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Sparse data bias: a problem hiding in plain sight
Open accessAbstract
Effects of treatment or other exposure on outcome events are commonly measured by ratios of risks, rates, or odds. Adjusted versions of these measures are usually estimated by maximum likelihood regression (eg, logistic, Poisson, or Cox modelling). But resulting estimates of effect measures can have serious bias when the data lack adequate case numbers for some combination of exposure and outcome levels. This bias can occur even in quite large datasets and is hence often termed sparse data bias. The bias can arise or be worsened by regression adjustment for potentially confounding variables; in the extreme, the resulting estimates could be impossibly huge or even infinite values that are meaningless artefacts of data sparsity. Such estimate inflation might be obvious in light of background information, but is rarely noted let alone accounted for in research reports. We outline simple methods for detecting and dealing with the problem focusing especially on penalised estimation, which can be easily performed with common software packages.
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“there is a sparse data risk66 because of small sample sizes and short study durations”
From How does hormone transition in transgender women change body composition, muscle strength and haemoglobin? Systematic review with a focus on the implications for sport participation (2021) · cites this paper as [66]
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“This analysis may also be limited by the possibility of sparse data bias in the pooled OR estimates, as indicated by the unconventional ORs and wide confidence limits produced by some studies.This is problematic as such bias can inflate the estimate of effect measures, which should be taken into account when interpreting the findings of the present analysis.37”
From Risk of atrial fibrillation in athletes: a systematic review and meta-analysis (2021) · cites this paper as [37]
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“However, confounder imprecision does not bias the target estimator, that is, the association of PA on severe COVID-19 outcomes. 29”
From Physical inactivity is associated with a higher risk for severe COVID-19 outcomes: a study in 48 440 adult patients (2021) · cites this paper as [29]
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Cites
A simulation study of the number of events per variable in logistic regression analysis
Peduzzi, P., Concato, J., Kemper, E., Holford, T. R., & Feinstein, A. R. (1996) · Journal of Clinical Epidemiology · doi:10.1016/s0895-4356(96)00236-3 · Cited by 9,655
Hapeman, D. E., & Agresti, A. (1991) · Technometrics · doi:10.1080/00401706.1991.10484817 · Cited by 9,407
Regression Modeling Strategies
Harrell, F. E. (2001) · Springer series in statistics · doi:10.1007/978-1-4757-3462-1 · Cited by 9,270
Harrell (2015) · Springer Series in Statistics · doi:10.1007/978-3-319-19425-7 · Cited by 6,878
Bias reduction of maximum likelihood estimates
FIRTH, D. (1993) · Biometrika · doi:10.1093/biomet/80.1.27 · Cited by 5,035
Relaxing the Rule of Ten Events per Variable in Logistic and Cox Regression
Vittinghoff, E., & McCulloch, C. E. (2007) · American Journal of Epidemiology · doi:10.1093/aje/kwk052 · Cited by 4,359
Clinical Prediction Models: A Practical Approach to Development, Validation, and Updating
Steyerberg, E. W. (2019) · Statistics for Biology and Health · doi:10.1007/978-3-030-16399-0 · Cited by 3,281
Simulation Study of Confounder-Selection Strategies
Maldonado, G., & Greenland, S. (1993) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a116813 · Cited by 2,491
Self-citationTHE IMPACT OF CONFOUNDER SELECTION CRITERIA ON EFFECT ESTIMATION
Mickey, R. M., & Greenland, S. (1989) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a115101 · Cited by 2,382
Self-citationRE:“;THE IMPACT OF CONFOUNDER SELECTION CRITERIA ON EFFECT ESTIMATION”
Greenland, S., & Mickey, R. M. (1989) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a115409 · Cited by 2,114
Self-citation(2010) · Sage eBooks · doi:10.4135/9781412961288.n40 · Cited by 2,028
Regression modelling strategies for improved prognostic prediction
Harrell, F. E., Lee, K. L., Califf, R. M., Pryor, D. B., & Rosati, R. A. (1984) · Statistics in Medicine · doi:10.1002/sim.4780030207 · Cited by 1,804
Why Propensity Scores Should Not Be Used for Matching
King, G., & Nielsen, R. (2019) · Political Analysis · doi:10.1017/pan.2019.11 · Cited by 1,706
- Statistical Models for Epidemiology
Broemeling, L. D. (2013) · Chapman & Hall/CRC eBooks · doi:10.1201/b15382-9 · Cited by 1,346
Confounding and Collapsibility in Causal Inference
Greenland, S., Pearl, J., & Robins, J. M. (1999) · Statistical Science · doi:10.1214/ss/1009211805 · Cited by 933
Self-citationHapeman, D. E., & Agresti, A. (1991) · Technometrics · doi:10.2307/1269056 · Cited by 814
Clinical Prediction Models: A Practical Approach to Development, Validation and Updating
Mann, C. J. H. (2009) · Kybernetes · doi:10.1108/k.2009.06738fae.002 · Cited by 794
Phenylpropanolamine and the Risk of Hemorrhagic Stroke
Kernan, W. N., Viscoli, C. M., Brass, L. M., Broderick, J. P., Brott, T. G., Feldmann, E. G., Morgenstern, L. B., Wilterdink, J. L., & Horwitz, R. I. (2000) · New England Journal of Medicine · doi:10.1056/nejm200012213432501 · Cited by 746
How to develop a more accurate risk prediction model when there are few events
Pavlou, M., Ambler, G., Seaman, S. R., Guttmann, O. P., Elliot, P. M., King, M., & Omar, R. (2015) · BMJ · doi:10.1136/bmj.h3868 · Cited by 698
Problems due to Small Samples and Sparse Data in Conditional Logistic Regression Analysis
Greenland, S., Schwartzbaum, J., & Finkle, W. D. (2000) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a010240 · Cited by 367
Self-citationThe Impact of Model Selection on Inference in Linear Regression
Hurvich, C. M., & Tsai, C. (1990) · The American Statistician · doi:10.1080/00031305.1990.10475722 · Cited by 299
Matched Sampling for Causal Effects: Contributor Acknowledgments
Rubin, D. (2006) · Cambridge University Press eBooks · doi:10.1017/cbo9780511810725 · Cited by 287
Statistical Foundations for Model-Based Adjustments
Greenland, S., & Pearce, N. E. (2015) · Annual Review of Public Health · doi:10.1146/annurev-publhealth-031914-122559 · Cited by 274
Self-citationGreenland, S., & Mansournia, M. A. (2015) · Statistics in Medicine · doi:10.1002/sim.6537 · Cited by 237
Self-citationControl of Confounding in the Assessment of Medical Technology
Greenland, S., & Neutra, R. (1980) · International Journal of Epidemiology · doi:10.1093/ije/9.4.361 · Cited by 201
Self-citationStatistical Models in Epidemiology
Ziegel, E. R., Clayton, D., & Hills, M. (1995) · Technometrics · doi:10.2307/1269644 · Cited by 180
On the Estimation and Use of Propensity Scores in Case-Control and Case-Cohort Studies
Mansson, R., Joffe, M. M., Sun, W., & Hennessy, S. (2007) · American Journal of Epidemiology · doi:10.1093/aje/kwm069 · Cited by 149
Bayesian perspectives for epidemiologic research: III. Bias analysis via missing-data methods
Greenland, S. (2009) · International Journal of Epidemiology · doi:10.1093/ije/dyp278 · Cited by 107
Self-citationAdjustments and their Consequences-Collapsibility Analysis using Graphical Models
Greenland, S., & Pearl, J. (2011) · International Statistical Review · doi:10.1111/j.1751-5823.2011.00158.x · Cited by 91
Self-citationBayesian regression in SAS software
Sullivan, S. G., & Greenland, S. (2012) · International Journal of Epidemiology · doi:10.1093/ije/dys213 · Cited by 87
Self-citationExact Analysis of Discrete Data
(2008) · Technometrics · doi:10.1198/tech.2008.s908 · Cited by 84
Exact Analysis of Discrete Data
Hirji, K. F. (2005) · Chapman & Hall/CRC eBooks · doi:10.1201/9781420036190 · Cited by 78
Predictors of Intensive Care Unit Admission After Total Joint Arthroplasty
Abdelsalam, H., Restrepo, C., Tarity, T. D., et al. (2011) · The Journal of Arthroplasty · doi:10.1016/j.arth.2011.09.027 · Cited by 76
On the Bias of Commonly Used Measures of Association for 2 x 2 Tables
Jewell, N. P. (1986) · Biometrics · doi:10.2307/2531055 · Cited by 60
Approximate Bayesian Logistic Regression via Penalized Likelihood by Data Augmentation
Discacciati, A., Orsini, N., & Greenland, S. (2015) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x1501500306 · Cited by 47
Self-citationPrior data for non‐normal priors
Greenland, S. (2007) · Statistics in Medicine · doi:10.1002/sim.2788 · Cited by 40
Self-citationGreenland, S. (2010) · The American Statistician · doi:10.1198/tast.2010.10006 · Cited by 13
Self-citationComment: Cautions in the use of preliminary‐test estimators
Greenland, S. (1989) · Statistics in Medicine · doi:10.1002/sim.4780080606 · Cited by 13
Self-citationReducing bias and mean squared error associated with regression-based odds ratio estimators
Lyles, R. H., Guo, Y., & Greenland, S. (2012) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2012.05.005 · Cited by 13
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Research works printed but not linked: 1
- Glymour MM, Greenland S. Causal diagrams. In: Rothman KJ, Greenland S, Lash TL, eds. Modern Epidemiology.3rd ed. Lippincott Williams & Wilkins, 2008: 183-209.
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Taylor, R. S., Taylor, R. J., Bayliss, S., Hagström, H., Nasr, P., Schattenberg, J. M., Ishigami, M., Toyoda, H., Wai-Sun Wong, V., Peleg, N., et al. (2020) · Gastroenterology · doi:10.1053/j.gastro.2020.01.043 · Cited by 1,069
Sallis, R., Young, D. R., Tartof, S. Y., Sallis, J. F., Sall, J., Li, Q., Smith, G. N., & Cohen, D. A. (2021) · British Journal of Sports Medicine · doi:10.1136/bjsports-2021-104080 · Cited by 789
Handling time varying confounding in observational research
Mansournia, M. A., Etminan, M., Danaei, G., Kaufman, J. S., & Collins, P. G. S. (2017) · BMJ · doi:10.1136/bmj.j4587 · Cited by 343
“23 The parametric G formula is the method of choice for estimating the effects of multiple risk factors (joint interventions) and dynamic interventions.”
MethodSelf-citationSeparation in Logistic Regression: Causes, Consequences, and Control
Mansournia, M. A., Geroldinger, A., Greenland, S., & Heinze, G. (2017) · American Journal of Epidemiology · doi:10.1093/aje/kwx299 · Cited by 302
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Metadata
- Authors
- Greenland, S., Mansournia, M. A., & Altman, D. G.
- Affiliations
- University of California, Los Angeles (US)
- University of Oxford (GB)
- Venue
- BMJ
- Publisher
- BMJ
- Published
- 2016-04-27
- Volume
- 352
- Pages
- i1981
- ISSN
- 1756-1833 (ISSN-L)
- OpenAlex
- W2343557095
- Semantic Scholar
- 30977540a580178337ada4e9b42e3df884bb51ce
- Cited by
- 898
- References
- 38
- Citations by year
- 2026: 77 · 2025: 83 · 2024: 92 · 2023: 94 · 2022: 82 · 2021: 98 · 2020: 99 · 2019: 80 · 2018: 75 · 2017: 109 · 2016: 8
- FWCI
- 91.86
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- BMJ (publishedVersion)
- PubMed (publishedVersion)
- HighWire Press Open Archive (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Keywords
- relative risk, odds ratio, rate ratios, confounding adjustment
- MeSH terms
- Humans, Bias, Likelihood Functions, Odds Ratio, Outcome Assessment, Health Care, Sample Size, Risk Assessment, Quality Improvement
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