Fig. 3

Feature selection was performed using the least absolute shrinkage and selection operator (LASSO) regression model. a, b Tuning parameter (λ) selection in the LASSO model used fivefold cross-validation via minimum criteria. Vertical lines were drawn at the optimal values using the minimum criteria and 1 standard error of the minimum criteria. For the selection of texture parameters based on the arterial phase CT images, the optimal λ value of 0.0363 with log (λ) =  − 3.3159 was chosen. For the selection of texture parameters based on the venous phase CT images, the optimal λ value of 0.0555 with log (λ) =  − 2.8914 was chosen. c, d For the selection of texture parameters based on the arterial and venous phase CT images, LASSO coefficient profiles of the 32 and 15 selected features, respectively. Two coefficient profile plots were generated versus the selected log (λ) value using fivefold cross-validation; five and four selected features with nonzero coefficients were retained