Despite these advantages, our work is subject to limitations and leaves several questions open for future exploration. First, although we have demonstrated large relative improvements in prediction accuracy, absolute prediction accuracies are currently not large enough to achieve clinical utility, which will require larger sample sizes (Chatterjee et al., 2013; Dudbridge, 2013); our simulations suggest that multi-ethnic polygenic risk scores will continue to produce improvements at larger sample sizes (Fig 1). Second, while our focus here was on prediction without using individual-level training data, when such data is available it may be possible to attain higher prediction accuracy using methods that fit all markers simultaneously, such as Best Linear Unbiased Predictor (BLUP) methods and their extensions (de los Campos et al., 2010; Golan & Rosset, 2014; Maier et al., 2015; Moser et al., 2015; Speed & Balding, 2014; Tucker et al., 2015; Weissbrod et al., 2016; Zhou et al., 2013). Third, our LDpred risk prediction method (Vilhjálmsson et al., 2015), which analyzes summary statistics in conjunction with LD information from a reference panel, is more accurate in European populations than
