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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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- 10.1177/1536867X0300300302 · DOI
- 10.1016/S0895-4356(02)00539-5 · DOI
- Mander A., 1999, Stata Technical Bulletin, 51, 32
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Gilbert, L., El-Bassel, N., Chang, M., Wu, E., & Roy, L. (2011) · Psychology of Addictive Behaviors · doi:10.1037/a0025869 · Cited by 91
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Han, D.-K. M., Braman, D., Monahan, J., Callahan, L., & Peters, E. (2010) · Law and Human Behavior · doi:10.1007/s10979-008-9174-4 · Cited by 91
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“To deal with the missing cases, we used the multiple imputation procedure originally developed by Rubin (1987) and recently applied in the program STATA (Royston, 2004).”
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“The validity of the multiple imputation pproach is contingent upon the data being missng at random, given a set of available informaion.(51,52) We believe missingness is accounted or largely by available variables, which inluded race, occupation, age, and health behavors.”
BackgroundGallos, I., Khairy, M., Chu, J., Rajkhowa, M., Tobías, A., Campbell, A., Dowell, K., Fishel, S., & Coomarasamy, A. (2018) · Reproductive Biomedicine Online · doi:10.1016/j.rbmo.2018.08.025 · Cited by 89
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“Missing data on covariates were imputed 20 times using Stata’s Imputation by Chained Equations (ICE) procedure (Royston, 2004, 2005, 2007, 2009; Royston, Carlin, & White, 2009; White, Royston, & Wood, 2011).”
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Glance, L. G., Li, Y., Osler, T., Mukamel, D., & Dick, A. (2014) · Annals of Surgery · doi:10.1097/sla.0000000000000330 · Cited by 89
“Demographics Age (median, interquartile range), yr 66 (35, 84) 47 (28, 73) 48 (34, 64) 47 (34, 60) 47 (34, 59) 46 (33, 57) <0.”
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“Multiple imputation was used to address missing data following procedures recommended by Allison [29] using STATA 10 and the ICE program [30].”
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“We used multiple imputations procedure (mvis) in Stata (v.8) ( Royston, 2004 ) to impute missing data for the regression analysis.”
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“For analyses that adjusted for covariates, missing values were multiply imputed by iterative multiple regression and the data analysed using multiple imputation methodology [38,39].”
MethodThe Cultural Orientation of Mass Political Opinion
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Redaniel, M. T., Martin, R. M., Ridd, M. J., Wade, J., & Jeffreys, M. (2015) · PLoS ONE · doi:10.1371/journal.pone.0126608 · Cited by 88
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Exposure to metals during pregnancy and neuropsychological development at the age of 4 years.
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Exploring the predictors of early readmission to psychiatric hospital
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“(2014), we used multiple imputation by chained equations to ‘fill in’ missing data (van Buuren et al. 1999; Royston, 2004).”
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“The estimates were corrected for predictor data missing using multiple imputations (see supplemental Table 1, http://links.lww.com/QAD/A616) [36].”
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Educational expectation trajectories and attainment in the transition to adulthood.
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Dietary patterns at 6, 15 and 24 months of age are associated with IQ at 8 years of age
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Feudtner, C., Carroll, K. W., Hexem, K., Silberman, J., Kang, T., & Kazak, A. (2010) · Archives of Pediatrics & Adolescent Medicine · doi:10.1001/archpediatrics.2010.146 · Cited by 85
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“Multiple imputation is becoming a common approach to account for the missing values of all covariables (25,26).”
BackgroundMobility Regimes and Parental Wealth: The United States, Germany, and Sweden in ComparisonPreprint
Pfeffer, F., & Hällsten, M. (2012) · SSRN Electronic Journal · doi:10.2139/ssrn.2166784 · Cited by 84
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Koole, O., Tsui, S., Wabwire-mangen, F., Kwesigabo, G., Menten, J., Mulenga, M., Auld, A., Agolory, S., Mukadi, Y., Colebunders, R., et al. (2014) · Tropical medicine & international health · doi:10.1111/tmi.12386 · Cited by 83
“The final Cox-regression model was corrected for missing data in the predictors of attrition using Multivariate Imputation by Chained Equations (Little 1992; Royston 2004).”
MethodA framework for multiple imputation in cluster analysis.
Basagaña, X., Barrera-Gómez, J., Benet, M., Antó, J., & Garcia-Aymerich, J. (2013) · American Journal of Epidemiology · doi:10.1093/aje/kws289 · Cited by 83
Frone, M., & Brown, A. L. (2010) · Journal of Studies on Alcohol and Drugs · doi:10.15288/jsad.2010.71.526 · Cited by 83
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“Therefore, a multiple imputation (MI) model was constructed to account for missing race and marital status, through use of a logit function, with parity, age, and treatment status as predictors of both race and marital status [31].”
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King, M., Jones, L., Richardson, A., Murad, S., Irving, A., Aslett, H., Ramsay, A., Coelho, H., Andreou, P., Tookman, A., et al. (2008) · British Journal of Cancer · doi:10.1038/sj.bjc.6604164 · Cited by 82
“Sixteen patients nominated at least one key professional; 13 nominated general practitioners, and 10 nominated secondary care professionals, seven of whom were nurses (see Nazareth et al, in press for further detail).”
BackgroundMethodPreoperative Thrombocytopenia and Postoperative Outcomes after Noncardiac Surgery
Glance, L. G., Blumberg, N., Eaton, M. P., Lustik, S. J., Osler, T. M., Wissler, R. N., Zollo, R. A., Karcz, M., Feng, C., & Dick, A. W. (2013) · Anesthesiology · doi:10.1097/aln.0b013e3182a4441f · Cited by 90
Delayed Special Education Placement for Learning Disabilities among Children of Immigrants
Hibel, J., & Jasper, A. D. (2012) · Social Forces · doi:10.1093/sf/sos092 · Cited by 81
Simsum: Analyses of Simulation Studies Including Monte Carlo Error
White, I. (2010) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x1001000305 · Cited by 81
“Then two methods of multiple imputation using chained equations (van Buuren, Boshuizen, and Knook 1999), implemented in Stata as ice (Royston 2004, 2009), were used.”
Butterworth, P., Pymont, C., Rodgers, B., Windsor, T., & Anstey, K. (2010) · Australian and New Zealand journal of psychiatry (Print) · doi:10.3109/00048671003620202 · Cited by 81
(2010) · Nature Medicine · doi:10.1038/nm0210-131 · Cited by 81
A Ki67/BCL2 index based on immunohistochemistry is highly prognostic in ER‐positive breast cancer
Ali, H. R., Dawson, S., Blows, F., Provenzano, E., Leung, S., Nielsen, T., Pharoah, P., & Caldas, C. (2012) · Journal of Pathology · doi:10.1002/path.2976 · Cited by 80
“9 cm 236 (36) 282 (42) 14 (48) 12 (46) 129 (52) 88 (62) ≥5 cm 13 (2) 17 (3) 0 (0) 0 (0) 11 (4) 8 (6) Spearman’s Rho 0.”
Epidemiology of Alcohol Abuse Among US Immigrant Populations
Szaflarski, M., Cubbins, L., & Ying, J. (2011) · Journal of Immigrant and Minority Health · doi:10.1007/s10903-010-9394-9 · Cited by 80
“The foreign-born population has more than tripled since 1970 [ 1 , 2], and it currently constitutes 12.5% of the US population [3, 4]. Past research indicates that when most immigrants enter the US, their risk of alcohol abuse is lower than in the native population, even among those of the same ethnicity [5].”
BackgroundInfluentialJaffee, S. R., Hulle, C. V. V., & Rodgers, J. (2011) · Child Development · doi:10.1111/j.1467-8624.2011.01611.x · Cited by 80
Asleep at the Wheel: The Prevalence and Impact of Drowsy Driving
Tefft, B. C. (2010) · doi:10.1037/e586372011-001 · Cited by 80
Dearing, E., Kreider, H., & Weiss, H. B. (2008) · Marriage & Family Review · doi:10.1080/01494920802072462 · Cited by 89
“For the present study, we used multiple imputation by chained equations (ie, MICE, Royston, 2004 ) to generate five complete data sets that combined observed and imputed values.”
MethodDawwas, M. F., Gimson, A. E., Lewsey, J., Copley, L. P., & van der Meulen, J. (2007) · Gut · doi:10.1136/gut.2006.111369 · Cited by 80
Eriksson, M., & Ng, N. (2015) · Social Science & Medicine · doi:10.1016/j.socscimed.2015.02.029 · Cited by 83
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“HRs for each outcome was calculated as the average HR of the five datasets, corrected for between-and within-imputation variation [34-36].”
Dyck, D. V., Cerin, E., Cardon, G., Deforche, B. I., Sallis, J. F., Owen, N. G., & Bourdeaudhuij, I. D. (2010) · Health & Place · doi:10.1016/j.healthplace.2010.05.011 · Cited by 71
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Persistence, Privilege, and Parenting: The Comparative Study of Intergenerational Mobility.
Smeeding, T., Erikson, R., & Jäntti, M. (2011) · Choice Reviews Online · doi:10.5860/choice.49-6398 · Cited by 77
Rhodes, S., McCoy, T., Vissman, A. T., DiClemente, R., Duck, S., Hergenrather, K. C., Foley, K., Alonzo, J., Bloom, F. R., & Eng, E. (2011) · Aids and Behavior · doi:10.1007/s10461-011-9903-4 · Cited by 77
“(77, 78) We performed multiple imputation using chained equations (MICE).(79, 80) Twenty imputed datasets were created and then pooled to account for the within and between imputation variation.”
MethodWang, C.-H. J., Patel, M. H., Schueth, A. J., Bradley, M. A., Wu, S., Crosson, J. C., Glassman, P. A., & Bell, D. S. (2009) · Journal of the American Medical Informatics Association · doi:10.1197/jamia.m2998 · Cited by 73
Casiraghi, E., Malchiodi, D., Trucco, G., Frasca, M., Cappelletti, L., Fontana, T., Esposito, A. A., Avola, E., Jachetti, A., Reese, J., et al. (2020) · IEEE Access · doi:10.1109/access.2020.3034032 · Cited by 81
“Our results confirm that, at least m = 20 imputed sets should be used for MI to reduce between-imputation variance [35], [125].”
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Freilich, J. D., Adamczyk, A., Chermak, S. M., Boyd, K. A., & Parkin, W. S. (2014) · Journal of Quantitative Criminology · doi:10.1007/s10940-014-9239-0 · Cited by 77
Community Violence Exposure and Positive Youth Development in Urban Youth
McDonald, C., Deatrick, J., Kassam-Adams, N., & Richmond, T. (2011) · Journal of community health · doi:10.1007/s10900-011-9391-5 · Cited by 76
“In order to address the loss of statistical power from missing data for the regression analysis, Imputation by Chained Equations (ICE) was conducted in Stata 11 [33].”
MethodLovasi, G., Quinn, J., Rauh, V., Perera, F., Andrews, H., Garfinkel, R., Hoepner, L., Whyatt, R., & Rundle, A. (2010) · American Journal of Public Health · doi:10.2105/ajph.2009.168419 · Cited by 76
“n=27) were filled in by multiple imputation.(49,50) Five imputed datasets were created”
Wen, M., & Wang, G.-X. (2009) · International Journal of Comparative Sociology · doi:10.1177/0020715208101597 · Cited by 76
“Missing values in the independent variables were imputed using multiple imputation method based on age, gender, length of residence in Shanghai, marital status, education, and monthly income (Royston, 2005).”
MethodZammit, S., Horwood, J. P., Thompson, A. D., Thomas, K., Menezes, P. R., Gunnell, D., Hollis, C. P., Dieter Wolke, C., Lewis, G., & Harrison, G. (2008) · Schizophrenia Research · doi:10.1016/j.schres.2008.04.036 · Cited by 67
Walker, A. S., Mulenga, V., Sinyinza, F., Lishimpi, K., Nunn, A., Chintu, C., & Gibb, D. (2006) · Journal of Acquired Immune Deficiency Syndromes · doi:10.1097/01.qai.0000226334.34717.dc · Cited by 76
O’Callaghan, F., O'Callaghan, M. J., Najman, J. M., Williams, G. M., Bor, W., & Alati, R. (2006) · Addiction · doi:10.1111/j.1360-0443.2006.01323.x · Cited by 68
“Imputations were performed with the multivariate imputations by the chained equations (MICE) method recently implemented for the STATA program (Royston 2004).”
Li, X., Tan, H., Huang, X., Zhou, S., Hu, S., Wang, X., Xu, X., Liu, Q., & Wen, S. W. (2016) · Pregnancy Hypertension: An International Journal of Women's Cardiovascular Health · doi:10.1016/j.preghy.2015.11.004 · Cited by 75
“For BMI, season of delivery and the income index, the missing data (<8%) were constructed by a multiple imputation method in the multiple logistical regression [21].”
MethodPeer Influences on Sexual Activity among Adolescents in Ghana
Bingenheimer, J., Asante, E. A., & Ahiadeke, C. (2015) · Studies in family planning · doi:10.1111/j.1728-4465.2015.00012.x · Cited by 75
The impact of the 1999 education reform in Poland
Jakubowski, M., Porta, E., Wiśniewski, J., & Patrinos, H. (2010) · doi:10.1596/1813-9450-5263 · Cited by 75
“To keep the sample size and performance distribution untouched by the matching exercise, missing values for matching covariates were imputed through multiple imputation models (Royston 2004).”
Spousal Dissimilarity, Race, and Marital Dissolution
Clarkwest, A. (2007) · Journal of Marriage and the Family · doi:10.1111/j.1741-3737.2007.00397.x · Cited by 64
Factors associated with pesticide safety practices in farmworkers.
Strong, L., Thompson, B., Koepsell, T., & Meischke, H. (2008) · American Journal of Industrial Medicine · doi:10.1002/ajim.20519 · Cited by 75
“First, we generated a set of five plausible values for each missing observation by regressing the variable with missing responses on specified predictors using a bootstrap sample with the program ICE in Stata 8.0, which performs multiple imputation with chained equations [Royston, 2004, 2005].”
InfluentialHandling Missing Data in the Modeling of Intensive Longitudinal Data
Ji, L., Chow, S.-M., Schermerhorn, A. C., Jacobson, N. C., & Cummings, E. M. (2018) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1080/10705511.2017.1417046 · Cited by 74
“However, with more complicated models and longitudinal data, some researchers have also proposed using a larger number of imputations to improve the stability of confidence interval estimation (Royston, 2004), obtain more accountable conclusions with empirical data (Spratt et al.”
Marital Status and Depressive Symptoms over Time: Age and Gender Variations
Lapierre, T. (2009) · Family Relations · doi:10.1111/j.1741-3729.2009.00562.x · Cited by 74
Lawlor, D., Fraser, A., Ebrahim, S., & Smith, G. (2007) · PLoS Medicine · doi:10.1371/journal.pmed.0040263 · Cited by 74
“This approach creates a number of copies of the data (in this case we generated ten copies) each of which has values that are missing imputed with an appropriate level of randomness using chained equations [24].”
BackgroundMethodInfluentialZheng, Y., Wang, W., Zhong, Y., Wu, F., Zhu, Z., Tham, Y.-C., Lamoureux, E., Xiao, L., Zhu, E., Liu, H., et al. (2021) · Journal of Medical Internet Research · doi:10.2196/24316 · Cited by 73
“Multiple imputation was used to create 20 copies of the data, and final results were obtained by averaging these data sets using the rules developed by Rubin [29].”
MethodMcClintock, E. A. (2014) · American Sociological Review · doi:10.1177/0003122414536391 · Cited by 73
How Does Religion Promote Forgiveness? Linking Beliefs, Orientations, and Practices
Escher, D. F. (2013) · Journal for the Scientific Study of Religion · doi:10.1111/jssr.12012 · Cited by 73
Spanopoulos, D., Britton, J., McNeill, A., Ratschen, E., & Szatkowski, L. (2013) · Tobacco Control · doi:10.1136/tobaccocontrol-2012-050765 · Cited by 73
Big Data Preprocessing: Enabling Smart Data
Luengo, J., García-Gil, D., Ramírez-Gallego, S., García, S., & Herrera, F. (2020) · doi:10.1007/978-3-030-39105-8 · Cited by 72
Temperament and depressive symptoms: What is the direction of the association?
Elovainio, M. J., Jokela, M. M., Rosenström, T. H., Pulkki-Råbäck, L., Hakulinen, C. A., Josefsson, K., Hintsanen, M., Hintsa, T., Raitakari, O. T., & Keltikangas‐Järvinen, L. (2014) · Journal of Affective Disorders · doi:10.1016/j.jad.2014.08.040 · Cited by 76
Bansal, N., Zelnick, L. R., Robinson‐Cohen, C., Hoofnagle, A. N., Ix, J. H., Lima, J. A. C., Shoben, A. B., Peralta, C. A., Siscovick, D. S., Kestenbaum, B. R., et al. (2014) · Journal of the American Heart Association · doi:10.1161/jaha.114.001278 · Cited by 80
“For the regression analyses, these subjects’ values were multiply imputed using chained equations.(37) The multiple analyses over the imputations were combined using Rubin’s rules to account for the variability in the imputation procedure.”
MethodCan New Inflammatory Markers Improve the Diagnosis of Acute Appendicitis?
Andersson, M., Rubér, M., Ekerfelt, C., Hallgren, H., Olaison, G., & Andersson, R. (2014) · World Journal of Surgery · doi:10.1007/s00268-014-2708-7 · Cited by 72
Dearing, E., Wimer, C., Simpkins, S., Lund, T. J., Bouffard, S. M., Caronongan, P., Kreider, H., & Weiss, H. (2009) · Developmental Psychology · doi:10.1037/a0017359 · Cited by 72
Lawlor, D., Lewcock, M., Rena-Jones, L., Rollings, C., Yip, V., Smith, D., Pearson, R., Johnson, L., Millard, L., Patel, N., et al. (2019) · Wellcome Open Research · doi:10.12688/wellcomeopenres.15087.2 · Cited by 71
“Early pregnancya 8 (6) 30 (25) 21 (23) 51 (33) 53 (32) 68 (44) 231”
Baker, A., Ames, B., Sokhey, A. E., & Rennó, L. (2015) · The Journal of Politics · doi:10.1086/683609 · Cited by 82
Vinogradova, Y., Coupland, C. A. C., & Hippisley‐Cox, J. (2013) · BMJ · doi:10.1136/bmj.f114 · Cited by 63
Fewer Diplomas for Men: The Influence of College Experiences on the Gender Gap in College Graduation
Ewert, S. (2012) · The Journal of Higher Education · doi:10.1080/00221546.2012.11777271 · Cited by 71
“I use multiple imputation by chained equations to impute the missing values in the data (Royston, 2004; Rubin, 1987).”
MethodEconomic Equality and Social Welfare: Policy Preferences in Five Nations
Breznau, N. (2010) · International Journal of Public Opinion Research · doi:10.1093/ijpor/edq024 · Cited by 70
Lawlor, D. A., Cooper, A. R., Bain, C., Smith, G. D., Irwin, A., Riddoch, C., & Ness, A. (2008) · European Journal of Epidemiology · doi:10.1007/s10654-008-9259-x · Cited by 69
“This approach creates a number of copies of the data (in this case we generated 10 copies) each of which has values that are missing imputed with an appropriate level of randomness using chained equations [ 37 ].”
MethodInfluentialRecreation, Informal Social Networks and Social Capital
Warde, A., Tampubolon, G., & Savage, M. (2005) · Journal of Leisure Research · doi:10.1080/00222216.2005.11950060 · Cited by 71
“tions do promote bridging capital of the strategic kind that Szreter (2003) identifies as "boundary-spanning".”
BackgroundBeyond Boys’ Bad Behavior: Paternal Incarceration and Cognitive Development in Middle Childhood
Haskins, A. R. (2016) · Social forces; a scientific medium of social study and interpretation · doi:10.1093/sf/sow066 · Cited by 70
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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