Cited by 892Statistical Methods and Bayesian InferenceStatistical Methods in EpidemiologyAdvanced Causal Inference Techniques

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A critical look at methods for handling missing covariates in epidemiologic regression analyses.

Greenland, Sander, Finkle, William D.·1995·American Journal of Epidemiology

DOI 10.1093/oxfordjournals.aje.a117592

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Abstract

Epidemiologic studies often encounter missing covariate values. While simple methods such as stratification on missing-data status, conditional-mean imputation, and complete-subject analysis are commonly employed for handling this problem, several studies have shown that these methods can be biased under reasonable circumstances. The authors review these results in the context of logistic regression and present simulation experiments showing the limitations of the methods. The method based on missing-data indicators can exhibit severe bias even when the data are missing completely at random, and regression (conditional-mean) imputation can be inordinately sensitive to model misspecification. Even complete-subject analysis can outperform these methods. More sophisticated methods, such as maximum likelihood, multiple imputation, and weighted estimating equations, have been given extensive attention in the statistics literature. While these methods are superior to simple methods, they are not commonly used in epidemiology, no doubt due to their complexity and the lack of packaged software to apply these methods. The authors contrast the results of multiple imputation to simple methods in the analysis of a case-control study of endometrial cancer, and they find a meaningful difference in results for age at menarche. In general, the authors recommend that epidemiologists avoid using the missing-indicator method and use more sophisticated methods whenever a large proportion of data are missing.

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Result
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“This method is not recommended for observational data because it may lead to inadequate control of confounding (Greenland and Finkle, 1995) but this criticism does not apply in randomized trials.”
Method
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“Subjects with missing data at all 4 time points for any variables in the two-level randomintercept models were excluded from analysis [24, 25].”
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“Missing values for household income, parental education, and body weight status were considered as separate covariate categories in the regression models [48]; the estimates were not presented.”
Background
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BackgroundMethod
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Impacts of self- and cross-sucking on cattle health and performance
Mahmoud, M. E., Mahmoud, F. A., & Ahmed, A. E. (2016) · Veterinary World · doi:10.14202/vetworld.2016.922-928 · Cited by 25
“Greenland, S. and Finkle, W.D. (1995) A critical look at methods for handling missing covariates in epidemiologic regression analyses.”
MethodInfluential
Identifying influential factors distinguishing recidivists among offender patients with a diagnosis of schizophrenia via machine learning algorithms
Kirchebner, J., Günther, M. P., & Lau, S. (2020) · Forensic Science International · doi:10.1016/j.forsciint.2020.110435 · Cited by 22
Does mental health treatment reduce recidivism among offenders with a psychotic illness?
Weatherburn, D., Albalawi, O., Chowdhury, N. Z., Wand, H. C., Adily, A., Allnutt, S., & Butler, T. G. (2021) · Journal of Criminology · doi:10.1177/0004865821996426 · Cited by 22
“We included missing values as an extra variable category to avoid the loss of data and potential bias created by removal of these observations from the dataset; however, some scholars have cautioned that this can itself create bias (Greenland & Finkle, 1995).”
Method
Missing Data and Imputation: A Practical Illustration in a Prognostic Study on Low Back Pain
Vergouw, D., Heymans, M. W., van der Windt, D., Foster, N. E., Dunn, K. M., van der Horst, H. E., & de Vet, H. C. W. (2012) · Journal of Manipulative and Physiological Therapeutics · doi:10.1016/j.jmpt.2012.07.002 · Cited by 24
“Then CCA is not only imprecise (because of loss of power) but may also give biased estimates of the investigated association(s).(3) A technique called imputation (ie, replacing the missing observation(s) with plausible estimates) is regarded as a good alternative for handling incomplete data.”
Background
Head Circumference of Infants Born to Mothers with Different Educational Levels; The Generation R Study
Bouthoorn, S. H., van Lenthe, F. J., Hokken‐Koelega, A. C. S., Moll, H. A., Tiemeier, H. W., Albert Hofman, D., Mackenbach, J. P., Jaddoe, V. W. V., & Raat, H. (2012) · PLoS ONE · doi:10.1371/journal.pone.0039798 · Cited by 21
“0 was used [34].”
Macro and microvascular complications are determinants of increased infection-related mortality in Brazilian type 2 diabetes mellitus patients
Cardoso, C. R. L., & Salles, G. F. (2006) · Diabetes Research and Clinical Practice · doi:10.1016/j.diabres.2006.04.008 · Cited by 22
A new diagnostic rule for deep vein thrombosis: safety and efficiency in clinically relevant subgroups
Toll, D. B., Oudega, R., Vergouwe, Y., Moons, K. G. M., & Hoes, A. W. (2007) · Family Practice · doi:10.1093/fampra/cmm075 · Cited by 22
An exploratory short‐term double‐blind randomized trial of varenicline versus nicotine patch for smoking cessation in women
Gray, K. M., McClure, E. A., Baker, N. L., Hartwell, K. J., Carpenter, M. J., & Saladin, M. E. (2015) · Addiction · doi:10.1111/add.12895 · Cited by 22
“Given missing baseline covariate data on some participants, adjusted analysis was completed on multiply imputed data sets (m=50) using the MCMC algorithm (SAS PROC MI) to avoid biased estimates [21,22].”
Method
Corpora amylacea in prostatectomy tissue and associations with molecular, histological, and lifestyle factors
DuPre, N. C., Flavin, R., Sfanos, K. S., et al. (2018) · The Prostate · doi:10.1002/pros.23692 · Cited by 22
“We used the missing indicator method for those with missing PSA at diagnosis (n = 38) and missing acute inflammation data (n = 7), and used simple single imputation to assign values for those with missing TMPRSS2:ERG fusion status (n = 3), vasectomy (n = 1), and BMI at diagnosis (n = 1).(25) The missingness of PSA was…”
Method
Comparison of the Missing-Indicator Method and Conditional Logistic Regression in 1:m Matched Case-Control Studies with Missing Exposure Values
Li, X. (2004) · American Journal of Epidemiology · doi:10.1093/aje/kwh075 · Cited by 21
“Am J Epidemiol 2004;159:603–610 The missing-indicator method has been extended to the context of matched case-control studies and applied to analyses of the risk of childhood leukemia (2) and endometrial cancer (3).”
Method
Waist circumference and metabolic risk factors have separate and additive effects on the risk of future Type 2 diabetes in patients with vascular diseases. A cohort study
Wassink, A. M. J., van der Graaf, Y., van Haeften, T. W., Spiering, W., Soedamah‐Muthu, S. S., Visseren, F. L. J., & on behalf of the SMART Study Group (2011) · Diabetic Medicine · doi:10.1111/j.1464-5491.2011.03318.x · Cited by 20
Effects of Different Missing Data Imputation Techniques on the Performance of Undiagnosed Diabetes Risk Prediction Models in a Mixed-Ancestry Population of South Africa
Masconi, K. L., Matsha, T. E., Erasmus, R. T., et al. (2015) · PLoS ONE · doi:10.1371/journal.pone.0139210 · Cited by 21
“Data missing completely at random (MCAR) has a low probability that the observation missing is related to any other patient characteristics and most simple techniques for handling missing data give unbiased results [4].”
Background
Occupational asbestos exposure is associated with pharyngeal squamous cell carcinoma in men from the greater Boston area
Langevin, S. M., O'Sullivan, M. H., Valerio, J. L., Pawlita, M., Applebaum, K. M., Eliot, M., McClean, M. D., & Kelsey, K. T. (2013) · Occupational and Environmental Medicine · doi:10.1136/oemed-2013-101528 · Cited by 21
“…the missing values in the logistic regression models, multiple imputation (5 imputations) was employed using multivariate normal regression, based on age and smoking data ( ever/never + pack-years ); multiple imputation results in less biased findings when dealing with missing covariate data 24 .”
Acute Basilar Artery Occlusion in the Basilar Artery International Cooperation Study
Arnold, M., Fischer, U., Compter, A., et al. (2010) · Stroke · doi:10.1161/strokeaha.110.594036 · Cited by 21
In utero exposure to alcohol and puberty in boys: a pregnancy cohort study
Håkonsen, L. B., Brath-Lund, M. L., Hounsgaard, M. L., Olsen, J., Ernst, A., Thulstrup, A. M., Bech, B. H., & Ramlau‐Hansen, C. H. (2014) · BMJ Open · doi:10.1136/bmjopen-2013-004467 · Cited by 21
“Since complete case analysis can lead to biased estimates and limited power, we addressed the missing data problem by using multiple imputations, which often yield unbiased and more precise estimates if data are missing at random.(22) 23 Briefly, the multiple imputations model is an approach that creates several (m>1)…”
Background
A Prediction Model to Determine Childhood Epilepsy After 1 or More Paroxysmal Events
Diessen, E. G. A. L. V., Lamberink, H. J., Otte, W. M., Doornebal, N., Brouwer, O. F., Jansen, F. E., & Braun, K. P. J. (2018) · PEDIATRICS · doi:10.1542/peds.2018-0931 · Cited by 21
Missing Data
Harrell, F. E. (2015) · Springer series in statistics · doi:10.1007/978-3-319-19425-7_3 · Cited by 21
Review of analytical methods for prospective cohort studies using time to event data: single studies and implications for meta-analysis
Bennett, D. (2003) · Statistical Methods in Medical Research · doi:10.1191/0962280203sm319ra · Cited by 21
Intra-abdominal fat and metabolic syndrome are associated with larger infrarenal aortic diameters in patients with clinically evident arterial disease
Gorter, P. M., Visseren, F. L. J., Moll, F. L., & van der Graaf, Y. (2008) · Journal of Vascular Surgery · doi:10.1016/j.jvs.2008.02.020 · Cited by 21
Low Cost Text Mining as a Strategy for Qualitative Researchers
Rose, J., & Lennerholt, C. (2017) · The Electronic Journal of Business Research Methods · Cited by 22
Investigation of bovine venereal campylobacteriosis in beef cow herds in New Zealand
McFadden, A., Heuer, C., Jackson, R., et al. (2005) · New Zealand Veterinary Journal · doi:10.1080/00480169.2005.36468 · Cited by 21
Estimating prognosis in heart failure: time for a better approach
Cowie, M. (2003) · Heart · doi:10.1136/heart.89.6.587 · Cited by 21
“Many of the published studies are small, and include highly selected patient populations, with different variables recorded in each dataset. Differences in the way measurements are made—for example, in the assessment of left ventricular systolic function—and the close correlation between many variables add further com…”
Background
Estimating the Influenza Vaccine Effectiveness against Medically Attended Influenza in Clinical Settings: A Hospital-Based Case-Control Study with a Rapid Diagnostic Test in Japan
Suzuki, M., Yoshimine, H., Harada, Y., Tsuchiya, N., Shimada, I., Ariyoshi, K., & Inoue, K. (2013) · PLoS ONE · doi:10.1371/journal.pone.0052103 · Cited by 20
“We instead coded those missing values as ‘‘unknown status’’ and included all patients for our primary analysis (missing-indicator method) [23].”
Predicting cumulative live birth for couples beginning their second complete cycle of in vitro fertilization treatment
Ratna, M. B., Bhattacharya, S., van Geloven, N., & McLernon, D. J. (2022) · Human Reproduction · doi:10.1093/humrep/deac152 · Cited by 20
“A Multiple Imputation by Chained Equations (MICE) technique was performed by generating a single imputed dataset to minimize biases and enhance statistical efficiency arising from excluding women with missing predictor values (Greenland and Finkle, 1995).”
Variables dépendantes du temps dans le modèle de Cox Théorie et pratique
Desquilbet, L., & Meyer, L. (2005) · Revue d Épidémiologie et de Santé Publique · doi:10.1016/s0398-7620(05)84572-9 · Cited by 20
Unequal treatment access and malaria risk in a community-based intervention program in the Philippines.
Bell, D., Go, R., Miguel, C. A., et al. (2005) · PubMed · Cited by 20
The role of early life factors in the development of ethnic differences in growth and overweight in preschool children: a prospective birth cohort
van Rossem, L., Groen, E. H., Jaddoe, V. W. V., Albert Hofman, D., Mackenbach, J. P., & Raat, H. (2014) · BMC Public Health · doi:10.1186/1471-2458-14-722 · Cited by 19
“0 on the early life risk factors to this analysis [14,15].”
Background
Associations between maternal age and socioeconomic status with smoking during the second and third trimesters of pregnancy: a register-based study of 932 671 women in Finland from 2000 to 2015
Roustaei, Z., Räisänen, S., Gissler, M., & Heinonen, S. T. (2020) · BMJ Open · doi:10.1136/bmjopen-2019-034839 · Cited by 19
Missing Value Imputation Improves Mortality Risk Prediction Following Cardiac Surgery: An Investigation of an Australian Patient Cohort
Karim, M. N., Reid, C. M., Tran, L., Cochrane, A. D., & Billah, B. (2016) · Heart Lung and Circulation · doi:10.1016/j.hlc.2016.06.1214 · Cited by 19
Estimation with Incomplete Data: The Linear Case
Mohan, K., Thoemmes, F. J., & Pearl, J. (2018) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2018/705 · Cited by 19
“…smoking behavior in insurance applications, longitudinal studies with attrition ([Little, 1995]), people with high income not revealing their incomes and a general reluctance to answer questions about sensitive topics such as religion, sexual preference and abortion ([Greenland and Finkle, 1995]).”
Background
Elevated uric acid and obesity-related cardiovascular disease risk factors among hypertensive youth
Reschke, L. D., Miller, E. R., Fadrowski, J. J., Loeffler, L. F., Holmes, K. W., Appel, L. J., & Brady, T. M. (2015) · Pediatric Nephrology · doi:10.1007/s00467-015-3154-y · Cited by 19
“random laboratory processing error, we conducted multiple imputation utilizing all available information on related covariates [23].”
Method

Authors: Greenland, S., & Finkle, W. D.
Affiliations: University of California, Los Angeles (US)
Corresponding author: Greenland, Sander
ORCID: Greenland, Sander
Venue: American Journal of Epidemiology
Publisher: Oxford University Press (OUP)
Published: 1995-12-15
Volume: 142
Issue: 12
Pages: 1255-1264
ISSN: 0002-9262 (ISSN-L)
1476-6256
DOI: 10.1093/oxfordjournals.aje.a117592
OpenAlex: W2166561686
Cited by: 891
References: 0
Citations by year: 2026: 13 · 2025: 18 · 2024: 13 · 2023: 24 · 2022: 26 · 2021: 21 · 2020: 33 · 2019: 29 · 2018: 34 · 2017: 32 · 2016: 27 · 2015: 40 · 2014: 57 · 2013: 53 · 2012: 67
FWCI: 6.57
Type: journal article
Language: en
Open access: closed
Locations: American Journal of Epidemiology (publishedVersion)
PubMed (publishedVersion)
American Journal of Epidemiology
Funders: National Institutes of Health (n01cp095680-001)
National Cancer Institute (N01 CP 95680)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
Keywords: missing covariates, missing data, logistic regression, bias, model misspecification, multiple imputation, maximum likelihood estimation, weighted estimating equations, endometrial cancer, age at menarche, case-control study
MeSH terms: Epidemiologic Methods, Female, Humans, Menarche, Research Design, Logistic Models, Odds Ratio, Case-Control Studies, Endometrial Neoplasms

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A critical look at methods for handling missing covariates in epidemiologic regression analyses.

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