Table 1.

Maximum Phenotypic Variance Explained by Optimized Polygenic Scores and the Maximum Cumulative Out-of-Sample Prediction $R^2$ for SOJO and GCTA-COJO in UKB

	Cumulative Prediction$R^2$(%)				$R^2$Explained by Polygenic Scores (%)
Trait	Top Variant	Standard COJO	Optimized COJO	SOJO	Top Variant	Standard COJO	Optimized COJO	SOJO
Height	14.35	17.38	23.42	24.52	13.76	16.71	21.42	22.70
BMI	1.88	1.99	2.42	2.52	1.84	1.94	2.35	2.46
WHRadjBMI	1.62	1.78	2.18	2.32	1.58	1.76	2.07	2.28

The $R^2$ for cumulative out-of-sample prediction was computed from a summation of all regional prediction $R^2$. $R^2$ explained by polygenic scores were the amount of phenotypic variance that could be explained by all regional polygenic scores.

Top variant: only the top variant was selected. Standard COJO: variants selected by COJO with $5\times {10}^{-8}$ as the threshold. Optimized COJO: variants selected by COJO with threshold maximizing regional prediction $R^2$. Coefficients of variants in each polygenic score were estimated by joint multiple regression in COJO. SOJO: variants selected by LASSO with tuning parameter maximizing regional prediction $R^2$. Coefficients of variants in each polygenic score were determined by the LASSO result at the tuning parameter.