In subsequent analyses, missingness was handled in two ways. The missing values were either imputed using mean imputation (i.e., missing values are imputed with the sample mean of the appropriate phenotype). This type of imputation, which was done for MANOVA, sum score, Simes and TATES, is standard in MultiPhen [11] and canonical correlation analysis in Plink [13]. Alternatively, the analyses were based on all available valid data. The sum score was then calculated as a weighted sum (i.e., the sum of all available data, divided by the total number of available data). For Simes and TATES, the univariate tests were based on all available data, and the p-values, now due to the missingness based on different sample sizes, were combined as usual. (Whether a correction is required to deal with the fact that the p-values are based on different sample sizes, is open to debate. In theory, the test statistic, and thus the p-value, already take N into account. In practice, however, a procedure that weights for the sample size can be more powerful [34]. We tried one type of
