Simpson's paradox and calculation of number needed to treat from meta-analysis

Cates, Christopher J

doi:10.1186/1471-2288-2-1

Cited by 251Meta-analysis and systematic reviewsStatistical Methods in Clinical TrialsStatistical Methods in Epidemiology

Simpson's paradox and calculation of number needed to treat from meta-analysis

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Cates, Christopher J·2002·BMC Medical Research Methodology

DOI 10.1186/1471-2288-2-1PMC PMC65632

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Abstract

BACKGROUND: Calculation of numbers needed to treat (NNT) is more complex from meta-analysis than from single trials. Treating the data as if it all came from one trial may lead to misleading results when the trial arms are imbalanced. DISCUSSION: An example is shown from a published Cochrane review in which the benefit of nursing intervention for smoking cessation is shown by formal meta-analysis of the individual trial results. However if these patients were added together as if they all came from one trial the direction of the effect appears to be reversed (due to Simpson's paradox). Whilst NNT from meta-analysis can be calculated from pooled Risk Differences, this is unlikely to be a stable method unless the event rates in the control groups are very similar. Since in practice event rates vary considerably, the use a relative measure, such as Odds Ratio or Relative Risk is advocated. These can be applied to different levels of baseline risk to generate a risk specific NNT for the treatment. SUMMARY: The method used to calculate NNT from meta-analysis should be clearly stated, and adding the patients from separate trials as if they all came from one trial should be avoided.

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Unlike risk ratios, which may be fairly independent of the patients' baseline risk status, absolute risk reduction and number needed to treat measures can be pooled together in meta-analyses if the event rates in the control groups are very similar.
“On the other hand, unlike risk ratios which “may be fairly independent of the patients’ baseline risk status,” ARR and NNT measures can be pooled together in meta-analyses if “the event rates in the control groups are very similar” [27].”
From Relative risk reduction: Misinformative measure in clinical trials and COVID-19 vaccine efficacy (2022) · cites this paper as [27]

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Authors: Cates, C. J.
Corresponding author: Cates, Christopher J
ORCID: Cates, Christopher J
Venue: BMC Medical Research Methodology
Publisher: Springer Science and Business Media LLC
Published: 2002-01-25
Volume: 2
Issue: 1
Pages: 1-1
ISSN: 1471-2288 (ISSN-L)
DOI: 10.1186/1471-2288-2-1
PMC: PMC65632
OpenAlex: W1576173198
Cited by: 251
References: 17
Citations by year: 2026: 2 · 2025: 4 · 2024: 7 · 2023: 3 · 2022: 3 · 2021: 20 · 2020: 13 · 2019: 14 · 2018: 16 · 2017: 22 · 2016: 23 · 2015: 8 · 2014: 13 · 2013: 13 · 2012: 10
FWCI: 10.16
Type: journal article
Language: en
Open access: gold
doi.org
Licence: www.springer.com/tdm (unspecified)
Locations: BMC Medical Research Methodology (publishedVersion)
Europe PMC (PubMed Central) (publishedVersion, other-oa)
PubMed Central (publishedVersion, other-oa)
PubMed (publishedVersion)
St George's Online Research Archive (St George's University of London) (acceptedVersion)
DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
Topics: Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
Keywords: Simpson's paradox, number needed to treat, meta-analysis, risk difference, odds ratio, relative risk, baseline risk, smoking cessation, nursing interventions
MeSH terms: Clinical Trials as Topic, Data Interpretation, Statistical, Humans, Statistics as Topic, Meta-Analysis as Topic, Reproducibility of Results, Bias, Odds Ratio, Smoking Cessation, Sample Size

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Simpson's paradox and calculation of number needed to treat from meta-analysis

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