Deep Semi-Supervised Survival Analysis for Predicting Cancer Prognosis

The Cox Proportional Hazards (PH) model is widely used in survival analysis. Recently, artificial neural network (ANN)-based Cox-PH models have been developed. However, training these Cox models with high-dimensional features typically requires a substantial number of labeled samples containing information about time-to-event. The limited availability of labeled data for training often constrains the performance of ANN-based Cox models. To address this issue, we employed a deep semi-supervised learning (DSSL) approach to develop single- and multi-modal ANN-based Cox models based on the Mean Teacher (MT) framework, which utilizes both labeled and unlabeled data for training. We applied our model, named Cox-MT, to predict the prognosis of several types of cancer using data from The Cancer Genome Atlas (TCGA). Our single-modal Cox-MT models, utilizing TCGA RNA-seq data or whole slide images, significantly outperformed the existing ANN-based Cox model, Cox-nnet, using the same data set across four types of cancer considered. As the number of unlabeled samples increased, the performance of Cox-MT significantly improved with a given set of labeled data. Furthermore, our multi-modal Cox-MT model demonstrated considerably better performance than the single-modal model. In summary, the Cox-MT model effectively leverages both labeled and unlabeled data to significantly enhance prediction accuracy compared to existing ANN-based Cox models trained solely on labeled data.

💡 Research Summary

This paper introduces Cox‑MT, a deep semi‑supervised learning (DSSL) framework for survival analysis that leverages both labeled (time‑to‑event and censoring information) and unlabeled data (gene expression or histopathology images without outcome labels). The core of Cox‑MT is the Mean Teacher (MT) paradigm: a “student” network is trained on labeled data using the negative partial likelihood loss (L_s) while simultaneously being regularized to produce predictions consistent with a “teacher” network on unlabeled data. The teacher’s parameters are an exponential moving average (EMA) of the student’s parameters, and the consistency loss (L_u) is weighted by a hyperparameter w, yielding a total loss L = L_s + w·L_u. This design enables the model to extract useful structure from the abundant unlabeled samples, improving generalization even when labeled data are scarce.

Experiments were conducted on four cancer types from The Cancer Genome Atlas (TCGA): breast invasive carcinoma (BRCA), lung adenocarcinoma (LUAD), lung squamous cell carcinoma (LUSC), and uterine corpus endometrial carcinoma (UCEC). For each cancer, the 4,000 most variable genes were selected from RNA‑seq data, and a multilayer perceptron (MLP) with two hidden layers (first layer 1,000–1,500 nodes, second layer 100–2,000 nodes) served as the backbone. The baseline model, Cox‑nnet, used a single hidden layer with 64 nodes. Across 20 random train‑test splits, Cox‑MT consistently outperformed Cox‑nnet: average C‑indices increased by 0.09–0.18 and Integrated Brier Scores (IBS) decreased by 0.038–0.082 for all four cancers. Notably, even without any external unlabeled data, Cox‑MT benefits from censored samples because its loss incorporates both uncensored (partial likelihood) and censored contributions, whereas Cox‑nnet relies solely on uncensored data.

To assess the impact of unlabeled data, the authors added breast cancer RNA‑seq samples from GEO (GSE96058) to the TCGA BRCA set, incrementally increasing the unlabeled pool from 1,000 to 3,409 samples. Performance improved monotonically: C‑index rose from 0.81 (no extra data) to 0.90 (3,409 extra samples), and IBS fell from 0.087 to 0.061. This demonstrates that the MT framework effectively extracts latent structure from large, unlabeled cohorts, yielding a more robust risk estimator.

The study also explored multimodal integration by combining RNA‑seq features with whole‑slide image (WSI) features. Gene expression embeddings were generated using DINOv2, while WSI patches were processed by a convolutional encoder; both modalities were projected to 64‑dimensional vectors and fused via a Transformer‑based cross‑attention module. The multimodal Cox‑MT achieved a C‑index of 0.83 and IBS of 0.079, surpassing multimodal Cox‑nnet (C‑index 0.80, IBS 0.091) and the single‑modal Cox‑MT variants (RNA‑seq only: C‑index 0.81, IBS 0.087; WSI only: C‑index 0.66, IBS 0.151). The cross‑attention mechanism proved effective at leveraging complementary information from molecular and histopathological data.

A thorough ablation study examined sensitivity to key hyperparameters: EMA decay α (optimal 0.9–0.999), consistency weight w (optimal 0.1–3), dropout rates (≤0.4 for both student and teacher), Gaussian noise σ (0–0.1), and learning rate (0.001–0.005). Results indicated that Cox‑MT is relatively robust to these settings. For image augmentation, color jitter (brightness/contrast/saturation ≈0.4) outperformed random rotations (10°–30°), suggesting that preserving spatial structure while varying color is more beneficial for histopathology feature learning.

In discussion, the authors argue that semi‑supervised learning mitigates the fundamental bottleneck in survival analysis—limited availability of fully labeled clinical outcomes—by exploiting the abundant censored and unlabeled data that are routinely collected in biomedical repositories. The MT‑based loss formulation allows censored cases to contribute meaningfully, and the addition of external unlabeled cohorts further refines the risk model. They also highlight the generality of Cox‑MT: the framework can be transferred to other domains where time‑to‑event data are sparse, such as education or finance.

Overall, the paper provides a compelling demonstration that deep semi‑supervised learning, instantiated via the Mean Teacher paradigm, can substantially boost the predictive performance of Cox proportional hazards models across single‑ and multimodal cancer datasets. The methodological contributions—integrating consistency regularization with partial likelihood, employing cross‑attention for multimodal fusion, and extensive hyperparameter robustness analysis—offer a solid foundation for future research aiming to harness large-scale unlabeled biomedical data for survival prediction.