Case-control studies of genetic markers: power and sample size approximations for Armitage's test for trend

The association of a candidate gene with disease can be efficiently evaluated by a case-control study in which allele frequencies are compared for diseased cases and unaffected controls. However, when the distribution of genotypes in the population deviates from Hardy-Weinberg proportions, the frequency of genotypes--rather than alleles--should be compared by the Armitage test for trend. We present formulas for power and sample size for studies that use Armitage's trend test. The formulas make no assumptions about Hardy-Weinberg equilibrium, but do assume random ascertainment of cases and controls, all of whom are independent of one another. We demonstrate the accuracy of the formulas by simulations.