It is more likely that the sample size is fixed (say, to provide sufficient power to detect a single association) and the goal is to minimise costs while achieving power close to that of the one-stage design [23]. In many situations, the cost can be halved while keeping power within 1 per cent of the one-stage design; thus, the total sample size can be calculated to achieve a certain power (say 81 per cent) in the one-stage design and parameters then optimised for a two-stage design. Considering a range of genetic models, a general guideline is to set the sample size of the first stage to have 97 per cent power for individual tests and carry forward all markers with nominal p-values less than 0.15. The sample size for the first stage cannot be calculated without knowledge of the true effects, however, so a more practical approach is to consider the ranks of test statistics of the true effects [24]. Here, it is shown that similar information to the one-stage design is obtained by genotyping all markers on 50 per
