Power of Logistic Model with Surrogate Measures for Both Outcome and Covariate in Genetic-Disease Association Study

This study deals with the combined effects of misclassifications incidental to diagnostics, or a binary response, and genotyping, or a discrete covariate, on the statistical power of a logistic model testing for a treatment effect. The loss of power due to differential and nondifferential misclassifications in a response and a covariate, respectively, has not been well documented. This paper first obtained a general expression for the loss of statistical power due to those misclassifications based on the Pitman asymptotic relative efficiency (ARE). Numerical studies confirmed the validity of the general expression for a reasonable sample size. It revealed that the effect of even low misclassification rates is not negligible. Misclassifications in both response and covariates should be taken into account when determining the sample size.