultiple imputation (25), which aims to effectively reduce unnecessary biases (25,26) by raising the power of the analysis and producing more reliable and applicable models within clinical practice (27–29).”
Development of a cardiovascular diseases risk prediction model and tools for Chinese patients with type 2 diabetes mellitus: A population‐based retrospective cohort study
Wan, E., Fong, D., Fung, C., Yu, E., Chin, W. Y., Chan, A. K. L., & Lam, C. (2018) · Diabetes, obesity and metabolism · doi:10.1111/dom.13066 · Cited by 31
“Multiple imputation was used to handle missing data for potential predictors.(21) Specifically, each missing value was imputed 5 times by the chained equation method, which attained a relative efficiency of 95%.”
Method
Is the medical financial assistance program an effective supplement to social health insurance for low-income households in China? A cross-sectional study
Liu, K., Yang, J., & Lu, C.-L. (2017) · International Journal for Equity in Health · doi:10.1186/s12939-017-0638-3 · Cited by 31
“We used regression imputation to address the issue of missing data [55, 56].”
Method
Venous thromboembolism in adults screened for sickle cell trait: a population-based cohort study with nested case–control analysis
Little, I., Vinogradova, Y., Orton, E., Kai, J., & Qureshi, N. (2017) · BMJ Open · doi:10.1136/bmjopen-2016-012665 · Cited by 34
“The results from the imputed sets were combined using Rubin’s rules.(46) To ensure the assumption that the data were missing at random, we ran a sensitivity analysis on”
Relationship Status and Long-Term Care Facility Use in Later Life.
Thomeer, M., Mudražija, S., & Angel, J. (2016) · The journals of gerontology. Series B, Psychological sciences and social sciences · doi:10.1093/geronb/gbv106 · Cited by 31
Social Risk Factors of Black and White Adolescents’ Substance Use: The Differential Role of Siblings and Best Friends
Rowan, Z. R. (2016) · Journal of Youth and Adolescence · doi:10.1007/s10964-016-0473-7 · Cited by 31
Bridging Religion and Politics: The Impact of Providential Religious Beliefs on Political Activity
Glazier, R. A. (2015) · Politics and Religion · doi:10.1017/s1755048315000139 · Cited by 31
Condom Use among Immigrant Latino Sexual Minorities: Multilevel Analysis after Respondent-Driven Sampling
Rhodes, S., & McCoy, T. (2015) · AIDS Education and Prevention · doi:10.1521/aeap.2015.27.1.27 · Cited by 31
“• Model 2: Model 1 after performing multiple imputation with 20 imputations (Royston, 2004, 2009; see below for more details).”
Method
Patient Retention, Clinical Outcomes and Attrition-Associated Factors of HIV-Infected Patients Enrolled in Zimbabwe's National Antiretroviral Therapy Programme, 2007–2010
Mutasa-Apollo, T., Shiraishi, R. W., Takarinda, K., Dzangare, J., Mugurungi, O., Murungu, J., Abdul-Quader, A., & Woodfill, C. (2014) · PLoS ONE · doi:10.1371/journal.pone.0086305 · Cited by 31
“Missing data were assumed missing at random (MAR) [23] and were multiple imputed via chained equations using the ice [24–26] procedure in Stata.”
Mothers’ Reading Skills and Child Survival in Nigeria: Examining the Relevance of Mothers’ Decision-Making Power
Smith‐Greenaway, E. (2013) · Social Science & Medicine (1967) · doi:10.1016/j.socscimed.2013.08.011 · Cited by 31
“Stuebing K. Maternal schooling and comprehension of child health information in urban Zambia: Is literacy a missing link in the maternal schooling-child health relationship?. 1997 UNICEF.”
BackgroundMethodInfluential
The Influence of Urban Form and Family Decision Making on Children's Travel to School
Pont, K., Wadley, D., Ziviani, J., & Khan, A. (2013) · Journal of Urban Design · doi:10.1080/13574809.2013.800452 · Cited by 31
“All regression analyses were conducted using data imputed by multiple chained equations to accommodate missing data (Royston 2004) and were performed for Site A and Site B separately.”
Method
Multigenerational: Households and the School Readiness of Children Born to Unmarried Mothers
Augustine, J., & Raley, R. K. (2013) · Journal of Family Issues · doi:10.1177/0192513x12439177 · Cited by 31
“All models are estimated in Stata with the ICE program, a sequential regression multivariate imputation producing five fully imputed data sets (Royston, 2004).”
Financial Factors and the Implementation of Medications for Treating Opioid Use Disorders
Knudsen, H. K., & Roman, P. (2012) · Journal of addiction medicine · doi:10.1097/adm.0b013e318262a97a · Cited by 31
“For all models, we used the “mi estimate” command, which pooled the estimates from the 20 imputed data sets into a single set of results (Barnard and Rubin, 1999; Royston, 2004).”
Method
Characterizing the Psychological Distress Response Before and After a Cancer Diagnosis
Schumacher, J., Palta, M., Loconte, N., Trentham-Dietz, A., Witt, W., Heidrich, S., & Smith, M. A. (2012) · Journal of behavioral medicine · doi:10.1007/s10865-012-9453-x · Cited by 31
“standard errors for uncertainty due to imputation (Royston, 2004).”
The Effect of Marital Status on Home Ownership among Low-Income Households
Grinstein-Weiss, M., Charles, P., Guo, S., Manturuk, K., & Key, C. C. (2011) · Social Service Review · doi:10.1086/662166 · Cited by 31
Activity Increase Despite Arthritis (AÏDA): phase II randomised controlled trial of an active management booklet for hip and knee osteoarthritis in primary care.
Williams, N., Amoakwa, E., Belcher, J., Edwards, R., Hassani, H., Hendry, M., Burton, K., Lewis, R., Hood, K., Jones, J. G., et al. (2011) · The British journal of general practice : the journal of the Royal College of General Practitioners · doi:10.3399/bjgp11x588411 · Cited by 31
Genetic Markers as Instrumental Variables:An Application to Child Fat Mass and Academic Achievement
Scholder, S. V. H. K., Smith, G. D., Lawlor, D. A., Propper, C., & Windmeijer, F. (2010) · doi:10.1920/wp.cem.2010.0310 · Cited by 31
Birth weight, cognitive development, and life chances: A comparison of siblings from childhood into early adulthood
Cheadle, J. E., & Goosby, B. J. (2010) · Social Science Research · doi:10.1016/j.ssresearch.2010.03.003 · Cited by 31
“…size to 5,947 cases.2 We addressed the missing data problem using multiple imputation which assumes that missing values are conditionally missing at random (Little and Rubin, 2002) using the MICE system of chained equations implemented via the Ice routine in Stata (Royston, 2004, 2005a, 2005b).”
The association between executive functioning and motivation to enter treatment among regular users of heroin and/or cocaine in Baltimore, MD
Severtson, S. G., von Thomsen, S., Hedden, S., & Latimer, W. (2010) · Addictive Behaviours · doi:10.1016/j.addbeh.2010.02.012 · Cited by 31
“Estimates were generated using multinomial logistic regression in the ICE addition to Stata (Royston, 2004).”
Method
Disengagement from education among 14-16 year olds
Ross, A. (2009) · doi:10.1920/re.ifs.2024.0723 · Cited by 31
Expert consensus vs empirical estimation of injury severity: effect on quality measurement in trauma.
Glance, L. G., Osler, T., Mukamel, D., Meredith, W., & Dick, A. (2009) · Archives of Surgery · doi:10.1001/archsurg.2009.8 · Cited by 31
Estimation of risk factor associations when the response is influenced by medication use: an imputation approach
McClelland, R., Kronmal, R., Haessler, J., Blumenthal, R., & Goff, D. (2008) · Statistics in Medicine · doi:10.1002/sim.3341 · Cited by 31
What Makes Retirees Happier: A Gradual or 'Cold Turkey' Retirement?Preprint
Calvo, E., Haverstick, K., & Sass, S. A. (2007) · SSRN Electronic Journal · doi:10.2139/ssrn.1296707 · Cited by 31
“This method is one of 39 the best available techniques to deal with non-response (Allison 2001; Royston 2004).”
Intimate Partner Violence and HIV Risks: A Longitudinal Study of Men on Methadone
Gilbert, L., El-Bassel, N., Wu, E., & Chang, M. (2007) · Journal of urban health · doi:10.1007/s11524-007-9214-2 · Cited by 31
Self-Reported Mental Health-Related Quality of Life and Mortality in Men and Women in the European Prospective Investigation into Cancer (EPIC-Norfolk): A Prospective Population Study
Myint, P., Luben, R., Surtees, P., Wainwright, N., Welch, A., Bingham, S., Wareham, N., Smith, R. D. J., Harvey, I., & Khaw, K. (2007) · Psychosomatic Medicine · doi:10.1097/psy.0b013e318068fcd4 · Cited by 31
“Missing values for smoking, BMI, prevalence of diabetes, systolic blood pressure, cholesterol, social class, and average daily alcohol intake were imputed using multiple imputation by chained equations (19,20).”
Method
Parental beliefs about nonresident fathers' obligations and rights.
Lin, I., & Mclanahan, S. (2007) · Journal of Marriage and the Family · doi:10.1111/j.1741-3737.2007.00372.x · Cited by 31
Cost-effectiveness of computerized cognitive–behavioural therapy for the treatment of depression in primary care: findings from the Randomised Evaluation of the Effectiveness and Acceptability of Computerised Therapy (REEACT) trial
Duarte, A., Walker, S., Littlewood, E., Brabyn, S., Hewitt, C., Gilbody, S., & Palmer, S. (2017) · Psychological Medicine · doi:10.1017/s0033291717000289 · Cited by 30
“To account for missing data, we used multiple imputation methods with chained equations (Royston, 2004) and predictive mean matching over 10 imputations to estimate cost aggregated by resource use category (see above) and EQ-5D-3L and SF-6D data items when these were missing.”
Method
Posttraumatic stress disorder and HIV risk among poor, inner-city women receiving care in an emergency department
El-Bassel, N., Gilbert, L., Vinocur, D., Chang, M., & Wu, E. (2011) · American Journal of Public Health · doi:10.2105/ajph.2009.181842 · Cited by 30

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
DOI: 10.1177/1536867x0400400301
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
Licence: journals.sagepub.com/page/policies/text-and-data-mining-license (tdm)
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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