The immune-related gene pairs (IRGPs) were constructed by pairwise comparison of the gene expression level in a specific sample or profile. If the expression level of the first IRG was higher than that of the second IRG, the score of this IRGP was 1; otherwise, the score was 0. Next, the establishment of immune-related gene pairs index (IRGPI) was based on previous description23. The RNA-FPKM data was identified as training dataset for establishing the IRGPI through using Lasso Cox proportion hazards regression with tenfold cross validation (glmnet R package, version: 3.0-2). The IRGPs of training dataset with a small variation and imbalanced distribution (MAD = 0) were excluded from the analysis. Then, we conducted 1000 times Lasso Cox proportion hazards regression analysis into training dataset, in which the model with the most occurrences was identified as the most stable gene pairs model and was used for the development of IRGPI.

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