Multi-omics data were downloaded from TCGA. The scale and platform of each cancer data are shown in Table 1. We selected the cancers which had HM450K DM data, RNA-seq data (GE), miRNA-seq data (ME), and SNP 6.0 copy number data (SCNA) simultaneously and whose sample size was greater than 200. Samples with sample type codes of “01” were retained, which represented “Primary Solid Tumor.” After being filtered, there were 13 types of cancers available. For SCNA data, a matrix was obtained after being processed by Gistic 2.0 (Mermel et al., 2011). Next, all omics data matrixes except ME were converted into gene matrixes based on the annotation information from TCGA. Genes with missing values in > 5% of the samples were removed in each matrix. Moreover, for GE and ME data, we retained the genes or miRNAs with values greater than 0 in > 50% of the samples and with values greater than 1 in > 10% of the samples, respectively. After converting if one gene had multiple signals in one sample, we calculated the average of the values as the final signal. For ME, miRNAs were specifically bound to mRNAs by complementary base pairing, therefore the corresponding relationships between miRNAs and genes were obtained through the miRNA–mRNA interactions which were downloaded from the Starbase database (Yang et al., 2011). Interactions with no less than five supporting experiments and anti-correlation in no less than one cancer type were selected. Since multiple miRNAs were bound to the same gene, the average value of the miRNAs was assigned to the gene.

Because of different scales for the omics data, the data were normalized based on the following rules. First, each omics data were organized into a matrix of the same genes and samples, separately. Second, the method z-score was used to transform a matrix into standardized one with the mean and standard deviation of 0 and 1, respectively. Finally, we uniformly kept the fourth decimal place for better integration of the standardized data.

Univariate Cox proportional hazards regression model (Cox, 1986) was used to identify candidate survival-related genes from each omics data through the formula:

where the explanatory variable X was the omics data (DM, GE, copy number variation, or miRNA expression) of a gene, and the response variable t was the survival time (Aalen, 1989). The proportional hazards regression model was calculated through the R package “survival.” β greater than zero meant the gene was a risk factor base on the corresponding omics data. Then using voting strategy, if a gene had a p-value of likelihood ratio test less than 0.05 (Yuan et al., 2014), the gene was denoted as “1”. Otherwise, it was denoted as “0.” Finally, a gene defined as a candidate survival-related gene should be marked as “1” in no less than two of the four omics data types (Figure 1A).

As shown in Figure 1B, prognostic biomarkers were further identified in the set of candidate survival-related genes. For each gene, a matrix M = [Omics_GE,Omics_SCNA,Omics_DM,Omics_ME] merged by the vectors of the four omics data of the gene was obtained. Then, the multivariate Cox proportional hazards model was applied on it. Briefly, the model assumed that a patient with covariate values has a cumulative hazard rate related to an unspecified baseline hazard rate seen in the equation:

where h(t, M) was the patient’s hazard of death at time t, h₀(t) was the baseline hazard rate, and B = [β₁,β₂,β₃,β₄] was a regression coefficient that gives the effect of each M covariate on the hazard rate (Alamartine et al., 1991). Each β could be interpreted as a risk coefficient (Collett, 2015). If the p-values of Cox fitting in all three overall tests (likelihood, Wald, and log-rank) were less than 0.05, the model was thought to be significant (Rodriguez-Martin et al., 2020). Therefore, we only kept genes whose all three p-values were less than 0.05.

For the retained genes, each gene had a vector including the value of four types of omics data in each sample V = [v₁,v₂,v₃,v₄]. The risk score (RS) for the gene in each sample was then calculated:

The RS score could be used to predict the patients’ risk.

Thereafter, RS scores of the genes were used to calculate each gene’s score (GS):

where m was the number of samples. At last, the scores of univariate and multivariate Cox proportional hazards model were combined to calculate the survival-related score of each gene (Score):

where A, B, C, and D represented whether the gene was survival-related at the GE level, copy number level, DM level, and miRNA level, respectively (“1” meant related and “0” meant not). The higher the score, the more relevant between the gene and patients’ survival. Therefore, high score genes were identified as prognostic biomarkers.

Cumulative hypergeometric inspection was applied to enrichment analysis of Gene Ontology (GO) functions (Gene Ontology, 2015) and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways (Kanehisa and Goto, 2000):

where N was the whole number of genes. M was the number of genes on a term or a pathway. n was the intersection of interested gene set and N. i was the intersection of M and n. Significant threshold of hypergeometric test was set to P < 0.05 (Liu et al., 2018). For the enrichment analysis of GO, we only investigated the biological process (BP) terms.

In order to identify differentially expressed genes, the corresponding normal samples of LUSC and KIRC were downloaded from TCGA. There were 49 LUSC normal samples and 72 KIRC normal samples. After organized into the same gene set, the differentially expressed genes between tumor and normal samples were identified using the R package “samr” with the threshold value q-value < 0.05 and |log₂(foldchange)| > 1 (Group et al., 2020). The package was based on significance analysis of microarrays (SAM). SAM was developed based on t-test and adjusted the p-value to assess the statistically significant changes for genes (Tusher et al., 2001).

For each cancer type, in order to evaluate the prognostic power of the biomarker fairly and accurately, the concordance index (C-index) (Harrell et al., 1996) was applied to assess the prognostic power of the classifier. The C-index was a non-parametric measure to quantify the discriminatory power of a predictive model with the value ranging from 0.5 to 1. A C-index of 1 represented perfect prediction accuracy, while C-index of 0.5 indicated a bad prediction like a random guess.

First, we randomly selected 90% of the samples. Second, the Cox regression model was used to calculate the RS score for each sample by multi-omics data of the identified biomarker genes. Based on the RS score, samples were classified into high and low risk groups. Patients in the high risk group were more likely to have poor prognosis while patients in the low risk group were more likely to have good prognosis. Finally, the predicted outcomes for patients were compared with the real status to calculate the C-indexes.

The procedure above was repeated 100 times to generate 100 C-indexes. If the median value of C-index was significantly higher than 0.5, indicating that the model had substantially prognostic power.

Decision curve analysis was performed through the multi-omics data and every single omics data, respectively. The method was based on the principle that the relative harms of false positives (e.g., unnecessary biopsy) and false negatives (e.g., missed cancer) could be expressed in terms of a probability threshold (Vickers et al., 2008). Therefore, this threshold probability could be used to determine both whether a patient was defined as test-positive or negative and to model the clinical consequences of true and false positives using a clinical net benefit function:

where n was the total number of patients in the study and p_t was the threshold probability. Net benefit was weighted by the relative harm of forgoing treatment compared with the negative consequences of an unnecessary treatment. In the decision curve, the thin oblique line represented the assumption that all patients have been treated. The black line represented the assumption that no patients have been treated.

We integrated GE, SCNA, DM, and miRNA expression data of 13 cancers from TCGA: bladder urothelial carcinoma (BLCA), breast invasive carcinoma (BRCA), cervical squamous cell carcinoma and endocervical adenocarcinoma (CESC), colon adenocarcinoma (COAD), head and neck squamous cell carcinoma (HNSC), kidney renal clear cell carcinoma (KIRC), kidney renal papillary cell carcinoma (KIRP), brain lower grade glioma (LGG), LIHC, lung adenocarcinoma (LUAD), lung squamous cell carcinoma (LUSC), sarcoma (SARC), and stomach adenocarcinoma (STAD). After data preprocessing, samples with all the four omics data were kept. Whereupon, we collected the DM, GE, copy number, and miRNA expression of 3279 samples (Figure 2A). The percentage of each cancer is shown in Figure 2B. We then summarized the clinical characteristics of the 3279 samples. As shown in Figure 2C, the majority of these patients were 60–79 years old. And the number of men and women was basically equal. Hence, the sample set could be used to study cancer without gender and age bias. In addition, most of the patients were white people. The complete clinical information for each sample is provided in Supplementary Table S1.

The survival-related gene list of each cancer is shown in Supplementary Table S2. We took top-10 genes as a prognostic biomarker of each cancer (Table 2) to draw Kaplan–Meier (KM) curves and calculated their log-rank p-values. As shown in Figure 3, the prognostic markers for each cancer significantly distinguished the high and low risk groups, except for SARC.

For each cancer type, we calculated the C-index which was a non-parametric measure to quantify the discriminatory power of a predictive model. Figure 4 shows the C-indexes of each cancer. All of the cancers had a C-index significantly higher than 0.5. BRCA had the highest C-index (0.96) while LUSC had the lowest (0.76).

In order to discover the relationship among different cancers based on function, we used the prognostic biomarker genes to perform functional enrichment analysis of GO and KEGG (Supplementary Table S3). The most significantly enriched functions and pathways of each cancer are displayed in Figure 5A. Among them, COAD, LGG, and SARC were enriched in “endocytosis.” BLCA was enriched in “RNA splicing” and CESC was enriched in “mitophagy.” The prognostic biomarker genes were enriched in closely cancer-related functions. Then, we calculated the counts of each function enriched by cancers. As shown in Figure 5B, “Mitophagy” was enriched by the most cancers. Mitophagy was a tumor suppression mechanism (Bernardini et al., 2017). Besides, we had some interesting findings. First, the most significantly enriched functions of each cancer were their specific functions, while the common functions of cancers were not highly significant generally. For example, “cytoskeleton-dependent cytokinesis” was the common enriched function of STAD, KIRC, COAD, and BLCA, and they had p-values about 0.03 which was less significant than their most significantly enriched functions (p-values < 0.003). And their most significant functions were all their specific functions. Second, even if different cancers were enriched in a same function, the enrichment of function in different cancers was caused by different gene sets. For instance, “Mitophagy” was the common function of LIHC, LGG, KIRP, COAD, and CESC, but the function was hit by different genes (BCL2L1 of LIHC, CITED2 of LGG, TBC1D17 of KIRP, USP8 of COAD, and PGAM5 of CESC). Whereafter, we sought the intersection of associated functions for the 13 cancers (Figure 6A top right corner). The result showed that the intersection of LGG and SARC was the largest, followed by BLCA and CESC.

In order to discover the relationship among different cancers based on survival-related genes, we first compared the intersection of the survival-related gene lists between each two cancers. We found there was always an overlap between each two gene lists (Figure 6A left bottom). The intersection of KIRP and KIRC was the largest. All of the intersections among KIRC, KIRP, and BLCA were large, which might be due to the reason that the three cancers had the largest number of genes. The intersections with other cancers were roughly proportional to the size of the gene list. Second, we compared the gene lists among the 13 types of cancers. We found that seven genes were associated with survival in three kinds of cancers (Figure 6B). Subsequently, we downloaded the list of cancer-related genes from the Candidate Cancer Gene Database (CCGD) (Abbott et al., 2015), and retained the human genes that appeared in at least one of the COSMIC and CGC (Sondka et al., 2018). A total of 9265 genes were retained. All of the seven pan-cancer survival-related genes were in the list, and have been verified cancer-related in no less than one literature (Table 3). In addition, we investigated the functions of the seven genes (Supplementary Table S4) and conducted UCSC Genome Browser (Tyner et al., 2017) analysis on the seven genes. We found that SLK had an unconservative exon region, which containing four missense variants (Figure 7A).

In order to further verify the close relationship of SLK and cancer, we checked the mutation of SLK in the COSMIC database (Tate et al., 2019), and found that missense substitution occurred in 36.93% of the samples (Figure 7B). Next, enrichment analysis in GO terms (BP) was performed by Enrichr (Kuleshov et al., 2016) and found SLK was mainly associated with cell adhesion (Figure 7C). Finally, we used STRING database (Szklarczyk et al., 2019) to check the interacted proteins of SLK. Figure 7D shows there were 10 genes interacting with SLK. Half of the interactions have been demonstrated through more than one method, and the genes interacting with SLK also had strong relationship between each other.

In order to explore the correlation among prognostic biomarkers of different cancers, we checked the genomic locations of these 130 genes (Figure 8A). There were many prognosis-related genes located in chr 6, chr 7, chr 8, chr 11, chr 12, and chr 17, while few genes in chr 13, chr 14, chr 18, chr 20, and chr 21. In addition, we constructed a protein–protein interaction network of these genes based on the STRING database (Figure 8B). As shown in the network, the prognosis-related genes of different cancers were connected to each other. The degree distribution (Figure 8C) and the betweeness centrality (Figure 8D) of the network satisfied the condition of scale-free network and were conformed as the general characteristics of biological network. In the network, the degree of EPRS had the highest degree of 33. The degrees of HNRNPA2B1, BPTF, LRRK1, and PUM1 were all greater than 20. These genes mentioned above were widely mutated in many cancers.

Based on the COSMIC database, we found extensive mutations occurred in EPRS, and 70% of them were missense mutation. EPRS has been shown to be associated with a wide range of cancers by 80 articles. The other four genes also had widespread mutations. In the COSMIC database, 78, 114, 113, and 83 studies confirmed the correlation between HNRNPA2B1, BPTF, LRRK1, and PUM1 with cancer, respectively.

In order to demonstrate the effectiveness of our method, we compared our prognostic biomarkers with previous works. The works using TCGA data were chosen to compare with our work. Chaudhary et al. (2018) used LIHC data of TCGA in their work. Their C-indexs of training and testing set were 0.70(±0.04) and 0.69(±0.08), while our median C-index of LIHC was 0.82. The prognostic power of our method was stronger than theirs. Next, both Yuan et al. (2014) and Zhang et al. (2016) used KIRC and LUSC data of TCGA in their works, so we compared our results of these two cancers with their studies. The comparisons of the C-indexes are shown in Figures 9A,B, which showed the higher prognostic power of our 10-gene biomarkers. For KIRC, the median C-index of our work was 0.91. The median C-index of the best performing data (clinical + miRNA) in Yuan’s work and the best performing subnetwork (subnetwork K1) of Zhang’s study were about 0.76 and 0.74, respectively. For LUSC, the median C-index of our work was 0.76. The median C-index of the best performing data (clinical + protein) in Yuan’s work and the best performing subnetwork (subnetwork L1) of Zhang’s study were about 0.66 and 0.62, respectively. Therefore, the biomarkers identified by our method could display the better prediction for the patients’ survival.

To further confirm reliability of the genes, we downloaded GE data of the corresponding normal samples and used the prognostic biomarkers to cluster the samples. The results showed that the prognostic biomarkers could distinguish the tumor and normal samples (Figures 9C,D).

Furthermore, we screened the differentially expressed genes between tumor and normal samples of LUSC and KIRC. After comparing them with the list of survival-associated genes, there were 12 differentially expressed genes in LUSC list (Figure 10A) and 49 differentially expressed genes in KIRC list (Figure 10D). Subsequently, we examined the copy number variation and chromosome location of both the differentially expressed genes and the top-10 biomarker genes (Figures 10B,C,E,F). It turned out that among the 22 LUSC genes, six were located in chr 6q, three were in chr 10q, three were in chr 11q, and three were in chr 15q. Of the 59 KIRC genes, 10 were located in chr 8, eight were located in chr 17, and seven were in chr 1. These locations were the peak regions of copy number alternation, suggesting a relationship between these genes and cancer. Moreover, it could be seen that the driver genes of the two cancers were located in different chromosomes, which supported the uniqueness of different cancer-related genes.

Moreover, in the process of univariate Cox regression model, we separately calculated the survival correlation of a gene in four different omics data and then counted them. We also tried the result of considering the same gene in different omics data as different features, and merged the four omics data into one matrix then performed multivariate Cox regression model on it. Only the genes identified as survival-related features more than twice were retained. Finally, the obtained genes were all involved in the gene lists identified through our method and had an incomplete coverage compared with our gene lists. Interestingly, most of these genes were related to survival in GE or SCNA.

In addition, in the process of multivariate Cox regression model, we involved all of the four types of omics data for each candidate gene to perform analysis. Actually, the genes were not survival-related at all of the four omics data in the univariate Cox regression model. To prove the validity of this process, we recalculated the Score of each gene by only using the types of omics data at which the gene was determined to be related to survival in univariate Cox regression model. The results showed that neither the Scores nor the ranks of the genes changed much after recalculation. In consequence, it could suggest the high predictive performance of our multivariable Cox regression model.

In the process of univariate Cox regression analysis, we found that a gene appeared to be survival-related in one omics dataset, while it might appear to be unrelated to survival on another omics data even under the same model, selection criteria and set of samples. Although this phenomenon might be caused by the error of the data or the imprecision of the experiment, it implied the necessity of multi-omics data integration.

To verify the superiority of integrating multi-omics data, we compared the results of integrating multi-omics data with the results of single omics data in LUSC and KIRC. As shown in Figure 11, the results of integrating multi-omics data were significantly higher than those of applying single omics data in decision curve analysis and C-index. The decision curve showed that compared with single omics data, the curve of multi-omics data was further apart from the two extreme curves, which had the greater application value.