Improved survival analysis by learning shared genomic information from pan-cancer data

TMO-Net: an explainable pretrained multi-omics model for multi-task learning in oncology

Cancer is a complex disease composing systemic alterations in multiple scales. In this study, we develop the Tumor Multi-Omics pre-trained Network (TMO-Net) that integrates multi-omics pan-cancer datasets for model pre-training, facilitating cross-omics interactions and enabling joint representation learning and incomplete omics inference. This model enhances multi-omics sample representation and empowers various downstream oncology tasks with incomplete multi-omics datasets. By employing interpretable learning, we characterize the contributions of distinct omics features to clinical outcomes. The TMO-Net model serves as a versatile framework for cross-modal multi-omics learning in oncology, paving the way for tumor omics-specific foundation models.

A deep profile of gene expression across 18 human cancers

Clinically and biologically valuable information may reside untapped in large cancer gene expression data sets. Deep unsupervised learning has the potential to extract this information with unprecedented efficacy but has thus far been hampered by a lack of biological interpretability and robustness. Here, we present DeepProfile, a comprehensive framework that addresses current challenges in applying unsupervised deep learning to gene expression profiles. We use DeepProfile to learn low-dimensional latent spaces for 18 human cancers from 50,211 transcriptomes. DeepProfile outperforms existing dimensionality reduction methods with respect to biological interpretability. Using DeepProfile interpretability methods, we show that genes that are universally important in defining the latent spaces across all cancer types control immune cell activation, while cancer type-specific genes and pathways define molecular disease subtypes. By linking DeepProfile latent variables to secondary tumor characteristics, we discover that tumor mutation burden is closely associated with the expression of cell cycle-related genes. DNA mismatch repair and MHC class II antigen presentation pathway expression, on the other hand, are consistently associated with patient survival. We validate these results through Kaplan-Meier analyses and nominate tumor-associated macrophages as an important source of survival-correlated MHC class II transcripts. Our results illustrate the power of unsupervised deep learning for discovery of novel cancer biology from existing gene expression data.

Pathogenomics for accurate diagnosis, treatment, prognosis of oncology: a cutting edge overview

The capability to gather heterogeneous data, alongside the increasing power of artificial intelligence to examine it, leading a revolution in harnessing multimodal data in the life sciences. However, most approaches are limited to unimodal data, leaving integrated approaches across modalities relatively underdeveloped in computational pathology. Pathogenomics, as an invasive method to integrate advanced molecular diagnostics from genomic data, morphological information from histopathological imaging, and codified clinical data enable the discovery of new multimodal cancer biomarkers to propel the field of precision oncology in the coming decade. In this perspective, we offer our opinions on synthesizing complementary modalities of data with emerging multimodal artificial intelligence methods in pathogenomics. It includes correlation between the pathological and genomic profile of cancer, fusion of histology, and genomics profile of cancer. We also present challenges, opportunities, and avenues for future work.

Learning Individual Survival Models from PanCancer Whole Transcriptome Data

PURPOSE

Personalized medicine attempts to predict survival time for each patient, based on their individual tumor molecular profile. We investigate whether our survival learner in combination with a dimension reduction method can produce useful survival estimates for a variety of patients with cancer.

EXPERIMENTAL DESIGN

This article provides a method that learns a model for predicting the survival time for individual patients with cancer from the PanCancer Atlas: given the (16,335 dimensional) gene expression profiles from 10,173 patients, each having one of 33 cancers, this method uses unsupervised nonnegative matrix factorization (NMF) to reexpress the gene expression data for each patient in terms of 100 learned NMF factors. It then feeds these 100 factors into the Multi-Task Logistic Regression (MTLR) learner to produce cancer-specific models for each of 20 cancers (with >50 uncensored instances); this produces "individual survival distributions" (ISD), which provide survival probabilities at each future time for each individual patient, which provides a patient's risk score and estimated survival time.

RESULTS

Our NMF-MTLR concordance indices outperformed the VAECox benchmark by 14.9% overall. We achieved optimal survival prediction using pan-cancer NMF in combination with cancer-specific MTLR models. We provide biological interpretation of the NMF model and clinical implications of ISDs for prognosis and therapeutic response prediction.

CONCLUSIONS

NMF-MTLR provides many benefits over other models: superior model discrimination, superior calibration, meaningful survival time estimates, and accurate probabilistic estimates of survival over time for each individual patient. We advocate for the adoption of these cancer survival models in clinical and research settings.

FGCNSurv: dually fused graph convolutional network for multi-omics survival prediction

MOTIVATION

Survival analysis is an important tool for modeling time-to-event data, e.g. to predict the survival time of patient after a cancer diagnosis or a certain treatment. While deep neural networks work well in standard prediction tasks, it is still unclear how to best utilize these deep models in survival analysis due to the difficulty of modeling right censored data, especially for multi-omics data. Although existing methods have shown the advantage of multi-omics integration in survival prediction, it remains challenging to extract complementary information from different omics and improve the prediction accuracy.

RESULTS

In this work, we propose a novel multi-omics deep survival prediction approach by dually fused graph convolutional network (GCN) named FGCNSurv. Our FGCNSurv is a complete generative model from multi-omics data to survival outcome of patients, including feature fusion by a factorized bilinear model, graph fusion of multiple graphs, higher-level feature extraction by GCN and survival prediction by a Cox proportional hazard model. The factorized bilinear model enables to capture cross-omics features and quantify complex relations from multi-omics data. By fusing single-omics features and the cross-omics features, and simultaneously fusing multiple graphs from different omics, GCN with the generated dually fused graph could capture higher-level features for computing the survival loss in the Cox-PH model. Comprehensive experimental results on real-world datasets with gene expression and microRNA expression data show that the proposed FGCNSurv method outperforms existing survival prediction methods, and imply its ability to extract complementary information for survival prediction from multi-omics data.

AVAILABILITY AND IMPLEMENTATION

The codes are freely available at https://github.com/LiminLi-xjtu/FGCNSurv.

SaBrcada: Survival Intervals Prediction for Breast Cancer Patients by Dimension Raising and Age Stratification

(1) Background: Breast cancer is the second leading cause of cancer death among women. The accurate prediction of survival intervals will help physicians make informed decisions about treatment strategies or the use of palliative care. (2) Methods: Gene expression is predictive and correlates to patient prognosis. To establish a reliable prediction tool, we collected a total of 1187 RNA-seq data points from breast cancer patients (median age 58 years) in Fragments Per Kilobase Million (FPKM) format from the TCGA database. Among them, we selected 144 patients with date of death information to establish the SaBrcada-AD dataset. We first normalized the SaBrcada-AD dataset to TPM to build the survival prediction model SaBrcada. After normalization and dimension raising, we used the differential gene expression data to test eight different deep learning architectures. Considering the effect of age on prognosis, we also performed a stratified random sampling test on all ages between the lower and upper quartiles of patient age, 48 and 69 years; (3) Results: Stratifying by age 61, the performance of SaBrcada built by GoogLeNet was improved to a highest accuracy of 0.798. We also built a free website tool to provide five predicted survival periods: within six months, six months to one year, one to three years, three to five years, or over five years, for clinician reference. (4) Conclusions: We built the prediction model, SaBrcada, and the website tool of the same name for breast cancer survival analysis. Through these models and tools, clinicians will be provided with survival interval information as a basis for formulating precision medicine.

Orchestrating information across tissues via a novel multitask GAT framework to improve quantitative gene regulation relation modeling for survival analysis

Survival analysis is critical to cancer prognosis estimation. High-throughput technologies facilitate the increase in the dimension of genic features, but the number of clinical samples in cohorts is relatively small due to various reasons, including difficulties in participant recruitment and high data-generation costs. Transcriptome is one of the most abundantly available OMIC (referring to the high-throughput data, including genomic, transcriptomic, proteomic and epigenomic) data types. This study introduced a multitask graph attention network (GAT) framework DQSurv for the survival analysis task. We first used a large dataset of healthy tissue samples to pretrain the GAT-based HealthModel for the quantitative measurement of the gene regulatory relations. The multitask survival analysis framework DQSurv used the idea of transfer learning to initiate the GAT model with the pretrained HealthModel and further fine-tuned this model using two tasks i.e. the main task of survival analysis and the auxiliary task of gene expression prediction. This refined GAT was denoted as DiseaseModel. We fused the original transcriptomic features with the difference vector between the latent features encoded by the HealthModel and DiseaseModel for the final task of survival analysis. The proposed DQSurv model stably outperformed the existing models for the survival analysis of 10 benchmark cancer types and an independent dataset. The ablation study also supported the necessity of the main modules. We released the codes and the pretrained HealthModel to facilitate the feature encodings and survival analysis of transcriptome-based future studies, especially on small datasets. The model and the code are available at http://www.healthinformaticslab.org/supp/.

GAN-based data augmentation for transcriptomics: survey and comparative assessment

MOTIVATION

Transcriptomics data are becoming more accessible due to high-throughput and less costly sequencing methods. However, data scarcity prevents exploiting deep learning models' full predictive power for phenotypes prediction. Artificially enhancing the training sets, namely data augmentation, is suggested as a regularization strategy. Data augmentation corresponds to label-invariant transformations of the training set (e.g. geometric transformations on images and syntax parsing on text data). Such transformations are, unfortunately, unknown in the transcriptomic field. Therefore, deep generative models such as generative adversarial networks (GANs) have been proposed to generate additional samples. In this article, we analyze GAN-based data augmentation strategies with respect to performance indicators and the classification of cancer phenotypes.

RESULTS

This work highlights a significant boost in binary and multiclass classification performances due to augmentation strategies. Without augmentation, training a classifier on only 50 RNA-seq samples yields an accuracy of, respectively, 94% and 70% for binary and tissue classification. In comparison, we achieved 98% and 94% of accuracy when adding 1000 augmented samples. Richer architectures and more expensive training of the GAN return better augmentation performances and generated data quality overall. Further analysis of the generated data shows that several performance indicators are needed to assess its quality correctly.

AVAILABILITY AND IMPLEMENTATION

All data used for this research are publicly available and comes from The Cancer Genome Atlas. Reproducible code is available on the GitLab repository: https://forge.ibisc.univ-evry.fr/alacan/GANs-for-transcriptomics.

Cancer survival prediction by learning comprehensive deep feature representation for multiple types of genetic data

BACKGROUND

Cancer is one of the leading death causes around the world. Accurate prediction of its survival time is significant, which can help clinicians make appropriate therapeutic schemes. Cancer data can be characterized by varied molecular features, clinical behaviors and morphological appearances. However, the cancer heterogeneity problem usually makes patient samples with different risks (i.e., short and long survival time) inseparable, thereby causing unsatisfactory prediction results. Clinical studies have shown that genetic data tends to contain more molecular biomarkers associated with cancer, and hence integrating multi-type genetic data may be a feasible way to deal with cancer heterogeneity. Although multi-type gene data have been used in the existing work, how to learn more effective features for cancer survival prediction has not been well studied.

RESULTS

To this end, we propose a deep learning approach to reduce the negative impact of cancer heterogeneity and improve the cancer survival prediction effect. It represents each type of genetic data as the shared and specific features, which can capture the consensus and complementary information among all types of data. We collect mRNA expression, DNA methylation and microRNA expression data for four cancers to conduct experiments.

CONCLUSIONS

Experimental results demonstrate that our approach substantially outperforms established integrative methods and is effective for cancer survival prediction.

AVAILABILITY AND IMPLEMENTATION

https://github.com/githyr/ComprehensiveSurvival .

Consensus clustering methodology to improve molecular stratification of non-small cell lung cancer

Recent advances in machine learning research, combined with the reduced sequencing costs enabled by modern next-generation sequencing, paved the way to the implementation of precision medicine through routine multi-omics molecular profiling of tumours. Thus, there is an emerging need of reliable models exploiting such data to retrieve clinically useful information. Here, we introduce an original consensus clustering approach, overcoming the intrinsic instability of common clustering methods based on molecular data. This approach is applied to the case of non-small cell lung cancer (NSCLC), integrating data of an ongoing clinical study (PROMOLE) with those made available by The Cancer Genome Atlas, to define a molecular-based stratification of the patients beyond, but still preserving, histological subtyping. The resulting subgroups are biologically characterized by well-defined mutational and gene-expression profiles and are significantly related to disease-free survival (DFS). Interestingly, it was observed that (1) cluster B, characterized by a short DFS, is enriched in KEAP1 and SKP2 mutations, that makes it an ideal candidate for further studies with inhibitors, and (2) over- and under-representation of inflammation and immune systems pathways in squamous-cell carcinomas subgroups could be potentially exploited to stratify patients treated with immunotherapy.

Joint learning sample similarity and correlation representation for cancer survival prediction

BACKGROUND

As a highly aggressive disease, cancer has been becoming the leading death cause around the world. Accurate prediction of the survival expectancy for cancer patients is significant, which can help clinicians make appropriate therapeutic schemes. With the high-throughput sequencing technology becoming more and more cost-effective, integrating multi-type genome-wide data has been a promising method in cancer survival prediction. Based on these genomic data, some data-integration methods for cancer survival prediction have been proposed. However, existing methods fail to simultaneously utilize feature information and structure information of multi-type genome-wide data.

RESULTS

We propose a Multi-type Data Joint Learning (MDJL) approach based on multi-type genome-wide data, which comprehensively exploits feature information and structure information. Specifically, MDJL exploits correlation representations between any two data types by cross-correlation calculation for learning discriminant features. Moreover, based on the learned multiple correlation representations, MDJL constructs sample similarity matrices for capturing global and local structures across different data types. With the learned discriminant representation matrix and fused similarity matrix, MDJL constructs graph convolutional network with Cox loss for survival prediction.

CONCLUSIONS

Experimental results demonstrate that our approach substantially outperforms established integrative methods and is effective for cancer survival prediction.

A systematic review on machine learning and deep learning techniques in cancer survival prediction

Cancer is a disease which is characterised by the unusual and uncontrollable growth of body cells. This usually happens asymptomatically and gets spread to other parts of the body. The major problem in treating cancer is that its progress is not monitored once it is diagnosed. The progress or the prognosis can be done through survival analysis. The survival analysis is the branch of statistics that deals in predicting the time of event of occurrence. In the case of cancer prognosis the event is the survival time of the patient from the onset of the disease or it can be the recurrence of the disease after undergoing a treatment. This study aims to bring out the machine learning and deep learning models involved in providing the prognosis to the cancer patients.

A convolutional neural network model for survival prediction based on prognosis-related cascaded Wx feature selection

Great advances in deep learning have provided effective solutions for prediction tasks in the biomedical field. However, accurate prognosis prediction using cancer genomics data remains challenging due to the severe overfitting problem caused by curse of dimensionality inherent to high-throughput sequencing data. Moreover, there are unique challenges to perform survival analysis, arising from the difficulty in utilizing censored samples whose events of interest are not observed. Convolutional neural network (CNN) models provide us the opportunity to extract meaningful hierarchical features to characterize cancer subtype and prognosis outcomes. On the other hand, feature selection can mitigate overfitting and reduce subsequent model training computation burden by screening out significant genes from redundant genes. To accomplish model simplification, we developed a concise and efficient survival analysis model, named CNN-Cox model, which combines a special CNN framework with prognosis-related feature selection cascaded Wx, with the advantage of less computation demand utilizing light training parameters. Experiment results show that CNN-Cox model achieved consistent higher C-index values and better survival prediction performance across seven cancer type datasets in The Cancer Genome Atlas cohort, including bladder carcinoma, head and neck squamous cell carcinoma, kidney renal cell carcinoma, brain low-grade glioma, lung adenocarcinoma (LUAD), lung squamous cell carcinoma, and skin cutaneous melanoma, compared with the existing state-of-the-art survival analysis methods. As an illustration of model interpretation, we examined potential prognostic gene signatures of LUAD dataset using the proposed CNN-Cox model. We conducted protein-protein interaction network analysis to identify potential prognostic genes and further analyzed the biological function of 13 hub genes, including ANLN, RACGAP1, KIF4A, KIF20A, KIF14, ASPM, CDK1, SPC25, NCAPG, MKI67, HJURP, EXO1, HMMR, whose high expression is significantly associated with poor survival of LUAD patients. These findings confirmed that CNN-Cox model is effective in extracting not only prognosis factors but also biologically meaningful gene features. The codes are available at the GitHub website: https://github.com/wangwangCCChen/CNN-Cox .

Interpretable generative deep learning: an illustration with single cell gene expression data

Deep generative models can learn the underlying structure, such as pathways or gene programs, from omics data. We provide an introduction as well as an overview of such techniques, specifically illustrating their use with single-cell gene expression data. For example, the low dimensional latent representations offered by various approaches, such as variational auto-encoders, are useful to get a better understanding of the relations between observed gene expressions and experimental factors or phenotypes. Furthermore, by providing a generative model for the latent and observed variables, deep generative models can generate synthetic observations, which allow us to assess the uncertainty in the learned representations. While deep generative models are useful to learn the structure of high-dimensional omics data by efficiently capturing non-linear dependencies between genes, they are sometimes difficult to interpret due to their neural network building blocks. More precisely, to understand the relationship between learned latent variables and observed variables, e.g., gene transcript abundances and external phenotypes, is difficult. Therefore, we also illustrate current approaches that allow us to infer the relationship between learned latent variables and observed variables as well as external phenotypes. Thereby, we render deep learning approaches more interpretable. In an application with single-cell gene expression data, we demonstrate the utility of the discussed methods.

Assessment of deep learning and transfer learning for cancer prediction based on gene expression data

BACKGROUND

Machine learning is now a standard tool for cancer prediction based on gene expression data. However, deep learning is still new for this task, and there is no clear consensus about its performance and utility. Few experimental works have evaluated deep neural networks and compared them with state-of-the-art machine learning. Moreover, their conclusions are not consistent.

RESULTS

We extensively evaluate the deep learning approach on 22 cancer prediction tasks based on gene expression data. We measure the impact of the main hyper-parameters and compare the performances of neural networks with the state-of-the-art. We also investigate the effectiveness of several transfer learning schemes in different experimental setups.

CONCLUSION

Based on our experimentations, we provide several recommendations to optimize the construction and training of a neural network model. We show that neural networks outperform the state-of-the-art methods only for very large training set size. For a small training set, we show that transfer learning is possible and may strongly improve the model performance in some cases.

A Novel Attention-Mechanism Based Cox Survival Model by Exploiting Pan-Cancer Empirical Genomic Information

Cancer prognosis is an essential goal for early diagnosis, biomarker selection, and medical therapy. In the past decade, deep learning has successfully solved a variety of biomedical problems. However, due to the high dimensional limitation of human cancer transcriptome data and the small number of training samples, there is still no mature deep learning-based survival analysis model that can completely solve problems in the training process like overfitting and accurate prognosis. Given these problems, we introduced a novel framework called SAVAE-Cox for survival analysis of high-dimensional transcriptome data. This model adopts a novel attention mechanism and takes full advantage of the adversarial transfer learning strategy. We trained the model on 16 types of TCGA cancer RNA-seq data sets. Experiments show that our module outperformed state-of-the-art survival analysis models such as the Cox proportional hazard model (Cox-ph), Cox-lasso, Cox-ridge, Cox-nnet, and VAECox on the concordance index. In addition, we carry out some feature analysis experiments. Based on the experimental results, we concluded that our model is helpful for revealing cancer-related genes and biological functions.

Transfer learning for non-image data in clinical research: A scoping review

BACKGROUND

Transfer learning is a form of machine learning where a pre-trained model trained on a specific task is reused as a starting point and tailored to another task in a different dataset. While transfer learning has garnered considerable attention in medical image analysis, its use for clinical non-image data is not well studied. Therefore, the objective of this scoping review was to explore the use of transfer learning for non-image data in the clinical literature.

METHODS AND FINDINGS

We systematically searched medical databases (PubMed, EMBASE, CINAHL) for peer-reviewed clinical studies that used transfer learning on human non-image data. We included 83 studies in the review. More than half of the studies (63%) were published within 12 months of the search. Transfer learning was most often applied to time series data (61%), followed by tabular data (18%), audio (12%) and text (8%). Thirty-three (40%) studies applied an image-based model to non-image data after transforming data into images (e.g. spectrograms). Twenty-nine (35%) studies did not have any authors with a health-related affiliation. Many studies used publicly available datasets (66%) and models (49%), but fewer shared their code (27%).

CONCLUSIONS

In this scoping review, we have described current trends in the use of transfer learning for non-image data in the clinical literature. We found that the use of transfer learning has grown rapidly within the last few years. We have identified studies and demonstrated the potential of transfer learning in clinical research in a wide range of medical specialties. More interdisciplinary collaborations and the wider adaption of reproducible research principles are needed to increase the impact of transfer learning in clinical research.

Analysis of cancer omics data: a selective review of statistical techniques

Cancer is an omics disease. The development in high-throughput profiling has fundamentally changed cancer research and clinical practice. Compared with clinical, demographic and environmental data, the analysis of omics data-which has higher dimensionality, weaker signals and more complex distributional properties-is much more challenging. Developments in the literature are often 'scattered', with individual studies focused on one or a few closely related methods. The goal of this review is to assist cancer researchers with limited statistical expertise in establishing the 'overall framework' of cancer omics data analysis. To facilitate understanding, we mainly focus on intuition, concepts and key steps, and refer readers to the original publications for mathematical details. This review broadly covers unsupervised and supervised analysis, as well as individual-gene-based, gene-set-based and gene-network-based analysis. We also briefly discuss 'special topics' including interaction analysis, multi-datasets analysis and multi-omics analysis.

A gradient tree boosting and network propagation derived pan-cancer survival network of the tumor microenvironment

Predicting cancer survival from molecular data is an important aspect of biomedical research because it allows quantifying patient risks and thus individualizing therapy. We introduce XGBoost tree ensemble learning to predict survival from transcriptome data of 8,024 patients from 25 different cancer types and show highly competitive performance with state-of-the-art methods. To further improve plausibility of the machine learning approach we conducted two additional steps. In the first step, we applied pan-cancer training and showed that it substantially improves prognosis compared with cancer subtype-specific training. In the second step, we applied network propagation and inferred a pan-cancer survival network consisting of 103 genes. This network highlights cross-cohort features and is predictive for the tumor microenvironment and immune status of the patients. Our work demonstrates that pan-cancer learning combined with network propagation generalizes over multiple cancer types and identifies biologically plausible features that can serve as biomarkers for monitoring cancer survival.

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Highly performing cancer survival prediction with XGBoost

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Pan-cancer training outperforms single-cohort training

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Combined approach consisting of machine learning and network propagation

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Tumor microenvironment is most strongly involved in cancer survival prediction

Exploring Pathway-Based Group Lasso for Cancer Survival Analysis: A Special Case of Multi-Task Learning

Motivation: The Cox proportional hazard models are widely used in the study of cancer survival. However, these models often meet challenges such as the large number of features and small sample sizes of cancer data sets. While this issue can be partially solved by applying regularization techniques such as lasso, the models still suffer from unsatisfactory predictive power and low stability.

Methods: Here, we investigated two methods to improve survival models. Firstly, we leveraged the biological knowledge that groups of genes act together in pathways and regularized both at the group and gene level using latent group lasso penalty term. Secondly, we designed and applied a multi-task learning penalty that allowed us leveraging the relationship between survival models for different cancers.

Results: We observed modest improvements over the simple lasso model with the inclusion of latent group lasso penalty for six of the 16 cancer types tested. The addition of a multi-task penalty, which penalized coefficients in pairs of cancers from diverging too greatly, significantly improved accuracy for a single cancer, lung squamous cell carcinoma, while having minimal effect on other cancer types.

Conclusion: While the use of pathway information and multi-tasking shows some promise, these methods do not provide a substantial improvement when compared with standard methods.

A disease network-based deep learning approach for characterizing melanoma

Multiple types of genomic variations are present in cutaneous melanoma and some of the genomic features may have an impact on the prognosis of the disease. The access to genomics data via public repositories such as The Cancer Genome Atlas (TCGA) allows for a better understanding of melanoma at the molecular level, therefore making characterization of substantial heterogeneity in melanoma patients possible. Here, we proposed an approach that integrates genomics data, a disease network, and a deep learning model to classify melanoma patients for prognosis, assess the impact of genomic features on the classification and provide interpretation to the impactful features. We integrated genomics data into a melanoma network and applied an autoencoder model to identify subgroups in TCGA melanoma patients. The model utilizes communities identified in the network to effectively reduce the dimensionality of genomics data into a patient score profile. Based on the score profile, we identified three patient subtypes that show different survival times. Furthermore, we quantified and ranked the impact of genomic features on the patient score profile using a machine-learning technique. Follow-up analysis of the top-ranking features provided us with the biological interpretation of them at both pathway and molecular levels, such as their mutation and interactome profiles in melanoma and their involvement in pathways associated with signaling transduction, immune system and cell cycle. Taken together, we demonstrated the ability of the approach to identify disease subgroups using a deep learning model that captures the most relevant information of genomics data in the melanoma network.

Stratified neural networks in a time-to-event setting

Deep neural networks are frequently employed to predict survival conditional on omics-type biomarkers, e.g., by employing the partial likelihood of Cox proportional hazards model as loss function. Due to the generally limited number of observations in clinical studies, combining different data sets has been proposed to improve learning of network parameters. However, if baseline hazards differ between the studies, the assumptions of Cox proportional hazards model are violated. Based on high dimensional transcriptome profiles from different tumor entities, we demonstrate how using a stratified partial likelihood as loss function allows for accounting for the different baseline hazards in a deep learning framework. Additionally, we compare the partial likelihood with the ranking loss, which is frequently employed as loss function in machine learning approaches due to its seemingly simplicity. Using RNA-seq data from the Cancer Genome Atlas (TCGA) we show that use of stratified loss functions leads to an overall better discriminatory power and lower prediction error compared to their non-stratified counterparts. We investigate which genes are identified to have the greatest marginal impact on prediction of survival when using different loss functions. We find that while similar genes are identified, in particular known prognostic genes receive higher importance from stratified loss functions. Taken together, pooling data from different sources for improved parameter learning of deep neural networks benefits largely from employing stratified loss functions that consider potentially varying baseline hazards. For easy application, we provide PyTorch code for stratified loss functions and an explanatory Jupyter notebook in a GitHub repository.