Table 3.

Average and overall results of model comparisons

		Average results on the testing dataset over 100 iterations	Overall results on the entire discovery cohort	Results on the replication cohort
	Models	Average adjusted R 2	Overall adjusted R 2	Overall adjusted R 2
FN-BMD	Model 1: conventional risk factors alone (sex, age, BMI, current smoking status, menopausal status)	0.33	0.33	0.36
	Model 2: selected metabolites alone	0.15	0.16	0.09
	Model 3: conventional risk factors + selected metabolites	0.34	0.36	0.39
			Overall p-value	Overall p-value
	Comparison of model 1 and model 3 by F-test		< 0.001	<0.001
LS-BMD	Model 1: conventional risk factors alone (sex, age, BMI, current smoking status, menopausal status)	0.23	0.23	0.30
	Model 2: selected metabolites alone	0.15	0.18	0.13
	Model 3: conventional risk factors + selected metabolites	0.25	0.28	0.35
			Overall p-value	Overall p-value
	Comparison of model 1 and model 3 by F-test		< 0.001	<0.001

Average adjusted R² calculates the mean of adjusted R² over 100 iterations using the testing dataset. Overall adjusted R² is the adjusted R² based on the final selected metabolites whose cumulative selection frequency ≥ 50 over 100 iterations using the entire dataset. Overall p-value calculated the p-value from the F-test between model 1 and model 3 on the entire dataset. BMD=bone mineral density. FN=femoral neck. LS=lumbar spine.