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Keywords:

  • association;
  • case-control;
  • allelic test;
  • Armitage's trend test;
  • Hardy-Weinberg equilibrium;
  • Slutzky's theorem

Summary

This paper reconsiders the relevant contribution of Sasieni in the validity of allele-based tests in case-control genetic association studies. In particular, the author clearly demonstrates that the classical chi-square test applied to allelic contingency tables is biased when the combined case-control population is not in Hardy-Weinberg equilibrium. As an alternative, he suggests using the Cochran-Armitage test for trends by basing his argument on the fact that these two tests are asymptotically equivalent at the Hardy-Weinberg equilibrium. However he only demonstrates the equality of the statistics when the observed genotypic proportions are strictly in equilibrium - which does not formally imply the suggested, and often accepted, asymptotic behavior.

In this short communication, we complement this contribution by providing the proof that allelic and trend statistics are asymptotically equivalent under the conditions mentioned above. In addition, since the ‘biased’ allelic test is still widely used in the literature, we briefly discuss the different alternatives that have been subsequently developed, based on Sasieni's conclusions.