Computing asymptotic power and sample size for case-control genetic association studies in the presence of phenotype and/or genotype misclassification errors.

It is well established that phenotype and genotype misclassification errors reduce the power to detect genetic association. Resampling a subset of the data (e.g, double-sampling) of genotype and/or phenotype with a gold standard measurement is one method to address this issue. We derive the non-centrality parameter (NCP) for the recently published Likelihood Ratio Test Allowing for Error (LRTae) in the presence of random phenotype and genotype errors. With the NCP, power and sample size can be analytically determined at any significance level. We verify analytic power with simulations using a 2**k factorial design given high and low settings of: case and control genotype frequencies, phenotype and genotype misclassification probabilities, total sample size, ratio of cases to controls, and proportions of phenotype and/or genotype double-samples. We also perform example applications of our method assuming equal costs for the LRTae method and the standard method that does not use double-sample information (LRTstd) to determine if power gain due to double-sampling a proportion of samples outweighs the reduction in sample size due to additional costs in obtaining double-samples. Our results showed a median difference of at most 0.01 between analytic and simulation power for the factorial design settings, with maximum difference of 0.054. For our cost/benefits analysis calculations, results for genotype errors are that double-sampling appears most beneficial (in terms of power gain) when cost of double-sampling is relatively low, irrespective of the proportion of individuals double-sampled. In the presence of phenotype error, there is always power gain using the LRTae method for the parameter settings considered. We have freely available software that performs power and sample size calculations for the LRTae method and cost/benefits analyses comparing power for LRTae and LRTstd methods assuming equal costs.