Fig. 4

Summary of the mutually adjusted associations identified by the data-shared lasso. Only the 19 features (8 isolated metabolites and 11 cluster representatives) for which the data-shared lasso identified an association with at least one cancer type are presented on the y-axis. Point estimates and 95% confidence intervals of the corresponding odds ratios were obtained through non-penalized conditional logistic regression models using the design matrix derived from the positions of the non-zero components in the data-shared lasso vector estimate \(\left(\hat{\boldsymbol{\mu}, \kern0.5em }{\hat{\boldsymbol{\delta}}}_1,\cdots, {\hat{\boldsymbol{\delta}}}_K\right)\); see Additional file 1: Section 3.a for details. They have to be interpreted with caution since they are the result of post-selection inference. In the labels of the columns, BrC stands for breast cancer, CRC for colorectal cancer, EnC for endometrial cancer, KiC for Kidney cancer, GBC for gallbladder and biliary tract cancer, HCC for hepatocellular carcinoma, and Adv.PrC and Loc.PrC for advanced and localized prostate cancers, respectively