Cited by 898Statistical Methods in EpidemiologyAdvanced Causal Inference TechniquesStatistical Methods and Inference

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Sparse data bias: a problem hiding in plain sight

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Greenland, Sander, Mansournia, Mohammad Ali, Altman, Douglas G·2016·BMJ

DOI 10.1136/bmj.i1981

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Abstract

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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Authors: Greenland, S., Mansournia, M. A., & Altman, D. G.
Affiliations: University of California, Los Angeles (US)
University of Oxford (GB)
ORCID: Greenland, Sander
Altman, Douglas G
Venue: BMJ
Publisher: BMJ
Published: 2016-04-27
Volume: 352
Pages: i1981
ISSN: 1756-1833 (ISSN-L)
DOI: 10.1136/bmj.i1981
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
Licence: www.bmj.org/licenses/tdm/1.0/terms-and-conditions.html (tdm)
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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