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

The American Journal of Cardiology, Available online 29 March 2012
William K. Chan, BHSca, b, Donald A. Redelmeier, MDa, b, c, d, ,
a Department of Medicine, University of Toronto, Toronto, Ontario, Canada
b Institute for Clinical Evaluative Sciences in Ontario, Toronto, Ontario, Canada
c Clinical Epidemiology Program, Sunnybrook Health Sciences Centre, Toronto, Ontario, Canada
d Center for Leading Injury Prevention Practice Education & Research, Toronto, Ontario, Canada
Received 28 January 2012. Revised 21 February 2012. Accepted 21 February 2012. Available online 29 March 2012.

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.

Figure 1.

When the full cohort of patients is analyzed as a whole, low levels of vitamin D are associated with increased heart disease (odds ratio 1.36, 95% confidence interval 1.16 to 1.59, p <0.001).
When the study is stratified into sedentary and active patient subgroups, however, the effect reverses,
and vitamin D deficiency seems to protect against heart disease (odds ratio 0.75, 95% confidence interval 0.57 to 0.99, p = 0.037).
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Wikpedia example

Low birth weight paradox
The low birth weight paradox is an apparently paradoxical observation relating to the birth weights and mortality of children born to tobacco smoking mothers.
As a usual practice, babies weighing less than a certain amount (which varies between different countries) have been classified as having low birth weight.
In a given population, babies with low birth weights have had a significantly higher infant mortality rate than others.
However, it has been observed that babies of low birth weights born to smoking mothers have a lower mortality rate than the babies of low birth weights of non-smokers.[15]