Simpson's Paradox and the Association Between Vitamin D Deficiency and Increased Heart Disease

  • William K. Chan
    Department of Medicine, University of Toronto, Toronto, Ontario, Canada

    Institute for Clinical Evaluative Sciences in Ontario, Toronto, Ontario, Canada
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  • Donald A. Redelmeier
    Corresponding author: Tel: 416-480-6999; fax: 416-480-6048
    Department of Medicine, University of Toronto, Toronto, Ontario, Canada

    Institute for Clinical Evaluative Sciences in Ontario, Toronto, Ontario, Canada

    Clinical Epidemiology Program, Sunnybrook Health Sciences Centre, Toronto, Ontario, Canada

    Center for Leading Injury Prevention Practice Education & Research, Toronto, Ontario, Canada
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      Several recent investigations have highlighted a potential link between vitamin D deficiency and increased heart disease. Observational studies suggest cardioprotective benefits related to supplementation, but randomized trials remain to be conducted. This report adds a caution based on a statistical paradox that is rarely mentioned in formal medical training or in common medical journals. Insight into this phenomenon, termed Simpson's paradox, may prevent clinicians from drawing faulty conclusions about vitamin D deficiency and heart disease.
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      Linked Article

      • Mixing of Confounding and Non-Collapsibility: A Notable Deficiency of the Odds Ratio
        American Journal of CardiologyVol. 111Issue 2
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          We read with interest the report by Chan and Redelmeier1 about Simpson's paradox in medical studies. Using a hypothetical example, the investigators aimed to draw clinicians' attention to this paradox in medical research. We would like to remind readers that the discrepancy between a crude and a stratified odds ratio (OR) actually conflates 2 different components, namely, a confounding bias and a noncollapsibility effect.2
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