Fig. 1: Biomarker selection by LASSO regression model and biomarker’s importance.

This figure illustrates the importance and direction of biomarkers selected through Lasso regression analysis. Panel A shows the average coefficients for each biomarker, with the color and length of the bars representing the magnitude and direction of their impact on the predictive outcome. Panel B illustrates the changes in coefficients of biomarkers during the LASSO regression process as a function of the L1 norm. Each colored line represents the coefficient trajectory of a different biomarker across varying levels of L1 norm regularization. The plot visualizes how coefficients are shrunk towards zero, highlighting which biomarkers remain significant as the regularization increases. Panel C illustrates the LASSO coefficient profiles for the 35 variables as the log-transformed regularization parameter λ varies. The vertical axis shows the partial likelihood deviance, indicating the model’s goodness of fit, while the horizontal axis displays the log(λ) values. A vertical line within the graph marks the λ value selected by 10-fold cross-validation, optimized for balancing model complexity and predictive accuracy. As λ decreases, model compression intensifies, which enhances the model’s ability to discern and retain only the most important variables. The sequence of numbers at the top indicates the count of variables retained in the model at each specific λ, helping to visualize how variable selection changes with increasing regularization.