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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”
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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”
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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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