We selected the optimal λ values for each disease: for RA, λ was set to 0.010, indicating the 2 genes as as the candidate genes for RA (ROMO1 and LSM3); for MS, λ was determined to be 0.012, identifying 2 genes for MS (ROMO1 and FAU); for T1D, λ was set at 5.14 × 10− 4, identifying 3 genes for T1D (ROMO1, LSM3 and TPT1). This evidence concerns the gene FAU and rheumatoid arthritis.