Optimization of two-stage genetic designs where data are combined using an accurate and efficient approximation for...

There is an increasing interest in the use of two-stage case-control studies to reduce genotyping costs in the search for genes underlying common disorders. Instead of analyzing the data from the second stage separately, a more powerful test can be performed by combining the data from both stages. However, standard tests cannot be used because only the markers that are significant in the first stage are selected for the second stage and the test statistics at both stages are dependent because they partly involve the same data. Theoretical approximations are not available for commonly used test statistics and in this specific context simulations can be problematic because of the computational burden. We therefore derived a cost-effective, that is, accurate but fast in terms of central processing unit (CPU) time, approximation for the distribution of Pearson's statistic on 2 xm contingency tables in two-stage design with combined data. We included this approximation in an iterative method for designing optimal two-stage studies. Simulations supported the accuracy of our approximation. Numerical results confirmed that the use of two-stage designs reduces the genotyping burden substantially. Compared to not combining data, combining the data decreases the required sample sizes on average by 15% and the genotyping burden by 5%.