Copy number and methylation as the best combination of omic modalities

We first analyzed the effect of data modalities on the clustering solutions. The combination of CNA and methylation data had the best performance on average (Fig 2A) across all algorithms and numbers of clusters, indicating that the clusters formed when using this combination of modalities were the most stable and compact. This combination also had the best performance when using the individual metrics (S1 Fig). The single-modality methods ranked at the lowest end of the performance comparison, indicating that integrating multiple omics layers provides a clear advantage in terms of cluster quality and stability.

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Fig 2. Benchmarking of modality combinations, number of clusters, and algorithm robustness.

(A) Evaluation of the clustering performance across the different combination of omic modalities. The most informative combination was DNA methylation and copy number alterations. The general performance score was computed as the harmonic mean of silhouette and adjusted mutual information scores, reflecting cluster compactness and stability, respectively. Combinations are ordered by decreasing mean score (green triangle). First heatmap indicates modalities present in combination (blue), second heatmap indicates total number of modalities in each combination, and third heatmap shows total number of features in each combination. (B) Evaluation of the clustering performance for different number of clusters. Two-cluster solutions consistently outperformed those with a higher number of clusters. The number of clusters are ordered by decreasing mean general performance score (green triangle). (C) Comparison of algorithm robustness to different percentages of missing data. NEMO demonstrated the most robust performance across all levels of missing data, shown as the average across all missingness patterns. Robustness was quantified by comparing clusters obtained with missing data to those found in complete data using the adjusted mutual information score.

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We also investigated the influence of individual modalities, the algorithm and the number of clusters on the clustering solutions. Combinations that included methylation achieved the highest overall performance, being in 9 of the top 10 results. This is confirmed when calculating the individual importance of the modalities, as combinations with methylation obtained the highest metrics (S2 Fig). Additionally, the IMSR algorithm achieved the best performance on average (S3 Fig). Overall, two-cluster solutions outperformed the alternatives with higher number of clusters (Figs 2B and S4), consistently exhibiting high values of the general performance score.

NEMO provides the most robust performance with missing data

Since patients had missing omic modalities, the robustness of the clustering algorithms was assessed using CNA and methylation data with two clusters (the best parameters) at increasing fractions of incomplete data. Overall, NEMO exhibited the most robust performance throughout all levels of missing data, even when only 20% of samples have all modalities available (Fig 2C). Algorithm performance was consistent across missingness patterns, indicating little effect of the pattern on model performance (S5 Fig).

In terms of GPS and robustness, this approach outperformed also standard imputation-based workflows (mean, median and K-nearest neighbors) (S6 Fig), where missing modalities were imputed before applying NEMO. Overall, these findings indicate that, in this setting, NEMO’s ability to operate directly on incomplete multi-omics data provides a clear advantage over a standard imputation-based strategies, yielding both greater robustness and improved clustering performance.

Robust final clusters formed applying the NEMO algorithm to methylation and CNA data

The final clusters (termed IMOC, for Incomplete Multi-Omics Clustering) were identified using consensus clustering with NEMO for all patients with DNA methylation and CNA data, provided that at least one omic modality was available: cluster 1 with 33 patients, and cluster 2 with 121 patients.

The consensus matrix showed near-perfect separation, with most values close to 0 or 1 (Fig 3A). Item consensus probabilities exhibited two distinct peaks at 0 and 1 for cluster 1 and 2, respectively, confirming clear cluster delineation (Fig 3B). Cluster stability remained high across iterations, as indicated by consistently elevated adjusted mutual information (AMI) scores (Fig 3C).

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Fig 3. Analysis of final IMOC clusters.

(A) The consensus matrix is nearly perfect, with almost all patients having values close to 0 or 1. A consensus value of 1 indicates patients that are always clustered together. (B) The pronounced peaks at the extremes for both clusters indicated high cluster agreement and stability. A kernel density estimation was applied to visualize a continuous probability density curve. (C) IMOC cluster stability remained high and consistent across all iteration numbers, indicating stability independent of this hyperparameter. (D) Patients in cluster 2 exhibited higher overall rates of copy number alterations. Differences between clusters were calculated by averaging the copy number alterations (in absolute values) per patient, and finding differences between the averages in each cluster. (E) Patients in cluster 2 had a predominantly hypermethylated DNA pattern. In (D) and (E), each point represents a patient, computed as the average across features. Statistical significance was assessed using the Kruskal-Wallis test.

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Differences in feature values between IMOC clusters were also observed, with patients in cluster 2 having overall higher rates of CNA () and higher values for methylation beta values () (Fig 3D–3E).

Patients in cluster 2 show a higher tumor mutational burden

We next analyzed the differences in clinical variables between patients in cluster 1 and cluster 2. In the post-hoc enrichment analysis of clinical parameters (S2 Table), statistically significant differences were found in three parameters, all related to mutations: mutation count (), fraction of the genome altered (), and tumor mutational burden (TMB) (). Patients from cluster 2 had higher mutation count and TMB, as well as a larger fraction of the genome altered, indicating differences in somatic mutation profiles (Fig 4A).

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Fig 4. Clinical relevance of IMOC clusters.

(A) Three clinical labels were significantly enriched in the clusters: mutation count, fraction of the genome altered and tumor mutational burden. P-values were calculated using the Kruskal-Wallis test and adjusted for multiple tests with the Benjamini-Hochberg correction. (B, C) Significant differences between the clusters in both, overall survival (B) and disease-free progression (C), were observed during the first 18 months and two years post initial diagnosis, respectively. RMST: restricted mean survival time (difference in months in Cluster 1 respective to Cluster 2).

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Differences in survival and disease-free progression within the first two-years post-diagnosis

Survival was recorded in the TCGA data for up to 6.5 years after initial diagnosis. For the survival data, the proportional hazards assumption was met (p = 0.74), whereas the random censoring assumption was not (p = 0.023). Across the study period, restricted mean survival time (RMST) analysis indicated that patients in cluster 1 lived, on average, one year longer than those in cluster 2 (Fig 4B). Statistically significant differences in the overall survival were found up to 18 months after the initial diagnosis, with patients in cluster 2 having lower survival probabilities. At 6 months, cluster 2 patients had over a 4.5-fold higher mortality risk than those in cluster 1, decreasing to about twice the risk by 18 months.

We next studied the tumor recurrence in all the patients that had disease-free progression information available (n = 113). In this case the assumption for censoring was met (p = 0.194), while the proportional hazards assumption was not (p = 0.035). Differences in disease-free progression remained statistically significant up to two years post-diagnosis, with patients in cluster 2 having higher recurrence rates (Fig 4C). At 6 months, the recurrence risk for cluster 2 patients was over 5.5 times higher, decreasing to approximately twice the risk at 2 years. RMST analysis indicated cluster 1 patients remained recurrence-free approximately 3.5 months longer at the two-year mark.

Identification of biomarkers for patient stratification

The multi-modal feature selection with Adaptive BEst Subset Selection (ABESS) [10] identified three methylation sites as potential biomarkers: cg00839579, cg06785999 and cg07095230, which were associated to the genes MEOX2, SIX6, and TBX2, respectively (Fig 5A). The features selected achieved strong classification performance, with an Matthews correlation coefficient (MCC) score of 0.79, compared to 0.92 obtained when all methylation and CNA features were used (Fig 5B). The feature selection applied individually to the CNA data resulted in the selection of four CNA corresponding to the 9p21.3, 17p12, 18q21.2, and 21q11.2 cytobands, while for the methylation data, it resulted in the same CpGs identified in the multi-modal feature selection.

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Fig 5. Statistical analysis of multi-modal selected features.

(A) Feature selection was performed using a multi-modal approach, applying the ABESS algorithm with an intermediate fusion strategy. The table shows information about the selected features, all of which were methylation CpG biomarkers, including the chromosome (chr), position (pos), and the associated genes. (B) Classification performance (average of the 5-fold stratified cross-validation) of a random forest classifier for both, the full feature set and the selected features. The three selected methylation biomarkers were sufficient to stratify patients into the IMOC clusters with high accuracy. (C) The selected CpG features were associated with overall survival and disease-free progression at several time points post initial diagnosis, highlighting their clinical relevance. (D) ShapIQ assessment of feature and feature interaction influence. The three selected CpGs were identified as the most influential features. Feature interactions showed low importance, possibly reflecting the effectiveness of the selection, which isolated their individual effects. MCC: Matthews correlation coefficient. s.d.: standard deviation.

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The Cox model results using selected features for overall survival were inconclusive, with irregular significance across timepoints (Fig 5C and S1 Data). The disease-free analysis showed a more consistent associations with cg07095230, and especially with cg06785999, having a statistitically significant association from 1 to 3 years (Fig 5B). Within this timeframe, patients with hypermethylation of cg06785999 have around 5 times higher risk of tumor recurrence compared to those with normal methylation of this site. However, no significant association was found between the disease-free progression and any of the selected CNA (S1 Data).

Shapley Interaction Quantification (ShapIQ) identified cg00839579 as the most influential variable (Fig 5D). Interestingly, feature interactions showed low importance, possibly reflecting the effectiveness of the selection, which isolated their individual effects.

Biological characterization of the IMOC clusters

After identification of the two distinct patient clusters using integrated DNA methylation and CNA data, we next aimed to characterize the biological differences between these groups of patients through comprehensive multi-omics analysis. We initially focused on DNA methylation and CNA, as these were the combined omic modalities selected for clustering. To evaluate the association strength between CNA in genomic regions (cytobands) and IMOC cluster classification, we calculated odds ratios for each cytoband (Fig 6A and S1 Appendix). The majority of CNA showing significant differential proportions between cluster 1 and cluster 2 patients were deletions (Figs 6A and S7 Fig). Notably, two of the four selected cytobands (17p12 and 9p21.3) demonstrated the strongest association with deletion events in cluster 2 patients. Differential methylation analysis comparing cluster 2 versus cluster 1 patients revealed 2773 CpG sites with significantly increased methylation in cluster 2, while 270 CpG sites were hypomethylated in cluster 2 (available in the results folder of the IMOC repository). Notably, all three CpGs identified as potential biomarkers were significantly hypermethylated in cluster 2 (Fig 6B). This hypermethylation pattern suggests distinct epigenetic regulation between the two IMOC patient clusters.

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Fig 6. Multi-omics analysis of biological differences in cluster 2 vs cluster 1.

(A) Three (bolded) of the four copy number features selected via unimodal feature selection were among the top 10 cytobands with the highest odds ratios for CNA events. The first two, also identified as biomarkers, showed a markedly larger difference than the others. (B) Volcano plot depicting the differential methylation analysis of CpG sites. Highlighted are the three CpGs identified in the biomarker selection. (C) Volcano plot showing the differential gene expression analysis. Indicated are the genes associated with the CNA or CpGs identified in the biomarker selection. (D) Dot plot showing the results from gene set enrichment analysis (GSEA) of methylomics data. The top 10 pathways with higher gene ratio (proportion of significantly enriched genes to the total number of genes in the gene set) and FDR < 0.25 are shown. (E) Dot plot showing the results from the GSEA of transcriptomics data. The top 10 pathways with higher absolute value of normalized enrichment score (NES) and FDR < 0.25 are shown. Key pathways in PDAC, including KRAS and P53, were among the most enriched in (D) and (F). The color of the dots indicate the value of the FDR. The horizontal dashed line in (B) and (C) indicate the Benjamini-Hochberg adjusted p-value < 0.05 threshold to assess significance. NS: not significant.

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To investigate whether the observed alterations could be associated with changes in gene expression, we performed differential gene expression analysis (Fig 6C). We identified 3183 and 3966 differentially expressed genes (DEGs) with significantly increased and decreased expression in cluster 2, respectively (S2 Data). Consistent with the established inverse relationship between DNA hypermethylation and gene expression, we observed significantly decreased expression of MEOX2, which showed a significant negative correlation with methylation levels of its associated CpG site (cg00839579, S7 Fig). Similarly, TBX2 expression demonstrated a significant negative correlation with its associated CpG (cg07095230) methylation (S7 Fig). While TBX2 expression showed a trend towards reduced expression in cluster 2 patients, this difference did not reach statistical significance (Fig 6C). The gene SIX6, associated with the third selected CpG (cg06785999), was not detected in the gene expression dataset. Most of the CNA observed affected only one of the alleles (S7 Fig), suggesting that even when a deletion was present, the genes could still be expressed by the other allele. To assess whether the observed chromosomal deletions translate into functional consequences, we evaluated the expression levels of genes located within the four selected cytobands. Among the 95 genes located within the selected cytobands (S1 Data and S7 Fig), 9 were identified in the gene expression dataset. Of these, 4 genes showed significantly reduced expression in cluster 2 patients (Fig 6C), suggesting that the identified chromosomal deletions might have functional consequences on gene expression levels.

To gain insights into the biological consequences of altered methylation and gene expression patterns, we performed gene set enrichment analysis (GSEA) using both methylomics and transcriptomics data (Fig 6D–6E). Both omic modalities revealed significant enrichment in multiple oncogenic gene sets involving KRAS signaling pathways (S2 Data). Particularly noteworthy was the positive enrichment of genes defining the KRAS dependency signature in cluster 2 (Fig 6E), suggesting altered KRAS pathway activity in this subgroup of patients. Finally, given the importance of protein expression and phosphorylation in the final biological outcome, we performed a differential regulation analysis of the RPPA data, encompassing both protein expression and phosphorylation levels. We identified 13 proteins with increased expression and 11 proteins with reduced expression or phosphorylation in cluster 2 (S7 Fig). However, only Cyclin B1, CD49b, INPP4B, and GAPDH showed a significant statistical difference after adjusting for multiple comparisons (S2 Data). Of particular interest was the reduced phosphorylation observed in several proteins involved in the mTOR signaling pathway, including decreased phosphorylation of AKT, mTOR, and S6 ribosomal protein (S7 Fig). This pattern strongly indicates downregulation of mTOR signaling in cluster 2 patients.

Over-representation analysis of KEGG pathways using the differentially expressed and phosphorylated protein data revealed enrichment in several cancer-relevant pathways, including the HIF-1 signaling pathway, EGFR tyrosine kinase inhibitor resistance, or the p53 signaling pathway (S7 Fig and S2 Data). These findings further support the distinct molecular phenotypes of the IMOC clusters.

IMOC clusters differs from previously reported PDAC subtypes

The IMOC clusters discovered in this study were compared to the three most widely established clustering studies for PDAC patient stratification (Fig 7A–7B).

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Fig 7. IMOC clusters show limited overlap with classic PDAC subtype labels.

(A) Alluvial plots showing correspondence between IMOC cluster assignments and established PDAC subtypes (Bailey, Collisson, Moffitt). Pairwise differences between subgroups were calculated using Fisher’s exact test and p-values were adjusted for multiple comparison testing using the Benjamini-Hochberg correction. (B) Quantitative concordance between IMOC cluster labels and classic PDAC subtype taxonomies measured using adjusted mutual information (AMI) and adjusted Rand index (ARI). Both metrics are corrected for agreement expected by chance; values close to 0 indicate agreement no better than expected by chance, while values close to 1 indicate full agreement. (C) Heatmap of centroid gene-expression profiles computed across the whole transcriptome (n = 17,123 genes). Centroids were calculated as the mean normalized expression within each subtype/cluster. For visualization, expression values were z-scored per gene across centroids and hierarchically clustered using UPGMA agglomeration method. (C) Pairwise Spearman correlations between centroid gene-expression profiles. Dot size and color indicate the magnitude and direction of Spearman correlation; only correlations significant after multiple-testing correction (FDR < 0.05) have a dot shown. The numbers inside the cells indicate the value of the Spearman correlations. (D) Multidimensional scaling (MDS) of centroid gene-expression profiles in whole-transcriptome space (n = 17,123 genes). (E) Heatmap of centroid pathway activity profiles based on GSVA scores for oncogenic gene sets (MSigDB C6; n = 189). GSVA scores were z-scored per gene set across centroids for visualization. (F) Pairwise Spearman correlations between centroid GSVA profiles (oncogenic gene sets); only significant correlations after correction (FDR < 0.05) have a dot shown. The numbers inside the cells indicate the value of the Spearman correlations. (G) MDS of centroid GSVA profiles across oncogenic gene sets (n = 189).

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Bailey et al. used gene expression profiles to identify four subtypes of PDAC patients that correlate with histopathological features: aberrantly differentiated endocrine exocrine (ADEX), immunogenic, pancreatic progenitor, and squamous subtype [4]. Patients from cluster 1 were divided between the ADEX and immunogenic groups (p = 0.95), while patients in cluster 2 were distributed across all subtypes.

Collisson et al. presented a 3-subtype classification - classical, exocrine, and quasi-mesenchymal (QM) - of PDAC patients [5]. Patients belonging to cluster 1 were distributed between the exocrine and QM subtypes in Collisson’s classification (p = 0.44), while patients in cluster 2 were again found distributed across all subtypes.

Moffitt et al. defined a two-subtype classification (basal-like and classical) [6]. The patients in the IMOC clusters were evenly distributed across these two subtypes, with no enrichment between either clusters and the Moffitt’s subtypes (p = 1).

The alluvial comparisons indicated that neither IMOC cluster maps cleanly onto a single Bailey, Collisson, or Moffitt subtype, consistent with incomplete correspondence between the IMOC stratification and classic derived taxonomies (Fig 7A). To quantify concordance between IMOC clusters and published PDAC subtype taxonomies, we computed the AMI and ARI between labelings (Fig 7B). Concordance was low for all three taxonomies (Bailey: AMI = 0.17, ARI = 0.08; Collisson: AMI = 0.11, ARI = 0.03; Moffitt: AMI0, ARI0), indicating that IMOC clustering shows very limited agreement to previously defined subtype classifications and is not explained by a simple relabeling of existing groups.

Centroid expression heatmaps and centroid–centroid correlations computed across the whole transcriptome (n = 17,123 genes) revealed strong differentiation between the IMOC clusters, with cluster 1 and cluster 2 showing marked anti-correlation at the centroid level (Fig 7C–7D). In multidimensional scaling (MDS) embeddings of centroid profiles, IMOC clusters occupied distinct positions relative to classic subtype centroids, supporting that the IMOC-derived transcriptional axis is not equivalent to any single published subtype label (Fig 7E).

Pathway-centric analyses based on gene set variation analysis (GSVA) [11] of oncogenic gene sets recapitulated the separation observed in expression space. Centroid GSVA profiles and correlation structure again differentiated cluster 1 from cluster 2 and positioned IMOC centroids apart from classic subtype centroids in MDS space (Fig 7F, 7G, and 7H, and S3 Data), indicating that the IMOC clusters capture coherent differences in oncogenic pathway activity.

To further interrogate the relationship between IMOC clusters and classic subtype contrasts, we compared centroid profiles within a DEG-union feature space (n = 11470 genes, S2 and S4 Data). The DEG overlap structure showed that the IMOC cluster contrast contributed the largest intersection among DEG sets and included 707 DEGs unique to cluster 2 vs cluster 1 that were not shared with any classic subtype-derived DEG set (S8 Fig). Consistently, centroid correlations and MDS embeddings computed in DEG-union space emphasized strong separation of IMOC clusters relative to classic subtype centroids (S8 Fig).

We then explored whether there were differences in oncogenic gene set enrichment in the IMOC clusters versus the subtypes from other PDAC classifications. For each subtype of the classical PDAC taxonomies, we performed one-versus-rest GSEA to identify enriched oncogenic gene sets for each subtype (S5 Data). We then filtered the enriched oncogenic gene sets with FDR < 0.25 in each subtype to generate a restricted set of enriched oncogenic gene sets (n = 27), to directly compare the enrichment landscapes across contrasts. The IMOC cluster contrast showed the largest number of enriched oncogenic gene sets compared with any individual classic subtype contrast (S8 Fig). Importantly, there were several subtypes in Bailey, Collisson, and Moffitt classifications for which no significant enrichment at FDR < 0.25 was found (S8 Fig). Centroid GSVA profiles in this enrichment-restricted space remained strongly differentiated between the IMOC clusters (S8 Fig).

To test whether IMOC clusters capture oncogenic pathway activity beyond that explained by established PDAC subtype taxonomies, we modeled GSVA oncogenic gene-set scores as a function of cluster membership while adjusting for Bailey, Collisson, or Moffitt labels in separate limma frameworks (S9 Fig and S6 Data). Across all three adjustments, multiple gene sets remained significantly associated with IMOC cluster status, indicating that the IMOC-defined stratification reflects pathway-level biology not reducible to classic subtype labels. Notably, the KRAS dependency signature (SINGH_KRAS_DEPENDENCY_SIGNATURE) kept consistently showing a higher activity in cluster 2 relative to cluster 1 after adjustment for each taxonomy, alongside persistent differences in p53-related signaling (P53_DN.V1_UP) and AKT/MEK-linked oncogenic programs (AKT_UP.V1_UP; MEK_UP.V1_UP).

We also evaluated how the overall survival and disease-free progression differences between the IMOC clusters compared to the differences between subtypes from the other PDAC classifications. The analysis was restricted to patients with all four classifications (IMOC, Bailey, Collisson, Moffitt) available (n = 133 for overall survival, n = 100 for disease-free progression). The overall survival curves and disease-free progression curves showed that all four classifications produced visually relevant separation in Kaplan-Meier curves S10 Fig). Only the IMOC clusters exhibited non-intersecting overall survival trajectories. In contrast, the overall survival curves corresponding to all the other classifications crossed at multiple time points, suggesting less stable patient stratification. The curve intersections evidenced violation of the proportional hazards assumption.

Because the proportional hazards assumption is violated across all the four classifications, we computed RMST differences between the worst- and best-prognosis subgroups within each classification, at the same landmarks. RMST is robust to proportional hazard violations and reflects the area between survival curves up to a pre-specified time point . For multi-level taxonomies, we compared each non-extreme subtype to the worst-prognosis reference at =12 (Squamous for Bailey; QM for Collisson).

The RMST extreme-subtype contrasts showed that IMOC’s RMST difference is comparable in magnitude to the strongest pairwise contrasts within multi-level taxonomies (Bailey Immunogenic-vs-Squamous, Moffitt Classical-vs-Basal-like) across all time points (S11A Fig and S7 Data). To compare the precision-adjusted prognostic signal across classifications at each landmark, we computed the Wald z-statistic () from RMST inference [12]. This statistic decomposes prognostic comparison into effect magnitude relative to estimation uncertainty, allowing direct comparison of binary classifiers (IMOC, Moffitt) against extreme-subtype contrasts within multi-level taxonomies (Bailey, Collisson). Importantly, the z-statistic comparison (S11B Fig) shows that IMOC achieves the highest signal-to-noise ratio for overall survival at () and (), exceeding all three established taxonomies and any extreme-subtype contrast within them. This early-overall survival precision advantage reflects two structural features of IMOC. First, its binary nature, which applies the stratification to the full cohort rather than relying on extreme-subtype contrasts within larger taxonomies. And secondly, its derivation from a systematic benchmark across omics modalities, algorithms, and cluster numbers, which yielded stable cluster assignments robust to the modest event counts at early landmarks. This is especially relevant for PDAC, since most tumor recurrences and associated mortality occur during the first 2 years post-diagnosis [2].

Finally, we performed a RMST comparison stratified by subtypes, to evaluate whether IMOC adds RMST-defined prognostic separation within each of the classical subtypes. We limited this analysis to the Moffitt classification because it was the only classification in which each subtype (Classical and Basal-like) contained patients assigned to both IMOC Cluster 1 and IMOC Cluster 2 (Fig 7A). In contrast, the Bailey and Collisson classifications showed little overlap between several subtypes and the IMOC clusters, precluding meaningful within-subtype survival comparisons. The stratified RMST analysis (S12 Fig and S8 Data) revealed distinct temporal patterns of IMOC prognostic separation within each Moffit subtype. For overall survival, IMOC clusters separated significantly within Moffitt-basal-like patients at early landmarks ( months at , BH adjusted p-value = 0.005; months at , BH adjusted p-value = 0.033), while within Moffitt-classical patients, separation became significant from onward and remained significant through ( months at , BH adjusted p-value = 0.01). For disease-free progression, IMOC produced significant separation only within Moffitt-classical patients ( months at , BH adjusted p-value = 0.02), with no significant separation within Moffitt-basal-like at any (S12 Fig). This pattern indicates that IMOC adds prognostic information beyond the binary Moffitt classification in two complementary ways: refining early overall survival stratification within Basal-like patients (where most early mortality occurs) and refining longer-term overall survival and disease-free outcomes within Classical patients.

Collectively, these analyses support that IMOC clustering captures a distinct, multi-gene transcriptional program and pathway activation pattern that is not encompassed by Bailey-, Collisson-, or Moffitt-defined subtypes. IMOC equals the global prognostic discrimination relative to established expression-based PDAC taxonomies, and it provides complementary information in specific contexts: early overall survival stratification (concentrated within Moffitt-Basal-like patients) and refined longer-term stratification within Moffitt-Classical patients. Together, these features support IMOC as a methodologically robust and clinically deployable stratification that captures complementary prognostic and molecular information alongside the established PDAC taxonomies.

Validation using the CPTAC cohort

To assess the generalizability of our IMOC framework, we used the Clinical Proteomic Tumor Analysis Consortium (CPTAC-PDA) cohort for validation. We applied our CNA-based stratification model to the CPTAC data to assign samples to IMOC-like clusters. This analysis revealed significant differences in overall survival between the two groups, with Cluster 1 exhibiting a better prognosis compared to Cluster 2 (p = 0.047, RMST = 6.74 months) (Fig 8A).

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Fig 8. Validation of IMOC clusters and biomarkers using a CNA-based stratification model in the independent CPTAC-PDA cohort.

(A) Cluster 2 (high-risk) exhibited significantly poorer survival compared to Cluster 1 (low-risk), with a RMST difference of 6.74 months (p = 0.047) (B) The high-risk Cluster 2 showed significantly elevated TMB compared to Cluster 1 (p = 0.019) (C) Association between specific cytoband deletions and RMST. Three of the four stratification features (18q21.2, 17p12, and 21q11.2) demonstrated significant associations with reduced survival (RMST difference ranging from 5 to 13 months; p < 0.05), while 9p21.3 was non-significant (p = 0.1245) (D) Odds ratio for the four copy number features used for the stratification. The high-risk phenotype is strongly associated with the presence of these chromosomal losses.

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Consistent with our findings in the TCGA-PAAD cohort, the higher-risk cluster in CPTAC demonstrated significantly elevated TMB (p = 0.019) (Fig 8B). Furthermore, the chromosomal alterations identified as key drivers of subtype definition in our discovery cohort, specifically deletions at 9p21.3, 17p12, 18q21.2, and 21q11.2, retained their prognostic relevance in the independent CPTAC dataset. The frequency of these losses was significantly higher in the high-risk cluster, and three of the four regions (18q21.2, 17p12, and 21q11.2) showed statistically significant associations with reduced RMST ranging from 5 to 13 months difference (Fig 8C-8D).

Dataset

Multi-omics data were downloaded from the Firehose Broad GDAC (https://gdac.broadinstitute.org/), using the R packages curatedTCGAData [48] and TCGAutils. Six types of omics data were downloaded: protein expression (Reverse Phase Protein Array, normalized expression values), micro-RNA (Illumina HiSeq, gene-level normalized RPM miRNA expression values), DNA methylation (Illumina Human Methylation 450, probe-level methylation beta values), gene expression (Illumina HiSeq, upper quartile normalized RSEM TPM gene expression values), mutations (somatic mutation calls), and somatic copy number alterations (GISTIC2 thresholded discrete copy number values in recurrent peak regions). There were a total of 154 patients, with each patient having information in at least one data type (S13 Fig). Preprocessing pipelines are described in S1 Appendix and S1 Table. Clinical data were downloaded from cBioPortal.

For the external validation, we downloaded CNA and methylation data from the CPTAC-PDA cohort using https://kb.linkedomics.org/download#PDAC [49]. Because CNA measurements in this cohort are provided at the gene level, whereas TCGA reports CNA at the chromosomal-region level, we harmonized the two datasets by aggregating gene-level measurements within each chromosomal region. This procedure showed a high concordance with the original data, with agreement ranging from 95% to 100% across the four prognostically relevant regions included in the model (0.95, 0.99, 1, 1 for 21q11.2, 17p12, 18q21.2 and 9p21.3, respectively).

Overview of the benchmarking strategy

To identify robust multi-omics subtypes of PDAC, we implemented a three-stage benchmarking framework. First, all possible combinations of omic modalities and cluster numbers were evaluated across multiple clustering algorithms using patients with complete multi-omics profiles. Cluster quality was assessed based on both compactness and reproducibility. Second, the robustness of the clustering algorithms was benchmarked under increasing levels of simulated modality-wise missing data while keeping the previously selected modality combination and cluster number fixed. Third, the algorithm demonstrating the highest robustness was used to generate the final clustering solution in the full cohort through consensus clustering. The resulting subgroups were then compared with established PDAC molecular classification systems.

Finding the best combination of modalities and optimal number of clusters

All combinations (57) of omic modalities were systematically evaluated, where each combination had at least two omic modalities present, plus the evaluation of single modalities (6). Only those patients containing information across all the data types (n = 89) were used at this first stage to reduce noise. Thus, at any degree of missing data, all experiments had the same number of samples, with the only variable being the distribution of the available data. This ensured results were not biased due to sample size for certain combinations.

Nine clustering algorithms (detailed in S1 Appendix), including two factorization-based methods [50,51], three kernel-based methods [52–54], and four graph-based methods [20,55–57] were tested for 2–5 clusters. These algorithms are available in the Python package iMML (https://github.com/ocbe-uio/imml) [58], and were selected due to their ease of use, scalability to high-dimensional data, and computational speed, reproducibility and performance in previous benchmarkings (software and pipelines are described in S1 Table). Additionally, hierarchical clustering and spectral clustering, two widely used and well-established methods, were used to provide appropriate single-modality baselines for comparison.

For our evaluation, we included methods that can handle bulk multi-omics data with an arbitrary number of modalities, do not require assumptions about specific missingness distributions, and provide a ready-to-use Python implementation, suitable for straightforward application by end users. Importantly, we did not include deep learning-based approaches since they generally require substantially larger training datasets than those usually available in survival datasets, as the ones in this study, to achieve reliable performance. The included multi-omics integration methods were therefore selected as established baselines that have been widely used in prior comparative studies, providing a meaningful reference for evaluating the proposed approaches, with MOFA [59] being the standard method for the integration of incomplete multi-omics data in recent studies [60–62].

To improve the reliability of the results, all experiments were tested with 10 independent repeats with subsets of 80% of patients (n = 71). To evaluate cluster quality, we assessed their compactness using the silhouette score and stability across runs through pairwise AMI (S1 Appendix). To obtain an unbiased view of both scores, we combined them using the harmonic mean, referred to as the general performance score (GPS), as was done in previous works [13]. Statistical differences in the GPS were analyzed using the Kruskal-Wallis test. All the results from the benchmarking are available in S9 Data.

Determining the most robust clustering algorithm

The robustness, quantified as the patients assigned to the same cluster in both the complete and missing-data solutions, was measured comparing the cluster assignments from the solutions with no missing data as a reference using pairwise AMI. The clustering algorithms were tested on various simulated, modality-wise missing data patterns generated from patients with complete multi-omics profiles with 80% subsampling. Each scenario was tested at increasing levels of incomplete samples (20%, 40%, 60%, and 80%) and with 10 independent repeats. The results of the evaluation are available in S10 Data

Obtaining the final clusters with consensus clustering

All the patients (n = 154) were used to identify the final clusters, provided that every patient had data from at least one of the omics from the best combination of the modalities. We employed consensus clustering to create the final clusters (S1 Appendix). The clusters identified were compared to previous works, focusing on the three most widely established clustering studies of PDAC patients: Bailey, Collisson and Moffitt subtypes [4–6]. Data was obtained from pdacR [63]. Pairwise differences between subgroups were calculated using Fisher’s exact test. The results with the consensus clustering evaluation are available in S11 Data.

Statistical analysis of final clusters

Post-hoc statistical analyses of the clusters were performed using the patients’ clinical data. 25 clinical labels (see S2 Table) were tested for enrichment, including data about the patient and tumor, by applying the Kruskal-Wallis test for numerical variables and Chi-square test for categorical variables. P-values were adjusted for multiple tests using the Benjamini-Hochberg correction. The results of the statistical analysis of clinical labels is available in S11 Data.

Survival and disease-free progression differences between patient clusters were evaluated using Heinze’s conditional log-rank test, which provides greater robustness to group imbalance compared to traditional log-rank test [23]. Associations between cluster membership and survival outcomes were further assessed using the Cox proportional hazards model. Both approaches rely on two key assumptions: random censoring and proportional hazards. These assumptions were evaluated using a simple linear regression model and the proportional hazards test, respectively. When these assumptions were not satisfied, results from the log-rank test and Cox model were reported over time, as previously recommended [24]. Accordingly, survival metrics were assessed at 6 months, 1 year, 18 months, 2, 3 and 5 years after initial diagnosis, as well as at the end of the study. Particular emphasis was placed on the first 2 years post-diagnosis, as most tumor recurrences and associated mortality occur during this period [2].

RMST was also used to evaluate the differences between the survival and disease-free curves up to specified time points. This test is also recommended when the proportional hazards assumption is not met [24].

To compare clusters, feature values for each modality were summarized at the patient level by averaging across all features (absolute values in the case of CNA). Differences in these patient-level averages between clusters were then assessed using the Mann-Whitney U rank test.

Biomarker identification and analysis

Biomarkers were identified using ABESS [10] with an intermediate fusion multi-modal framework, taking the cluster labels as predictive targets (S1 Appendix). For comparison, unimodal feature selection was also performed using ABESS. The MCC was calculated using 5-fold stratified cross-validation with a random forest classifier and balanced subsampling for both the full feature set and the feature subset to compare model performances. The Cox model was applied to the features selected to obtain the hazard ratio and p-value. ShapIQ was used to explain the influence of the features and quantify the synergy effect between them [64].

Omics analysis

Differential and Gene Enrichment analyses of transcriptomics, methylomics, and proteomics data were performed using standardized workflows in R (v4.4.1) (S1 Appendix). For the evaluation of the association between CNA and the cluster groups, odds ratios were calculated from contingency tables and Fisher’s exact test was used to compare proportions in each cluster.