An association measurement between two variables X and Y may be dramatically changed from positive to negative by omitting a third variable Z, which is called Simpson’s paradox or the Yule-Simpson paradox (Yule, 1903; Simpson, 1951). A numerical example is shown in Table 1. The risk difference (RD) is defined as the difference between the recovery proportion in the treated group and that in the placebo group, RD = (80 ∕ 200) − (100 ∕ 200) = − 0. 10. If the population is split into two populations of male and female, a dramatic change can be seen from Table 2. The risk differences for male and female are both changed to 0. 10. Thus we obtain a self-contradictory conclusion that the new drug is effective for both male and female but it is ineffective for the whole population. Should patients in the population take the new drug or not? Should the correct answer depend on whether the doctor know the gender of patients?
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References and Further Reading
Chen H, Geng Z, Jia J (2007) Criteria for surrogate endpoints. J R Stat Soc B 69:919–932
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Geng, Z. (2011). Simpson’s Paradox. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_519
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