In this analysis the replication sample was smaller than the training sample, and we may ask what balance of sample sizes is optimal. Given the total sample size of 3322+2687 = 6009 cases and 3587+2656 = 6243 controls, the non-centrality parameter can be numerically maximised over the proportion of subjects allocated to the training sample. It is found that the optimal split is close to one-half regardless of the proportion of null SNPs or the P-value threshold, and the non-centrality parameter is roughly symmetrical around one-half. This suggests that given two samples of different size, it matters little which is chosen for training and which for testing. Furthermore, given an initial sample to be split into training and replication subsets, an obvious rule of thumb is to make an even split. Similar properties are seen under different genetic models (results not shown). Note that these results apply to association testing and not to individual prediction, which is discussed in the next subsection. For association testing there is a balance to be made between the precision of estimating the score in
