(i) Multiple linear regression analysis

To identify which FE parameters were the most important determinants of fracture risk, multiple linear regression analysis was performed with each FE parameter serving as the dependent variable [11]. Based on our previous study [11], fracture status and the demographic parameters, age, sex, height, and weight were considered as candidate independent variables. All FE parameters, height, and weight are standard normalized using the z-score normalization algorithm. To select the most important independent variables in the multiple linear regression, we first performed a simple linear regression model to test the association between each of the candidate independent variables and each of the 12 FE parameters. In the multiple linear regression, we only retained the independent variables with p-value < 0.1. Interactions between fracture status and demographic parameters were also considered as independent variables. Also, if an interaction term was retained, the individual independent variables making up that interaction were retained, regardless of the p-value for the individual independent variable. The multiple linear regression analyses were performed for each of the FE parameters accounting for the retained independent variables. In all of these analyses, FE parameters, age, height, and weight were standardized by subtracting the mean and dividing by the SD of the pooled data.