High as the sample sizes are in Table II, they are underestimates because in reality both G and E are likely measured with error. As discussed below, accurate measurement of environmental exposures is the exception rather than the rule. Genotypes are also subject to measurement errors but these are generally small compared with errors in environmental exposures. However, in GWAS, the vast majority of the common SNPs are not measured directly but rather are captured through tag SNPs. When testing for SNP main effects, it is well known that imperfect tagging inflates the required sample size by a factor of approximately 1/r2 [Pritchard and Przeworski, 2001]. Under certain assumptions, this applies more generally to covariates measured with error, specifically the required sample is inflated by the reciprocal of the square of the correlation coefficient between the true value of the covariate and its measurement [Devine and Smith, 1998]. Thus, if rG2 is the LD between a tag SNP and the causal SNP, and rE2 is the squared correlation coefficient between the true exposure and the measured exposure, we can expect
