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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“73 In the presence of sparsity, the effect size is difficult to interpret.”
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Hargreaves, J., Krishnaratne, S., Mathema, H., Lilleston, P. S., Sievwright, K. M., Mandla, N., Mainga, T., Vermaak, R., Piwowar‐Manning, E., Schaap, A., et al. (2018) · AIDS · doi:10.1097/qad.0000000000001757 · Cited by 66
“Wide confidence intervals for some associations reflect few events for some outcomes, limited intercluster variation for some exposure variables and the small number of clusters [22].”
Background
Small steps, strong shield: directly measured, moderate physical activity in 65 361 adults is associated with significant protective effects from severe COVID-19 outcomes
Steenkamp, L., Saggers, R. T., Bandini, R. M., Stranges, S., Choi, Y., Thornton, J. S., Hendrie, S., Patel, D., Rabinowitz, S., & Patricios, J. (2022) · British Journal of Sports Medicine · doi:10.1136/bjsports-2021-105159 · Cited by 66
Selection and co-selection of antibiotic resistances among Escherichia coli by antibiotic use in primary care: An ecological analysis
Pouwels, K. B., Müller‐Pebody, B., Smieszek, T., Hopkins, S., & Robotham, J. V. (2019) · PLoS ONE · doi:10.1371/journal.pone.0218134 · Cited by 64
“Elastic net regularization is especially useful when encountering situations with high collinearity, such as strong correlations in antibiotic usage, and a relatively large number of variables (antibiotic groups) compared to the amount of observations [16,18,19].”
Background
Clinical outcomes in adult athletes with hypertrophic cardiomyopathy: a 7-year follow-up study
Pelliccia, A., Caselli, S., Pelliccia, M., Musumeci, B., Lemme, E., Paolo, F. M. D., Maestrini, V., Russo, D., Limite, L. R., Borrazzo, C., et al. (2020) · British Journal of Sports Medicine · doi:10.1136/bjsports-2019-100890 · Cited by 64
Harnessing the Power of Machine Learning in Dementia Informatics Research: Issues, Opportunities, and Challenges
Tsang, G., Xie, X., & Zhou, S. (2019) · IEEE Reviews in Biomedical Engineering · doi:10.1109/rbme.2019.2904488 · Cited by 64
“…the employment of sparse optimised feature selection, dimensionality reduction or representation learning for effective biomarker and risk factor identiﬁcation; and adequate data coverage producing meaningless artefacts and bias termed sparse data bias , potential solutions of which exist [98].”
Background
Tenets for the Proper Conduct and Use of Meta-Analyses: A Practical Guide for Neurosurgeons
Lee, K. S., Zhang, J. J. Y., Nga, V. D. W., Ng, C. H., Tai, B. C., Higgins, J. P. T., & Syn, N. L. X. (2022) · World Neurosurgery · doi:10.1016/j.wneu.2021.09.034 · Cited by 63
Baseline Prostate-specific Antigen Level in Midlife and Aggressive Prostate Cancer in Black Men
Preston, M. A., Gerke, T. A., Carlsson, S., et al. (2018) · European Urology · doi:10.1016/j.eururo.2018.08.032 · Cited by 61
Which Factors Are Associated with Local Control and Survival of Patients with Localized Pelvic Ewing’s Sarcoma? A Retrospective Analysis of Data from the Euro-EWING99 Trial
Andreou, D., Ranft, A., Gosheger, G., Timmermann, B., Ladenstein, R. L., Hartmann, W., Bauer, S., Baumhoer, D., van den Berg, H., Dijkstra, P. D. S., et al. (2019) · Clinical Orthopaedics and Related Research · doi:10.1097/corr.0000000000000962 · Cited by 61
“Furthermore, the observational nature of this analysis meant that adequate patient numbers may have been lacking some combinations of risk factors and investigated outcomes in our cohort, leading to possible sparse-data bias [12, 22], which is highlighted by the very wide confidence intervals of the persistent extraos…”
Background
Coping With the “Small Sample–Small Relevant Effects” Dilemma in Elite Sport Research
Skorski, S., & Hecksteden, A. (2021) · International Journal of Sports Physiology and Performance · doi:10.1123/ijspp.2021-0467 · Cited by 60
Is breast feeding associated with offspring IQ at age 5? Findings from prospective cohort: Lifestyle During Pregnancy Study
Strøm, M., Mortensen, E. L., Kesmodel, U. S., et al. (2019) · BMJ Open · doi:10.1136/bmjopen-2018-023134 · Cited by 59
“Associations tended to be attenuated with increasing number of covariates in our analyses, suggesting unadjusted confounding or sparse data bias.(55) As is always the case in observational studies, we cannot exclude that our results are affected by residual confounding or confounding by factors not accounted for in ou…”
Time-to-event analysis for sports injury research part 2: time-varying outcomes
Nielsen, R. O., Bertelsen, M. L., Ramskov, D., Møller, M., Hulme, A., Theisen, D., Finch, C. F., Fortington, L. V., Mansournia, M. A., & Parner, E. T. (2018) · British Journal of Sports Medicine · doi:10.1136/bjsports-2018-100000 · Cited by 60
Self-citation
Genome-wide association study of extreme high bone mass: Contribution of common genetic variation to extreme BMD phenotypes and potential novel BMD-associated genes
Gregson, C. L., Newell, F., Leo, P. J., Clark, G. R., Paternoster, L., Marshall, M. S., Forgetta, V., Morris, J. A., Ge, B., Bao, X. Y., et al. (2018) · Bone · doi:10.1016/j.bone.2018.06.001 · Cited by 58
“Because gender was not evenly distributed within study populations (only 44 male individuals, all amongst unexplained HBM cases), inclusion as a covariate risks introducing sparse data bias [26], hence gender was not used as a covariate.”
Background
Perceived influence of street-level visible greenness exposure in the work and residential environment on life satisfaction: Evidence from Beijing, China
Wu, W., Yao, Y., Song, Y., He, D., & Wang, R. (2021) · Urban forestry & urban greening · doi:10.1016/j.ufug.2021.127161 · Cited by 56
Fifteen-week window for recurrent muscle strains in football: a prospective cohort of 3600 muscle strains over 23 years in professional Australian rules football
Orchard, J. W., Orchard, J. W., Jomaa, M. C., et al. (2020) · British Journal of Sports Medicine · doi:10.1136/bjsports-2019-100755 · Cited by 56
Treating low back pain in athletes: a systematic review with meta-analysis
Thornton, J. S., Cañeiro, J. P., Hartvigsen, J., Ardern, C. L., Vinther, A., Wilkie, K., Trease, L., Ackerman, K. E., Dane, K., McDonnell, S., et al. (2020) · British Journal of Sports Medicine · doi:10.1136/bjsports-2020-102723 · Cited by 57
To tune or not to tune, a case study of ridge logistic regression in small or sparse datasets
Šinkovec, H., Heinze, G., Blagus, R., & Geroldinger, A. (2021) · BMC Medical Research Methodology · doi:10.1186/s12874-021-01374-y · Cited by 64
“Moreover, it also enables valid Bayesian inference [1, 13].”
BackgroundMethodInfluential
Bias in Odds Ratios From Logistic Regression Methods With Sparse Data Sets
Gosho, M., Ohigashi, T., Nagashima, K., Ito, Y., & Maruo, K. (2021) · Journal of Epidemiology · doi:10.2188/jea.je20210089 · Cited by 64
“Greenland et al (2016) stated that the sparse data bias of OR could be more serious than the bias removed by covariate adjustment.2 However, to the best of our knowledge, there is no insightful study that has simultaneously evaluated the “sparse data bias” and “covariate omission bias.””
Background
Effects of different doses of exercise and diet-induced weight loss on beta-cell function in type 2 diabetes (DOSE-EX): a randomized clinical trial
Legaard, G. E., Lyngbæk, M. P. P., Almdal, T., Karstoft, K., Bennetsen, S. L., Feineis, C. S., Nielsen, N. S., Durrer, C. G., Liebetrau, B., Nystrup, U., et al. (2023) · Nature Metabolism · doi:10.1038/s42255-023-00799-7 · Cited by 55
“As sparsity of dichotomous outcomes (as expected for medications) invalidates the confidence intervals, exact logistic regression (exlogistic in Stata) was used when cases were 5 59,60 .”
Method
Quantification of selection bias in studies of risk factors for birth defects among livebirths
Heinke, D., Rich-Edwards, J. W., Williams, P. L., Hernández–Dı́az, S., Anderka, M., Fisher, S. C., Desrosiers, T. A., Shaw, G. M., Romitti, P. A., Canfield, M. A., et al. (2020) · Paediatric and Perinatal Epidemiology · doi:10.1111/ppe.12650 · Cited by 55
Effects of previous infection, vaccination, and hybrid immunity against symptomatic Alpha, Beta, and Delta SARS-CoV-2 infections: an observational study
Altarawneh, H. N., Chemaitelly, H. S., Ayoub, H. H., Tang, P., Hasan, M. R., Yassine, H. M., Al-Khatib, H. A., Thani, A. A. A., Coyle, P. V., Kanaani, Z. A., et al. (2023) · EBioMedicine · doi:10.1016/j.ebiom.2023.104734 · Cited by 58
Malnutrition as a Risk Factor in Cleft Lip and Palate Surgery
Escher, P. J., Zavala, H., Lee, D., et al. (2020) · The Laryngoscope · doi:10.1002/lary.29209 · Cited by 53
“Sparse data bias can substantially bias maximum likelihood estimates of the logit model coefficients.(19)”
Background
Safety and efficacy of cerliponase alfa in children with neuronal ceroid lipofuscinosis type 2 (CLN2 disease): an open-label extension study
Schulz, A., Specchio, N., Reyes, E. D. L., Gissen, P., Nickel, M., Trivisano, M., Aylward, S. C., Chakrapani, A., Schwering, C., Wibbeler, E., et al. (2023) · The Lancet Neurology · doi:10.1016/s1474-4422(23)00384-8 · Cited by 58
Predicting Functional Dependence in Mild Cognitive Impairment: Differential Contributions of Memory and Executive Functions
Mansbach, W. E., & Mace, R. A. (2018) · The Gerontologist · doi:10.1093/geront/gny097 · Cited by 58
Prevalence of suicidal behaviour among nursing and midwifery college students in Ghana
Quarshie, E. N., Cheataa-Plange, H. V., Annor, F., Asare‐Doku, W., & Lartey, J. K. S. (2019) · Nursing Open · doi:10.1002/nop2.271 · Cited by 50
The Impact of Workload on Operational Risk: Evidence from a Commercial Bank
Xu, Y., Tan, T. F., & Netessine, S. (2021) · Management Science · doi:10.1287/mnsc.2021.4019 · Cited by 52
“Even if the model converges, the estimated coefficients might be biased (Greenland et al., 2016).”
Association of Kidney Function Biomarkers with Brain MRI Findings: The BRINK Study
Vemuri, P., Knopman, D. S., Jack, C. R., Lundt, E. S., Weigand, S. D., Zuk, S. M., Thostenson, K. B., Reid, R. I., Kantarci, K., Slinin, Y., et al. (2016) · Journal of Alzheimer s Disease · doi:10.3233/jad-160834 · Cited by 50
“This reduction in bias can often come at the cost of increased variance and model instability, but PML estimation is recommended as the most principled method to counter this problem and is an important aspect of this work [30].”
Association between early childhood caries and malnutrition in a sub-urban population in Nigeria
Foláyan, M., Arije, O., Tantawi, M. E., Kolawole, K., Obiyan, M. O., Arowolo, O., & Oziegbe, E. (2019) · BMC Pediatrics · doi:10.1186/s12887-019-1810-2 · Cited by 44
Factors associated with food safety compliance among street food vendors in Can Tho city, Vietnam: implications for intervention activity design and implementation
Huynh-Van, B., Vuong-Thao, V., Huynh-Thi-Thanh, T., Dang-Xuan, S., Huynh-Van, T., Tran-To, L., Nguyen-Thi-Thao, N., Huynh-Bach, C., & Nguyen‐Viet, H. (2022) · BMC Public Health · doi:10.1186/s12889-022-12497-2 · Cited by 49
“Type of vendors was treated as a predictor variable to avoid the sparseness of data (stratification would reduce the sample size, which might have negatively impacted the performance of the models) [25] and to avoid computational complexities given that we had to include, simultaneously, other covariates and confounde…”
Background
On the 12th Day of Christmas, a Statistician Sent to Me . . .
Riley, R. D., Cole, T. J., Deeks, J. J., Kirkham, J. J., Morris, J., Perera, R., Wade, A. M., & Collins, P. G. S. (2022) · BMJ · doi:10.1136/bmj-2022-072883 · Cited by 50
Association Between Mental Health and Reproductive System Disorders in Women
Zaks, N., Batuure, A., Lin, E. S., Rommel, A., Reichenberg, A., Grice, D. E., Bergink, V., Fox, N. S., Mahjani, B., & Janecka, M. (2023) · JAMA Network Open · doi:10.1001/jamanetworkopen.2023.8685 · Cited by 54
Neurological, psychiatric, and sleep investigations after treatment of anti-leucine-rich glioma-inactivated protein 1 (LGI1) encephalitis in Spain: a prospective cohort study
Lopetegi, A. M., Guasp, M., Prades, L., et al. (2024) · The Lancet Neurology · doi:10.1016/s1474-4422(23)00463-5 · Cited by 49
Favorable Antiviral Effect of Metformin on SARS-CoV-2 Viral Load in a Randomized, Placebo-Controlled Clinical Trial of COVID-19
Bramante, C. T., Beckman, K. B., Mehta, T., Karger, A. B., Odde, D. J., Tignanelli, C. J., Buse, J. B., Johnson, D. M., Watson, R. H. B., Daniel, J. J., et al. (2024) · Clinical Infectious Diseases · doi:10.1093/cid/ciae159 · Cited by 63
Significant Correlation between High-Risk HPV DNA in Semen and Impairment of Sperm Quality in Infertile Men.
Moghimi, M., Zabihi-Mahmoodabadi, S., Vakilabad, A. A. K., & Kargar, Z. (2019) · Europe PMC (PubMed Central) · doi:10.22074/ijfs.2019.5421 · Cited by 49
“Penalized logistic regression model with data augmentation was performed to compare the frequency of high-risk HPV DNA between infertile and fertile men (16).”
Method
Does Site Matter? Impact of Inertial Measurement Unit Placement on the Validity and Reliability of Stride Variables During Running: A Systematic Review and Meta-analysis
Horsley, B. J., Tofari, P. J., Halson, S. L., Kemp, J. G., Dickson, J., Maniar, N., & Cormack, S. J. (2021) · Sports Medicine · doi:10.1007/s40279-021-01443-8 · Cited by 49
Prevalence and factors associated with SARS-CoV-2 seropositivity in the Spanish HIV Research Network Cohort
Berenguer, J., Díez, C., Martin‐Vicente, M., Micán, R., Pérez-Elı́as, M. J., García-Fraile, L. J., Vidal, F., Suárez‐García, I., Podzamczer, D., Romero, J. D., et al. (2021) · Clinical Microbiology and Infection · doi:10.1016/j.cmi.2021.06.023 · Cited by 48
Do physical interventions improve outcomes following concussion: a systematic review and meta-analysis?
Reid, S. A., Farbenblum, J., & McLeod, S. (2021) · British Journal of Sports Medicine · doi:10.1136/bjsports-2020-103470 · Cited by 47
How street greenery facilitates active travel for university students
Bai, Y., Cao, M., Wang, R., Liu, Y., & Wang, S. (2022) · Journal of Transport & Health · doi:10.1016/j.jth.2022.101393 · Cited by 47
“’ To avoid sparse data bias (Greenland et al., 2016), we recorded this variable as a binary variable rather than a scale variable, for which a response of ‘Yes ’ was recorded as 1 and ‘No ’ was recorded as 0.”
Methods matter: population attributable fraction (PAF) in sport and exercise medicine
Khosravi, A., Nielsen, R. O., & Mansournia, M. A. (2020) · British Journal of Sports Medicine · doi:10.1136/bjsports-2020-101977 · Cited by 46
Self-citation

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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Sparse data bias: a problem hiding in plain sight

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