Optimal robust two-stage designs for genome-wide association studies

Optimal robust two-stage designs for genome-wide association studies are proposed using the maximum of the recessive, additive and dominant linear trend test statistics. These designs combine cost-saving two-stage genotyping with robustness against misspecification of the genetic model and are much more efficient than designs based on a single model specific test statistic in detecting multiple loci with different modes of inheritance. For given power of 90%, typical cost savings of 34% can be realised by increasing the total sample size by about 13% but genotyping only about half of the sample for the full marker set in the first stage and carrying forward about 0.06% of the markers to the second stage analysis. We also present robust two-stage designs providing optimal allocation of a limited budget for pre-existing samples. If a sample is available which would yield a power of 90% when fully genotyped, genotyping only half of the sample due to a limited budget will typically cause a loss of power of more than 55%. Using an optimal two-stage approach in the same sample under the same budget restrictions will limit the loss of power to less than 10%. In general, the optimal proportion of markers to be followed up in the second stage strongly depends on the cost ratio for chips and individual genotyping, while the design parameters of the optimal designs (total sample size, first stage proportion, first and second stage significance limit) do not much depend on the genetic model assumptions.