The DOI matches its Crossref record; 39 of the 39 references it cites were found in a registry or an index.
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]
In the citing paper
“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
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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
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- 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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Calculating the sample size required for developing a clinical prediction model
Riley, R. D., Ensor, J., Snell, K. I. E., Harrell, F. E., Martin, G. P., Reitsma, J. B., Moons, K. G. M., Collins, G., & van Smeden, M. (2020) · BMJ · doi:10.1136/bmj.m441 · Cited by 2,917
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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