Methodology overview of CancerSD

Our CancerSD has the advantage to accurately diagnose cancer subtypes by leveraging incomplete multi-omics data of patients and to reduce its dependence on the quantity of in-house cancer samples for training by absorbing knowledge from external datasets, as depicted in Fig 1. The CancerSD pipeline comprises four components dedicated to accomplishing reliable and flexible cancer subtype diagnosis in scenarios characterized by incomplete data and scarce samples. (i) It firstly establishes the patient feature encoder, a tensor-based fusion network, to efficiently integrate multi-omics data from samples. (ii) Then, it constructs the missing omics imputation network to reliably impute missing omics of samples, which consists of an encoder, a projector, and multiple omics-specific generators. After that, it defines Contrastive Learning tasks alongside Masking-And-Reconstruction (MAR) tasks to optimize this imputation network. The former explores the consistent patient representations across different augmented views, while the latter utilizes such representations to impute the missing omics data. (iii) Next, it introduces the cancer subtype diagnosis network that fuses available and imputed omics data to calculate the probability of each patient suffered from a particular subtype. (iv) To enable model optimization on the scarce in-house clinical samples, CancerSD further proposes a knowledge transfer network to extract meta-knowledge from external datasets. We wanted to remark that the first three networks are collectively referred as CancerSD backbone or the base learner (CancerSD_b), while the last network is designated as the meta learner (CancerSD_m).

The detailed description of the CancerSD framework is presented in S1 Fig. For clarity, we illustrated the operational workflow of CancerSD using the GC dataset as a paradigmatic example. It is important to emphasize that our CancerSD framework can be readily extended to subtype diagnosis for various cancers. The framework takes incomplete multi-omics from GC patients as input and finally outputs the probability of them being diagnosed with a certain subtype. Here, incomplete multi-omics implies that certain omics data for some patients are absent due to loss or lack of measurement. M denotes the number of omics types, and is the data matrix for the m-th omics with N patients (or samples) and d_m-dimensional features. Specifically, CancerSD starts by constructing a shared encoder, which encodes the multi-omics features of each patient into an integrated representation. The encoder captures distinctive features of different omics through the omics-specific encoding networks and explores inter-omics relationships using tensor outer products.

Afterward, CancerSD extracts cross-omics underlying information from available omics data of GC patients to reliably impute their missing omics. To this end, CancerSD first generates diverse augmented views by masking certain omics in samples with completely-paired multi-omics data. Then, it employs contrastive learning to guide the patient feature encoder, thereby discerning consistency across different views of the same GC patient. This acquired information is subsequently fed into generators to reconstruct the masked omics and recover the missing omics. Finally, CancerSD inputs the imputed multi-omics data along with available ones into its diagnostic network to discriminate the GC subtypes of patients.

To address the practical challenge of collecting a sufficient number of well-annotated GC samples, CancerSD extends the meta-learning framework to facilitate the circulation of knowledge from external public datasets to the in-house GC samples. It introduces a category-level contrastive loss to minimize differences between samples of the same subtype across different datasets at the distribution level, which aims to selectively learn knowledge from external datasets. Finally, CancerSD utilizes the assimilated knowledge to initialize the backbone, enabling rapid adaptation to the target dataset with limited samples and consequently improving the diagnosis performance.

CancerSD outperforms existing comparison cancer subtype diagnosis methods in the standard supervised learning setting

To assess the effectiveness of CancerSD, we first evaluated and compared it against representative cancer subtype diagnosis methods. Considering that the existing algorithms are based on conventional supervised learning models, we adjusted the training pipeline of CancerSD to adapt to this scenario for a fair comparison. Specifically, we designated the training set as an external dataset for training and fine-tuning, while the testing set serves as the target dataset for evaluating diagnostic performance. Since the experiments conducted here do not involve cross-dataset knowledge transfer, they validated the effectiveness of CancerSD backbone. Overall, the comparison methods can be broadly categorized into three groups: Traditional Machine Learning (TML), Multi-omics Integration (MI)-based methods, and incomplete Multi-omics Integration (iMI)-based methods. A detailed description of these methods is provided in Section A in S2 Text.

The experimental results presented in Fig 2a and Tables B-C in S1 Text demonstrate that CancerSD consistently makes top performance in subtype diagnosis. Then, we utilized t-SNE [33] to reduce dimensionality and visualized the embedding spaces of better-performing methods (MOGONET, DCP, and CancerSD). As depicted in Fig 2b, the challenge posed by incomplete data manifests in the distortion of sample distributions, leading to a noticeable division into two distinct clusters. This distortion greatly heightens the difficulty of subtype diagnosis. Despite these challenges, CancerSD still exhibits the best clustering result, with samples of the same subtype more concentrated in the same cluster. These observations underscore the capability of CancerSD in representation learning and its superiority in cancer subtype diagnosis using incomplete multi-omics data. In Section B in S2 Text, we conducted more analyses of the above results, thus gaining a more comprehensive and detailed perspective on the performance differences among different methods.

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Fig 2. Diagnostic performance on the GC dataset in the standard supervised learning setting.

(a) The cancer subtype diagnosis performance of CancerSD vs. comparison methods, including kNN, RFC, AE-XGBoost, MOMA, MOGONET, DCP, and APADC on the STAD dataset.(b) Sample clustering using original data and embedded representations given by CancerSD and other methods.(c) The diagnosis performance of the tested methods under different degrees of omics missingness.(d) The diagnostic accuracy of CancerSD for different GC subtypes.(e) The diagnostic probability of CancerSD for different GC subtypes.

https://doi.org/10.1371/journal.pcbi.1012710.g002

Next, we evaluated the diagnostic performance of these methods under diverse degrees of multi-omics missingness. We intentionally simulated omics missing scenarios by randomly masking specific omics in samples with completely-paired multi-omics data. Specifically, the simulated missing rates are set at 0%, 25%, 50%, and 75% in sequence, indicating the specified proportion of samples selected for missing certain omics. Fig 2c and Table D in S1 Text demonstrate that CancerSD consistently makes the top performance across all the missing rates. In line with the previous analyses, the performance of the tested methods at different rates manifests a step-like distribution. iMI-based methods generally outshine their MI-based counterparts, while traditional machine learning methods display relatively poor performance. As the simulated missing rate increases, there is a gradual performance decline in all methods, with the most significant decrease witnessed in methods that involve sample similarity calculations, such as kNN and MOGONET. Moreover, it is noteworthy that when multi-omics data for samples is either complete or involves minor incomplete issues, iMI-based methods also marginally outperform MI-based ones, primarily due to the auxiliary tasks constructed for recovering the missing omics. As the degree of omics missing intensifies, a substantial performance gap becomes evident between them. Besides the simulated scenarios of multi-omics data with random missing, we also recognize that the missingness of omics data may not be entirely random in the clinical practice. Therefore, we have conducted experiments focusing on the specific omics absence, displayed the results in Tables E-G in S1 Text, and provided further analysis in Section C in S2 Text.

Finally, we investigated the identification preferences of CancerSD for different GC subtypes, including Epstein-Barr virus (EBV), microsatellite instability (MSI), genomically stable (GS), and chromosomal instability (CIN) categorized by the Cancer Genome Atlas (TCGA) Research Network [34]. As shown in Fig 2d, CancerSD can easily and accurately diagnose the EBV and CIN subtypes while maintaining high accuracy for the MSI subtype. However, CancerSD struggles with the identification of the GS subtype. In Fig 2e, it is evident that the accuracy of CancerSD in diagnosing the GS subtype is significantly lower than others. Based on Fig 2b, we noted that the clusters containing samples of GS and CIN subtypes are consistently close to each other, even overlapping. We further analyzed samples where diagnostic errors occurred in the experiments and find that compared to other subtype pairs, these two subtypes are more likely to be misdiagnosed as each other (see S2 Fig). In fact, Lee et al. [35] observed cases of subtype transition between these two subtypes after metastasis (transitions from CIN to GS and vice versa), while the subtype of metastatic tumors is generally the same as the primary tumor. These findings suggest a potential similarity between the GS and CIN subtypes, which gives rise to the confusion of CancerSD toward these two subtypes.

As mentioned above, the experiments conducted under standard supervised learning settings actually highlight the capabilities of CancerSD_b. Furthermore, we studied more details for CancerSD_b, including evaluation its robustness (see S3 Fig and Section D in S2 Text), exploring its optimal architecture (see Table H in S1 Text and Section E in S2 Text), investigating the impact of different data augmentation operations (see S4 Fig and Section F in S2 Text), and examining its sensitivity to changes in hyper-parameters (see S5 Fig and Section G in S2 Text). These experiments and analyses provide a more in-depth and comprehensive perspective on why CancerSD can make superior subtype diagnosis performance.

CancerSD demonstrates superior diagnostic performance in the few-sample scenario

Cancer subtype diagnosis is a classical few-sample scenario, where in-house datasets often contain only a limited number of samples, posing challenges in optimizing an accurate diagnostic model. Moreover, variations in sample collection sources and biases in sample selection contribute to significant differences among different datasets (i.e., sample distribution disparities, as illustrated in S6 Fig). Disregarding this situation and directly transferring knowledge from external datasets to in-house ones can lead to negative transfer, which potentially undermines the performance of the diagnostic model. To assess the effectiveness of CancerSD in addressing these issues, we constructed knowledge transfer tasks across different datasets. The detailed experimental setups and description of comparison approaches are presented in Section Material and methods.

First, we evaluated the performance of certain cancer subtype diagnosis methods on the GSE62254 dataset under the conventional supervised learning settings, which serves as the baseline performance. In this scenario, all methods only use the data from GSE62254, with no knowledge learned from external datasets. As shown in Fig 3a, it is observed that various methods exhibit similar diagnostic performance. Particularly, there is minimal difference among the performance of iMI-based methods, including CancerSD, DCP, and APADC. This phenomenon mainly arises from the fact that GSE62254 contains mRNA expression profiles as the sole omics data, leading all methods to degrade into simple classifiers. Nonetheless, owing to auxiliary tasks such as data reconstruction, iMI-based methods still perform slightly better than others. Additionally, we observed a significant performance decline when training CancerSD with only a small amount of samples (4-way 10-shot, ten samples for each subtype). In fact, by referring to Fig 3a and Table I in S1 Text, we noted that all methods perform poorly under this scenario, which could be attributed to two main reasons. On the one hand, since only mRNA data is accessible in GSE62254 dataset, MI-based and iMI-based methods essentially degrade into single-model classifier, losing their advantage in modeling multi-omics interactions. On the other hand, all compared methods can only use a limited amount of data from GSE62254, preventing sufficient optimization and causing underfitting.

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Fig 3. Diagnostic performance on the GC datasets in the few-sample scenario.

(a) The cancer subtype diagnosis performance of CancerSD vs. comparison methods on the GSE62254 dataset under the standard supervised learning setting.(b) The cancer subtype diagnosis performance (Accuracy and F1 Score) of different methods under the multi2mRNA (upper figure) and mRNA2mRNA (lower figure) settings. Here, the red dot dash line represents the performance obtained by optimizing CancerSD with the entire training set, while the gray dotted line indicates that obtained by optimizing CancerSD with a 4-way 10-shot set.(c) The similarity of representations for samples from different datasets.

https://doi.org/10.1371/journal.pcbi.1012710.g003

Next, we attempted to transfer knowledge from the STAD dataset, supporting the optimization of diagnostic models on GSE62254. Specifically, we initialized and trained diagnostic models on STAD and subsequently select a small number of samples (4-way 10-shot) from the training set of GSE62254 to fine-tune these models. To include traditional machine learning methods into the experiment, we combined STAD and the data used for fine-tune from GSE62254 into a unified training set, which was then provided to these methods. Here, we explored knowledge transfer under two strategies: from multi-omics data of STAD to the mRNA expression profile of GSE62254 (multi2mRNA) and from the mRNA expression profile of STAD to that of GSE62254 (mRNA2mRNA). As illustrated in Fig 3b, and Tables J-K in S1 Text, We observed that even if TML approaches are granted access to external datasets, they struggle to make reasonable use of these data, due to the lack of effective knowledge extraction strategies. This demonstrates the difficulty of TML methods in adapting to the few-sample scenario, compared to few-shot learning-based approaches. We also found that meta-learning-based methods generally exhibit superior transfer performance compared to pretraining-based ones. This is likely due to the emphasis of meta-learning on the cross-dataset generalization ability of the models, while pretraining strategies focus on models’ performance on the current dataset. Notably, with only a 4-way 10-shot set sampled from the training set, our CancerSD achieves performance comparable to using the entire training set. This observation emphasizes the capability of CancerSD_m in cross-dataset knowledge transfer. Moreover, the performance of tested methods under the mRNA2mRNA strategy is superior (or comparable) to that under the multi2mRNA. This could be attributed to the fact that embedding spaces generated from mRNA data in different datasets are more similar in distribution than those generated separately from multi-omics and mRNA data. Consequently, under the mRNA2mRNA strategy, the models can more easily absorb knowledge from external datasets.

Taking results under mRNA2mRNA as example, we further analyzed the effectiveness of CancerSD_m and the importance of category-level contrastive loss. In the knowledge transfer task, CancerSD achieves an Accuracy of 67.5%, AUROC of 83.7%, Precision of 73.3%, and F1 Score of 67.6%, outperforming its comparison methods and variations across almost all metrics. The superior performance can be attributed to its powerful backbone and domain-specific knowledge transfer capabilities. Specifically, CancerSD outperforms its variants CancerSD-MOMA and CancerSD-DCP, whose backbone networks are replaced with MOMA and DCP, respectively. This superiority underscores the capability of CancerSD_b to effectively impute missing omics data and integrate multiple omics for accurate and reliable cancer subtype diagnosis. On the other hand, the significant performance decline of CancerSD-w/oCLC highlights the importance of the distribution-based category-level contrastive loss. By leveraging this loss, CancerSD can alleviate the sample distribution discrepancy across different datasets and focus on extracting knowledge relevant to the assigned downstream diagnosis tasks from external datasets. Fig 3c supports this perspective by showing that representations obtained by CancerSD for samples of the same subtype from different datasets exhibit higher similarity. This observation indicates that CancerSD effectively captures the consistency of cancer subtypes across different datasets and integrates the consistency into sample representations, thereby improving the similarity among samples of the same subtype. The comparison results also demonstrate that the similarity-based category-level contrastive loss fails to acquire knowledge from datasets with more samples effectively and may even hamper the generalization ability of CancerSD_b. This is because CancerSD-SIM utilizes the instance-level similarity to cluster samples of the same subtype, which potentially leads to severe overfitting problems and is susceptible to noise and outliers. In contrast, CancerSD attempts to cluster samples of the same subtype at the distribution level, thereby alleviating such issues.

The above analyses provide insights into why CancerSD_m can effectively extract knowledge from other datasets. In summary, CancerSD_m adopts a meta-learning strategy to mine and transfer meta-knowledge from external datasets and utilizes the category-level contrastive loss to maximize the agreement of distributions between samples with the same subtype across different datasets, thereby improving the diagnostic performance of the model on target dataset.

Diagnostic performance of CancerSD under different omics data types

Although CancerSD fuses three types of omics data (DNA methylation profiles, miRNA expression profiles, and mRNA expression profiles) for cancer subtype diagnosis in the above experiments, it can readily adapt to different numbers of omics data types. To verify the importance of multi-omics integration in improving the diagnosis performance and to assess the capability of CancerSD in multi-omics integration, we evaluate CancerSD using various combinations of omics data. Here, we only consider samples with completely-paired multi-omics data.

Fig 4a shows that the diagnostic performance of CancerSD is improved continuously by integrating more omics data. In concrete terms, CancerSD trained with all three omics outperforms the model using a combination of two types of omics. The performance of CancerSD trained with two omics is also superior to that of only single omics. These results highlight the advantages of integrating multiple omics data for more accurate subtype diagnosis. Moreover, it is worth noting that CancerSD trained with mRNA expression data performs best when employing only single omics for training. This finding suggests that mRNA features contain information conducive to distinguishing GC subtypes, potentially harboring valuable biomarkers. In contrast, the performance of CancerSD trained using miRNA data is the poorest. This may be attributed to the lower dimensionality of its original data compared to the other two types of omics (702 vs. 3278 and 4089), which provide less discriminative information for subtyping.

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Fig 4. Diagnostic performance under different omics data types.

(a) Performance comparison for subtype diagnosis using different types of omics. Among them, methylation, miRNA, and mRNA refer to make diagnosis via CancerSD using DNA methylation data, miRNA expression data, and mRNA expression data, respectively; meth+miRNA, miRNA+mRNA, and meth+mRNA refer to diagnosis with two types of omics; meth+miRNA+mRNA refers to diagnosis with three types of omics.(b) Sample similarity heatmaps obtained from representation at different levels.(c) Diagnostic performance of CancerSD using only a single type of omics under different training strategies.(d) Sample clustering based on omics and fusion representations output by CancerSD under multi-omics joint training strategy.(e) Sample clustering based on omics and fusion representations output by CancerSD under single-omics independent training strategy.

https://doi.org/10.1371/journal.pcbi.1012710.g004

Expanding upon the results mentioned above, we delve deeper into the effectiveness of CancerSD in integrating multi-omics data. First, we focus on the sample similarity pattern as an illustrative example to elucidate the capability of CancerSD in extracting cross-omics consistency information. As depicted in Fig 4b, after mining subtype-related discriminative information in the corresponding omics data using omics-specific feature extractors, samples of the same subtype exhibit relatively high similarity across different omics. CancerSD adeptly identifies and captures this cross-omics consistent pattern of sample similarity, incorporating these patterns into the multi-omics fusion representation. Meanwhile, CancerSD takes into account discrepant patterns across multiple omics to mitigate the impact of erroneously high similarity (i.e., the globally high similarity from miRNA embedding). Consequently, the fusion representation learned by CancerSD more accurately reflects the correct similarity relationships between samples.

Next, we conduct extensive experiments to assess the capability of CancerSD in exploring cooperation between diverse omics data. To this end, we compare the subtype diagnosis performance of CancerSD in two distinct training strategies: (i) multi-omics joint learning, which uses multiple omics data simultaneously to optimize the model; (ii) single-omics independent learning, which uses only a single type of omics to optimize the model each time. As shown in Fig 4c and Table L in S1 Text, it is evident that under the identical condition of diagnosing, CancerSD optimized by multi-omics joint learning more accurately identifies patient subtypes compared to the model optimized by single-omics independent learning strategy. To gain further insights, we investigate the omics embeddings obtained under different training strategies and evaluate the diagnostic potential of multi-omics fusion representations derived from these embeddings. Specifically, we separately construct and optimize multi-omics fusion networks (see Experimental Section) to integrate multiple omics embeddings obtained under joint learning and independent learning strategies. Then, we utilize the resulting fusion representations to perform cancer subtype diagnosis tasks. The results presented in Table L in S1 Text suggest that the fusion representations integrated from omics embeddings learned by joint learning are more conducive to identifying subtypes. Furthermore, we visualize sample clustering for different training strategies. From Fig 4d and 4e, we can find that, in comparison with the output obtained by initially performing single-omics independent learning and then integrating the resulting omics embeddings, the fusion representations obtained through multi-omics joint learning can generate a more compact clustering structure, with more apparent margins between clusters. These observations prove that CancerSD has effectively learned cooperation between different omics during the multi-omics joint optimization process, thereby enhancing the performance of multi-omics fusion.

In summary, multi-omics data can offer more prosperous and more comprehensive patient features. CancerSD effectively integrates these data by extracting cross-omics consistency and cooperation information, significantly improving the performance of cancer subtype diagnosis. To further highlight the superiority of our CancerSD, we also evaluated the diagnostic performance of several comparison methods across different omics types (see Table M in S1 Text), with a concise analysis provided in Section H in S2 Text. In addition to integrating multi-omics, CancerSD also possesses a notable capability in handling missing omics data. Even in cases of extensive omics data missingness (see Table N in S1 Text), CancerSD effectively recovers biologically meaningful expression values, affirming its authenticity and effectiveness in imputing missing omics. The details regarding this aspect are presented in S7–S13 Figs and are discussed more extensively in Section I in S2 Text.

CancerSD identifies important molecules related to gastric cancer

Identifying important biomarkers is crucial for understanding the underlying mechanisms of GC and interpreting the corresponding diagnostic decision made by CancerSD. To this end, we investigated the importance of each molecular characteristic on the diagnostic outcomes to find potential biomarkers. Specifically, we systematically shuffled the values of each molecular characteristic across all samples in the testing set and then evaluate the diagnostic performance of CancerSD using these modified features. After that, we compared the performance with results obtained when using all features, allowing us to discern the contribution of each molecule to diagnosis tasks, where the diagnosis loss (Eq 10) serves as a quantitative indicator for multi-classification tasks. The more loss increases, the more important the currently permutated molecule is. For a more robust result, we conduct ten random experiments and take the average performance degradation as the final result. Within each type of omics, we selected the top-ranked molecular characteristics for further analysis and validation.

First, we presented importance scores of the top ten ranked molecules from each omics. As shown in Fig 5a and 5b, it is evident that there are significant importance differences of molecules across various omics. Among them, mRNA features obtain the highest importance scores, while miRNA features have the lowest, indicating that CancerSD relies more on mRNA expression profiles in the diagnostic decision-making process. This perspective is further highlighted in Fig 5c, where clusters from mRNA embeddings are closer to clusters from fusion representations than from other omics embeddings for patients. We speculated that the prominence of mRNA features may be mainly attributed to two reasons. On the one hand, owing to the higher dimensionality of the raw data, mRNA features can provide richer discriminative information for subtype diagnosis. On the other hand, mRNA expression data more directly reflects the activity of genes and cellular functions. Meanwhile, mRNA expression is influenced by multiple regulatory layers, including DNA methylation and miRNA regulation, among others, potentially more comprehensively reflecting the integrated effects of gene expression regulation. The division of cancer subtypes is often associated with changes in genes. Therefore, mRNA features play a more crucial role in the diagnostic process.

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Fig 5. Important molecules identified by CancerSD.

(a) Importance scores of the top-ranked molecules identified by CancerSD in various omics.(b) Differences in the importance scores of molecules across various omics.(c) Clustering for samples of different subtypes using omics embeddings and fusion representation output by CancerSD, respectively.(d) The methylation levels of the top 100 CpG sites ranked by importance, where the CpG sites are secondary sorting based on the average values across all samples.(e) The expression levels of mRNA characteristics across different GC subtypes.(f) The expression levels of mRNA and miRNA characteristics across different GC subtypes, where the expression values subjected to log2 transformation and normalization. Wilcoxon rank-sum test is employed to evaluate the differences in the expression levels of specific molecules among patients of distinct subtypes.(g) Gene co-expression analysis result for EBV subtype.(h) KEGG Pathway Enrichment results for module-2 (ME-2, top) and module-4 (ME-4, bottom), respectively.

https://doi.org/10.1371/journal.pcbi.1012710.g005

Then, we visualized the expression of molecules identified by CancerSD in each omics type to preliminarily showcase the authenticity of CancerSD in making diagnostic decisions. The molecules selected in this step are detailed in Table 1 (genes and miRNAs are listed) and Table O in S1 Text (CpG sites are listed). For the DNA methylation profile, we explored differences in methylation patterns at CpG sites among patients of distinct subtypes, focusing on the top 100 ranked features. As depicted in Fig 5d, differences in methylation patterns emerge across GC subtypes. Specifically, EBV patients exhibit elevated methylation levels at most CpG sites in comparison to other subtypes, with MSI patients ranking second. Patients with the other two subtypes show a relatively similar DNA methylation pattern. These observations are consistent with the previous study [34]. For miRNA and mRNA expression profiles, we investigated the differences in the expression levels of the top 10 important molecules among various subtypes. Based on Fig 5e–5f and S14 Fig, we could observe that most top-ranked characteristics exhibit significantly different expression levels across various subtypes. These observations indicate that CancerSD primarily relies on molecules that exhibit distinction across different subtypes in the diagnostic process.

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Table 1. Important molecules identified by CancerSD.

https://doi.org/10.1371/journal.pcbi.1012710.t001

Next, we explored the relationship between top-10 important molecules in each omics (see Table 1) and GC. Among them, characteristics derived from DNA methylation and mRNA expression profiles are inferred as their corresponding genes. Notably, nearly half of these molecules have been extensively studied. For instance, Yasumoto et al. [36] discovered that the CXCR4/CXCL12 axis plays a role in the development of peritoneal carcinomatosis, which is an incurable complication during the advanced stages of GC. Subsequent research by Hashimoto et al. [37] revealed that blocking the CXCR4/mTOR signaling pathway may contribute to the treatment of this complication. Moreover, Xiang et al. [38] demonstrated that CXCR4 can cross-activate with CXCR2, promoting the epithelial-mesenchymal transition, metastasis, and invasion in GC. Simultaneous inhibition of these two genes has been shown to reduce the metastasis of GC effectively. These studies highlight the close association between CXCR4 and GC. Besides important genes, the miRNAs identified by CancerSD have also been confirmed to have profound associations with GC. Taking hsa-mir-488 as an example, several studies [39, 40] demonstrated that its overexpression can delay the malignant progression of GC, suggesting that hsa-mir-488 holds promise as a valuable biomarker for the diagnosis and treatment for GC. Alongside the molecules mentioned above, existing studies (see Table P in S1 Text) have reported that CD9, KLK6, HLA-B, MUC1, MET, hsa-mir-7–2, hsa-mir-944, hsa-mir-942, hsa-mir-219a-2, and hsa-mir-1305 also play an important role in the occurrence, progression, or diagnosis and treatment of GC.

While the relationships between certain molecules in Table 1 and GC remain unclear, some are closely associated with other digestive tract cancers. For example, Fujita et al. [41] found that the overexpression of ENC1 may suppress the differentiation of colon cells, potentially leading to the development of colorectal cancer. This process could be achieved through JAK2/STAT5/AKT axis-mediated epithelial-mesenchymal transition and stemness. [42] In addition, Than et al. [43] indicated that CFTR is a tumor suppressor gene in intestinal cancer. Similarity mechanisms might exist in GC, and further exploration of these genes could contribute to a more profound understanding of GC, as well as elucidating connections and distinctions among various digestive tract cancers.

Finally, we conducted a detailed analysis of important genes identified by CancerSD for each GC subtype, including genes derived from DNA methylation and mRNA expression profiles. During the calculation of diagnosis loss, we individually assessed the impact of feature shuffling on the diagnosis for each subtype. These processes involve partitioning the testing set based on subtypes and separately calculating diagnosis loss for each subtype. By quantifying the increase of the loss, we assign importance to specific characteristics. For the top-10% ranked important genes (619 / 6186) identified for each subtype, we utilized the WGCNA R package [44] and OmicVerse [45] to conduct gene co-expression analysis and select certain co-expression modules for subsequent analysis. Taking the EBV subtype as an example, the selected genes are clustered into six co-expression modules (as illustrated in Fig 5g). Among these modules, genes in module-2, 3, 4, 5, and 6 exhibit significant co-expression relationships, with 75, 54, 50, 33, and 32 genes within each module. We further conducted KEGG enrichment analysis on these five modules, and the results are presented in Fig 5h and Table Q in S1 Text. In module-2 (ME-2), pathways such as ECM-receptor interaction (ko04512) and cell adhesion molecules (ko04514) are prevalent in cancer and play crucial roles in GC [46, 47]. Some pathways enriched in ME-2 are also highly associated with EBV. Liang et al. [48] reported that focal adhesion (ko04510) signal pathways are often dysregulated due to EBV-associated genomic and epigenomic alterations, which may play a crucial role in the development of EBV-associated GC. Other three myocarditis-related pathways (ko05412, ko05410, and ko05414) are associated with a rare but severe complication of EBV infection [49]. In module-4 (ME-4), numerous immune-related pathways are significantly enriched, such as PD-L1 expression and PD-1 checkpoint pathway in cancer (ko05235), TNF signaling pathway (ko04668), antigen processing and presentation (ko04612). Among them, NF-κB signaling pathway (ko04064) exhibits higher positivity in EBV-positive GC than EBV-negative one [50]. It promotes the proliferation of GC cells infected with EBV, which could be attributed to the regulation of the EBV-encoded BARF1 [51]. Similarly, the overexpression of PD-L1 has been reported as a typical characteristic of the EBV subtype [34], and PD-1 inhibition is an effective treatment for patients of this subtype [52]. These two mechanisms are closely related to ko05235 pathway. Cytokine-cytokine receptor interaction (ko04060) is also one of the core pathways dysregulated in EBV-associated GC [48].

Collectively, the aforementioned pathways may play important roles in the development of EBV-associated GC. Therefore, we hypothesized that key genes within these pathways could serve as potential biomarkers or therapeutic targets for the EBV subtype. For example, CXCL10 and CXCL11, both small-molecule cytokines in the CXC chemokine family, are significantly overexpressed in the EBV subtype compared to other subtypes (see S15 Fig). These two genes regulate the migration, differentiation, and activation of immune cells through the CXCL9/10/11/CXCR3 axis, which is also directly involved in the proliferation and metastasis of cancer cells. [53] Given their roles in guiding immune cells such as T cells and leukocytes to move towards inflammatory or infected sites, [54]CXCL10/11 may contribute to better immunotherapeutic effects in EBV-positive GC patients. In more detail, CXCL10/11 are regulated by EBV-related miRNAs, with the former being regulated by ebv-miR-BART1–3p [55] and the latter being regulated by ebv-mir-BHRF1–3. [56] It is possible that EBV promotes the occurrence and development of GC through these pathways, implying the potential of CXCL10/11 as diagnostic factors for the EBV subtype. Moreover, for other GC subtypes (CIN, GS, MSI), the co-expression and KEGG pathway enrichment results are presented in S16 Fig.

The above results and analysis verify the authenticity and interpretability of CancerSD in cancer subtype diagnosis, which also prove the potential of CancerSD in assisting clinical diagnosis.

Outcomes of CancerSD are associated with stemness features of gastric cancer subtypes and patient prognosis

In the previous analyses, CancerSD demonstrates the capability to accurately diagnose cancer subtypes using incomplete multi-omics data. Experiments conducted on the GC dataset also indicate its ability to identify key molecular signatures associated with GC. These results provide preliminary evidence of its reliability in assisting clinical diagnosis. To further investigate the role of CancerSD in diagnostic decision-making, we explored its relationship with gastric cancer subtypes and patient prognosis. Stem cells are characterized by their capacity for self-renewal, either infinitely or perpetually, alongside their ability for multi-lineage differentiation, while stemness is defined as the potential of stem cells in these two aspects [57]. Within tumor tissues, a small proportion of relatively stable cells possessing both proliferative and tumor-reconstructing abilities are identified as cancer stem cells or cancer stem-like cells [58]. These cells may cause various tumor malignancies, such as recurrence, metastasis, multidrug resistance, and radioresistance [59]. Thus, determining the stem-cell characteristic of each GC subtype is of significant importance for gaining deeper insights into mechanisms underlying tumor initiation and progression, as well as for the development of effective therapeutic strategies. To this end, we employed the stemness index model [57], known as mRNAsi, to score the stemness features of GC samples and then conduct further analysis.

We first collected gene expression profiles of pluripotent stem cells from the Progenitor Cell Biology Consortium dataset [60, 61] (syn2701943). The data are preprocessed with mean-centering. Subsequently, the stemness signature is identified through the one-class logistic regression algorithm. Next, spearman correlation analysis is performed between the normalized expression matrix of GC samples and the stemness signature. The resulting correlation coefficients are scaled to the range [0, 1] to determine the stemness index. Finally, we assessed the relationship between mRNAsi scores and our CancerSD.

From Fig 6a, we observed an association between the stemness index and clinical features in GC patients. In particular, there are significant differences in mRNAsi among patients of distinct GC subtypes (see Fig 6b). While there is typically a negative correlation between mRNAsi and the prognosis of cancer patients [62, 63], an opposite trend is noted in GC [64]. This is further highlighted in Fig 6c, where patients with higher mRNAsi tend to exhibit a favorable prognosis. Consistently, mRNAsi is the lowest in samples of the GS subtype, which corresponds to the poorest prognosis among the four subtypes [65]. Interestingly, a correlation analysis of the stemness index with the CancerSD score for each subtype shows that the GS subtype is significantly negatively correlated with the mRNAsi (r = −0.353, p = 4.94 × −10³, Fig 6d), where CancerSD scores represent the probability of a patient being diagnosed with a certain cancer subtype. There is currently no consensus on why the GS subtype often corresponds to the lowest mRNAsi. Considering the high overlap between samples of GS subtype and of diffuse-type GC (see Fig 6e), we might gain insights into the mechanisms behind this phenomenon from diffuse-type GC [66], which similarly obtains the lowest mRNAsi scores within its corresponding Lauren [67] classification system (see Fig 6f). In addition, CancerSD scores of samples with other subtypes also show significant correlations with mRNAsi. Given the significant correlation between mRNAsi and patient prognosis, the aforementioned observations suggest that GC subtype scores may be associated with the prognosis of GC patients.

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Fig 6. The relationship among CancerSD outcomes, mRNAsi scores, and patient clinical characteristics.

(a) An overview of the association between the mRNAsi and clinical features. The median of mRNAsi score is used to categorize mRNAsi levels.(b) mRNAsi scores across different molecular subtypes.(c) Kaplan-Meier survival curves of different mRNAsi levels. Among them, HR and 95CI are abbreviations of Hazard Ratio and 95% Confidence Interval, respectively.(d) The relationship between CancerSD scores (with normalization) and mRNAsi scores in GC patients. The former is derived from the output of CancerSD before the softmax layer, while the latter is obtained through the mRNAsi model.(e) The integrated sankey diagram portrays the underlying correlations across the mRNAsi, molecular subtypes and Lauren classification.(f) mRNAsi scores across different Lauren subtypes.(g) The relationship between Integrated CancerSD Score (ICS) and mRNAsi scores in GC patients.(h) Kaplan-Meier survival curves of different ICS levels.(i) Correlation of mRNAsi and expression levels of important genes identified by CancerSD. The regression lines in figures are fitted by the corresponding data. The significance in the figure is estimated by pearson correlation coefficient.

https://doi.org/10.1371/journal.pcbi.1012710.g006

To delve deeper into this association, we aggregated CancerSD scores for different subtypes in a manner analogous to TCGA Risk Score [65], yielding the Integrated CancerSD Score (ICS) that estimates patient prognosis risk. To ensure a smoother ICS, we replaced the softmax function with the sigmoid function, constraining all CancerSD scores to the (0, 1) interval. Specifically, we formulated ICS as follow: ICS = e^ICSraw, where ICSraw = CIN score + (1—MSI score) + (2 × GS score) + (1—EBV score). Among that, the coefficients preceding the subtype prediction scores were determined based on their relationship with prognosis [65]. Since EBV and MSI are commonly associated with favorable prognosis, we used the inverse of their CancerSD scores. The weighting coefficient for the GS score was assigned to 2, reflecting its strong correlation with poor prognosis. The CIN score remained unchanged, as this subtype is only moderately associated with poor prognosis. Using 16.2 (the optimal cutoff value confirmed by maxstat R package [68]) as the cutoff point, we categorized ICS into low and high levels. As illustrated in Fig 6g, ICS exhibits a significant negative correlation with mRNAsi (r = −0.601, p = 6.5 × −10³⁷), indicating that a high level of ICS may correspond to a poorer patient prognosis. Fig 6h validates this perspective, demonstrating a significant difference in overall survival among patients with different ICS levels (p = 0.04). While the stratification of patients based on ICS levels does not show a significant difference in disease-free survival (p = 0.16), noticeable distinctions can be observed in Fig 6h. This lack of significance may be attributed to the problem of insufficient data related to disease-free survival, with only 201 out of 415 GC patients possessing corresponding disease-free survival information. To further evaluate the prognostic value of the ICS, we conducted univariate and multivariate Cox proportional hazards regression analyses on ICS and other seven clinical variables. As listed in Table R in S1 Text, in addition to well-known prognostic factors such as T stage, N stage, M stage, and TNM stage, ICS emerged as a significant predictor for overall survival in univariate analysis. Even when incorporating all relevant clinical variables in a multivariate Cox regression analysis, ICS remains an important prognostic factor (HR, 1.7; 95% CI, 1.07–2.70, p = 0.03). Collectively, ICS may serve as a potential predictive factor for overall survival and even disease-free survival, highlighting the utility of CancerSD.

We further extended our investigation to the relationship between mRNAsi and the top-ranked genes identified by CancerSD. Specifically, we analyzed the correlation between the expression levels of the top 25 genes (including those identified from DNA methylation and mRNA expression profiles) across all samples and mRNAsi scores. The results are presented in Fig 6i and S17 Fig. We observed that 13 genes exhibit a significant correlation with mRNAsi. Among them, five genes are directly or indirectly involved in various biological processes, exerting impacts on the stemness characteristics of cancer cells. For example, c-Met, the protein product of the MET proto-oncogene, has been demonstrated to promote tumor angiogenesis, growth, and metastasis [69]. Several studies [70, 71] reported that c-Met is implicated in the stemness of cancer stem cells in various cancers. In gastric cancer, Yashiro et al. [72] found that the combination of c-Met inhibitors with SN38 may effectively target cancer stem cells in diffuse-type GC. Bahrami et al. [73] also reported that c-Met/ALK inhibitors could reduce the expression of cancer stem cell markers in gastrointestinal cancers. These evidences suggest that elevated expression of MET can promote the characteristics of GC stem cells, thereby positively influencing mRNAsi scores. Moreover, ECRG4 serves as an inhibitory upstream regulator of the NF-κB pathway [74], while the latter is persistently activated in cancer stem cells across various malignancies, participating in several crucial biological processes of cancer stem cells [75]. The role of NF-κB in GC has been widely reported, where its activation can stimulate the proliferation and stemness of GC cells [76]. Ding et al. [77] found that the PEAK1-PPP1R12B axis can inhibit cell growth and metastasis in colorectal cancer by attenuating the Grb2/PI3K/Akt signaling pathway, and a similar mechanism might exist in GC. Considering the activation effect of PI3K/Akt pathway on the NF-κB system [78], the high expression of genePPP1R12B might indirectly play a role in suppressing the stemness of GC cells. Consequently, we observe a significant negative correlation between the expressions of ECRG4 and PPP1R12B and mRNAsi scores. Besides MET mentioned above, ECRG4 and PPP1R12B, another two genes (see Table S in S1 Text), whose expression levels are significantly correlated with mRNAsi scores, are also associated with the stemness features of cancer cells. Although not all of these genes have been confirmed to play a role in GC, there might be similar mechanisms promoting or inhibiting the stemness of GC cells.

In summary, CancerSD scores for samples show a significant correlation with the stemness features of different GC subtypes and patient prognosis. Moreover, the majority of top-ranked important genes identified by CancerSD are closely associated with cancer cell stemness features. These findings once again validate the authenticity and reliability of CancerSD in GC subtype diagnosis, suggesting its potential to assist real-world clinical decision-making.

CancerSD maintains good performance on multiple cancer datasets

In the above analyses, we primarily discussed experimental results related to GC. To investigate the generalization capability of CancerSD, we also conducted a series of experiments on lung cancer and breast cancer datasets. The relevant results are presented in Tables B, L, T in S1 Text and S8–S9 Figs. Overall, we could draw similar observations from these results as those observed in GC datasets. First, CancerSD exhibits superior (or comparable) performance in subtype diagnosis for lung cancer and breast cancer than the competitive methods. Second, experiments involving multi-omics integration and missing omics imputation on these two cancer datasets further highlight the effectiveness of our method in these regards. Furthermore, we observed that the importance of different omics varies across different cancers during the diagnostic process. Lastly, experiments involving knowledge transfer between two lung cancer datasets once again demonstrate the capabilities of CancerSD in addressing sample scarcity and mitigating negative transfer. In addition to these observations, a more detailed exposition of the relevant experiments and corresponding results is provided in Section J in S2 Text. In summary, CancerSD emerges as an effective and authentic model for cancer subtype diagnosis, which can be readily deployed to different cancers.

Datasets

To study the effectiveness of CancerSD, we apply it to subtype three representative cancers using benchmark datasets: STAD and GSE62254 for gastric cancer (GC) TCGA subtype [34] diagnosis; LUAD, LUSC and CPTAC [79, 80] for lung cancer subtype diagnosis; and BRCA for breast invasive carcinoma PAM50 subtype [81] diagnosis. Three types of omics data are employed for experiments, including DNA methylation profile, miRNA expression profile, and mRNA (protein-coding gene) expression profile. Among the aforementioned datasets, only samples with molecular subtype diagnoses are selected. An overview of these datasets is provided in Table A in S1 Text.

Data preprocessing

In the data preprocessing stage, we first apply a log2 transformation to the miRNA and mRNA expression data. Then, we filter out features with low variance [14] (the threshold set as 0.2 for the DNA methylation profile, 0.1 for the miRNA expression profile, and 0.8 for the mRNA expression profile). These variance thresholds are consistently used across all experiments. Additionally, we select specific molecular characteristics following the analysis configuration proposed by Hoadley et al. [82] and incorporate them into the filtered features. Consequently, we retain 3287 DNA methylation characteristics, 702 miRNA expression characteristics, and 4089 mRNA expression characteristics. Finally, we individually normalize miRNA and mRNA data to a range of [0, 1] (the original range of DNA methylation data is already within the interval [0, 1], where 0 represents a lower level of methylation, and 1 represents a high level of methylation).

The shared patient feature encoder

To integrate multi-omics data of patients, CancerSD constructs a module-shared patient feature encoder, which is capable of providing high-quality patient representations for both missing omics imputation and cancer subtype diagnosis. The encoder comprises M omics-specific feature extractors and a multi-omics fusion network.

The omics-specific feature extractors are feedforward networks designed to reduce dimensionality and capture discriminative characteristics and patterns of the corresponding omics data as: (1) where is the embedded representation for the m-th omics data of the i-th patient. f^m(⋅) corresponds to the feature extractor of the m-th omics.

To capitalize on the advantages of multi-omics data, we employ LMF [83] (Low-rank Multimodal Fusion) and formulate our multi-omics fusion network for data integration. In comparison to alternative methods [14, 84], LMF stands out by its ability to explore cross-omics cooperation while retaining omics-specific information, allowing more informative integration. We first concatenate an extra constant value of 1 after , namely , which can prevent the loss of the original features of each omics. Next, the fusion sub-network performs the outer product operation on and transforms the resulting fused tensor into a low-dimensional space as: (2) where is a (M + 1)-order transformation tensor, along with a bias term , and d_h is the dimensionality of patient embedded representations. denotes the tensor outer product operation. is a form of decomposition of W, and R is the number of low-rank tensors obtained after decomposition. By decomposing W to make a separate linear transformation for , we can significantly reduce the computational complexity of the multi-omics integration. denotes the Hadamard product of M vectors: .

In this way, the module-shared patient feature encoder can be formalized as: (3) where f_enc represents the patient feature encoder, is the multi-omics data for the i-th patient, and is a concatenation operator. In detail, we first split x _i into M omics features, such as DNA methylation, miRNA, and mRNA features used here. Then, each omics data is fed into the corresponding feature extractor f^m(⋅). Finally, the resulting omics embeddings are integrated as a fusion representation z _i through the fusion sub-network.

Incomplete data imputation module

In real clinical scenarios, it is common to have access to only several or even a single type of omics data for some patients. The multi-omics data for these patients are incomplete, potentially leading to information loss and data bias, resulting in misleading diagnostic outcomes. To avoid risks arising from such incomplete data, we utilize available patient omics to impute their missing ones. To this end, we partition X into two parts to perform different training tasks. Specifically, N^cp samples with completely-paired multi-omics data, denoted as , are utilized to execute contrastive learning and masking-and-reconstruction (MAR) tasks. Meanwhile, N^inc samples with incomplete data are exclusively employed for the reconstruction tasks.

Firstly, we devise contrastive learning tasks to enhance the representational capacity of information learned by CancerSD for incomplete multi-omics data, providing generators with more informative representations. These processes begin by randomly generating two distinct masking strategies, which are then applied to . For each patient, we can garner two different but correlated augmented views, denoted as and , which together constitute the positive pair. Subsequently, and are fed into the patient feature encoder (see Eq 3), yielding and . These patient representations are further mapped into a projection space, where the contrastive loss is applied. In this way, we obtain higher-level representations and for the augmented patient views. When taking as the input, a representation set can be assembled, encompassing 2N^cp augmented representations. Finally, we formulate contrastive learning tasks within the projection space with the objective of maximizing the agreement among different augmented views of the same sample. Specifically, given a positive pair , the remaining 2(N^cp − 1) representations in S_u are treated as negative samples [85]. Thus, the loss of the pair can be formulated as: (4) where τ denotes a temperature parameter. represents the set without from S_u. Consequently, the instance-level contrastive loss can be further calculated as: (5)

Next, we proceed to construct M omics-specific generators based on feedforward networks to purposefully impute the missing omics data using latent features extracted from available patient omics as: (6) where is the generated omics data and g^m(⋅) denotes the generator designed for the m-th omics. The binary variable indicates whether the m-th omics of the i-th patient is missing or not.

To acquire the imputation ability of the generators, we define MAR tasks on patient features. On the one hand, we utilize N^cp samples with completely-paired multi-omics data to perform the MAR tasks. These tasks involve randomly masking out certain omics of some samples (setting all data within the masked omics to zero) and subsequently reconstructing these masked values. The loss can be calculated as: (7) where MSE(⋅, ⋅) denotes the mean square error loss function, and indicates whether the m-th omics is masked out or not for the i-th patient.

On the other hand, for N^inc samples with incomplete data, we only consider the reconstruction loss pertaining to the existing omics as: (8)

Finally, the generation loss can be calculated as: (9)

Cancer subtype diagnosis module

To alleviate adverse efforts posed by the absence of certain omics, CancerSD fuses both available and imputed omics data to make cancer subtype diagnosis and calculates the diagnosis loss as: (10) (11) where the representation z _i is obtained by feeding the multi-omics data into the patient feature encoder f_enc. In cases where all omics for a patient are available, we input them directly into the encoder; otherwise, we first impute the missing omics and then encode them. f_diag denotes the subtype diagnosis network, y_i is the subtype label of the i-th patient, and CE(⋅, ⋅) represents the cross entropy loss function. is the weight of subtype y_i when calculating the diagnosis loss, which is used to alleviate the problem of sample imbalance. N^tr is the number of samples in the training set, N^s is the number of subtypes, and is the number of samples of subtype y_i.

In a word, CancerSD_b is an end-to-end architecture involving two modules that are optimized simultaneously in one stage, and the total loss can be calculated based on the individual loss of each module as: (12) where λ₁, and λ₂ are trade-off parameters among three individual losses. In practice, we set both of them to 1 by default. It is worth noting that although we integrate the losses from each module into , each loss affects different sub-networks during the backpropagation process. For instance, updates f_enc solely and does not impact the other modules. optimizes both f_enc and the omics-specific generator g^m. Meanwhile, updates the parameters of f_enc as well as f_diag.

By optimizing CancerSD, the missing omics data can be reliably imputed from available ones. Meanwhile, CancerSD extracts essential and meaningful information from incomplete multi-omics data of samples. As a result, it can make a more accurate and flexible cancer subtype diagnosis.

Knowledge transfer module

Cancer subtype diagnosis is a typical few-sample scenario where well-annotated cancer samples are challenging to collect. To cope with scarce training samples, meta-learning strategies emerge as promising solutions, which enable the backbone model to learn and adapt to new tasks with limited data rapidly. Among them, MAML [86] stands out as a renowned optimization-based [87] meta-learning algorithm. Its exceptional performance, flexibility, and model-agnostic nature make it widely applicable across various tasks and domains. However, the direct application of meta-learning strategies potentially leads to negative transfer issues when significant differences exist in sample distributions across different datasets. In such cases, knowledge learned from external datasets may fail to assist the model in adapting to the target dataset and even mislead its optimization. To address this issue, we aim to align the representations of samples of the same subtype and push away that of samples of different subtypes at the distribution level. Inspired by MAML and Eq 4, we construct a meta learner and formulate a distribution-based category-level contrastive loss to facilitate the desired distribution alignment during knowledge transfer.

As illustrated in Fig 1c, given an external dataset and a target dataset (where and share the same label space ), the meta learner CancerSD_m aims to learn a better initialization ψ_ini for the backbone CancerSD_b parameterized by ψ. In detail, CancerSD_m first forms a set of sub-batches from the external dataset. Each sub-batch contains a support set and a query set , both of which are N-way K-shot (each subtype sample K patients). Then, CancerSD_m undergoes a bi-level optimization procedure with two nested loops: an inner loop for learning sub-batch-specific knowledge and an outer loop for improving the model generalization capability based on multiple sub-batches. The two loops operate on a batch at each iteration, which is composed of N^sub related sub-batches [88]. Meanwhile, to facilitate the distribution alignment, CancerSD_m uses a fine-tuning query set sampled from along with query sets from the current batch to calculate the category-level contrastive loss in the outer loop. In this step, is only involved in optimizing the encoder. Finally, we use to fine-tune the entire initialization ψ_ini learned by CancerSD_m and utilize the remaining data of the target dataset to evaluate CancerSD_b characterized by these further refined parameters.

Specifically, in the inner loop, CancerSD_m changes ψ_ini to sub-batch-specific for the t-th sub-batch by gradient descent on the support set as: (13) where α is the inner loop learning rate, represents the sub-batch-related training loss of the base learner (see Eq 12). In this process, CancerSD_m separately acquires knowledge from each sub-batch.

To further explore cross-sub-batch knowledge, CancerSD_m comprehensively considers all sub-batches within and calculates the loss using query sets and fine-tuning query set to update ψ_ini in the outer loop as: (14) where β is the outer loop learning rate. is a subset of , which represents the parameters in the patient feature encoder f_enc. In addition, represents the category-level contrastive loss, which can be formulated as: (15) (16) where KDE(⋅) denotes Kernel Density Estimation [89], which is used to construct sample distribution. and are subsets of samples with subtype l. dist(⋅, ⋅) is used to measure the distance between two distributions, and we employ Jensen-Shannon divergence in this context, which offers advantages over the Kullback-Leible divergence here due to its symmetry and boundedness properties. When dealing with multiple external datasets, we abstain from considering relationships among them. Instead, we designate the target dataset as the anchor and calculate the contrastive loss individually between and each . In brief, the category-level contrastive loss allows CancerSD_m to focus on extracting knowledge relevant to the target dataset from external datasets.

In summary, CancerSD_m inherits the merits of meta-learning. It leverages abundant samples available in external datasets to gain a better initialized CancerSD_b, reduces the dependence on the quantity of training samples, and rapidly adapts to cancer subtype diagnosis tasks on the target dataset with limited samples.

Experimental settings

To evaluate the effectiveness of CancerSD, we evaluated and compared its diagnostic performance for cancer subtyping in both standard supervised learning and few-sample learning scenarios.

On the one hand, we evaluated and compared various cancer subtype diagnostic methods under the standard supervised learning setting. Specifically, we first applied a random 80/20 split to each cancer dataset, where 80% of the samples were used for training and 20% for testing. To highlight the advantages of CancerSD, we then selected thirteen representative methods for comparison, covering wide-range popular and state-of-the-art approaches: (i) traditional machine learning, including k-Nearest Neighbor classifier (kNN) and Random Forest Classifier (RFC) [90]; (ii) Multi-omics Integration based methods, including AE-XGBoost [91], MOGONET [14], MOMA [15], MOFA+ [92], FactorCL [93], VICReg [94]; (iii) incomplete Multi-omics Integration based methods, including Subtype-GAN [95], scVAEIT [96], DCP [20], and APADC [21]. More detailed descriptions of these methods are provided in Section A in S2 Text. Among the comparison methods, kNN and RFC are trained with the direct concatenation of the preprocessed multi-omics data, while other methods explored effective integration of multi-omics data. It is worth noting that we included all comparative methods in the critical performance comparison experiments. However, considering the architecture or integration strategy similarities among these compared methods, we only deployed seven methods: KNN, RFC, AE-XGBoost, MOMA, MOGONET, DCP, and APADC in the subsequent experiments.

On the other hand, we designed few-sample learning scenarios to investigate the cross-dataset knowledge transfer capability of CancerSD. Taking knowledge transfer tasks on GC datasets as examples, we conducted extensive experiments on the TCGA-STAD and GSE62254 datasets. In these experiments, STAD serves as the external dataset from which we sample N-way K-shot [97] sub-batches to optimize the models. Each sub-batch consists of a support set and a query set , both and include K samples for each of the N subtypes. Meanwhile, GSE62254 is treated as the target dataset, which is split into a training set containing one N-way K-shot set for fine-tuning and a testing set for evaluation. Since GSE62254 only contains mRNA data for samples, we conduct experiments to transfer knowledge from mRNA data and from multi-omics data of STAD to GSE62254. For a more comprehensive evaluation, we also conducted aforementioned experiments on lung cancer datasets (including TCGA-LUAD, TCGA-LUSC, and CPTAC [79, 80]). We selected four competitive approaches for comparison, including MOMA [15]-PT, DCP [20]-PT, QSFormer [98], and DeepBDC [99]. Among them, MOMA-PT and DCP-PT follow a pretraining strategy, where they first undergo pretraining on the external dataset and subsequently fine-tune themselves using a limited amount of samples from the target dataset. QSFormer and DeepBDC are few-shot classification methods based on the meta-learning framework. Moreover, five variants of CancerSD are developed for a more comprehensive evaluation, including (i) CancerSD-PT replaces the meta-learning framework with a pretraining strategy; (ii) CancerSD-MOMA replaces the CancerSD backbone with MOMA; (iii) CancerSD-DCP replaces the CancerSD backbone with DCP; (iv) CancerSD-SIM utilizes representation similarity in the category-level contrastive loss; (v) CancerSD-w/oCLC ignores sample distribution differences among different datasets.

Each experiment randomly repeats ten times to take the average performance and standard deviations, where the diagnosis performance is measured in terms of Accuracy, AUROC, Precision, and average F1 Score weighted by the proportion of corresponding categories.