Fig. 3

Summary of the main results from the multivariate pan-cancer analysis. It evaluated mutually adjusted associations between each feature (more precisely, their residuals after adjustment for BMI) and the risk of the eight cancer types, using a data-shared lasso penalty. White entries correspond to the absence of identified associations, while green and red entries correspond to inverse and positive associations, respectively. The more intense the colour, the larger the absolute value of the log-odds ratio (that were re-estimated in multivariate unpenalized conditional regression models; see Additional file 1: Section 3.a for details). The x-axis represents the 50 features (33 cluster representatives and 17 isolated metabolites). In the labels of the y-axis, numbers correspond to the numbers of pairs for each type-specific cancer, while 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