Multimodality Stacking with Blockwise missing values and application to the PIONeeR biomarkers study for prediction of resistance to immunotherapy

Technical Summary: Multimodality Stacking with Blockwise Missing Values (MSB)

Problem Statement
The paper addresses three concurrent challenges in clinical oncology survival analysis: high dimensionality ($n \sim p$ or $n \ll p$), substantial proportions of missing data, and high multicollinearity within data sources. Specifically, the authors focus on blockwise missingness, a structural issue where entire data modalities (sources) are unavailable for specific patient subsets due to heterogeneous collection protocols across multi-center studies. Standard approaches often rely on listwise deletion (excluding patients with incomplete data), which reduces sample size and introduces systematic bias, or standard imputation techniques that lose fidelity as dimensionality increases. Existing multimodal learning methods often treat tabular data on a per-feature basis rather than as unified modalities, or they are deep learning models requiring sample sizes larger than those available in typical clinical cohorts.

Methodology: The MSB Framework
The authors propose Multimodality Stacking with Blockwise missing values (MSB), a late-fusion meta-learning framework designed to handle these constraints without requiring complete data across all modalities.

1. Architecture: MSB decouples modality-specific learning from global aggregation.

   • Base Learners: For each of the $S$ data sources (modalities), three independent models are trained: a penalized Cox model (CoxNet), a Random Survival Forest (RSF), and a Component-wise Gradient Boosting model (CWXGB).
   • Handling Missingness: The framework explicitly accounts for blockwise missingness. If a source is missing for a patient, the corresponding base learner for that source is not applied.
   • Meta-Learner: The outputs (risk scores) from the base learners are aggregated by a meta-learner. To prevent overfitting, the meta-learner is trained on out-of-fold cross-validated predictions from the base learners.
   • Missingness Indicators: The rate of missingness per block is added as a feature to the meta-learner to control for potential bias, though the study investigates whether the model learns from these patterns or the biomarker values themselves.

2. Imputation Strategies: The paper evaluates three variations of MSB:

   • MSB$_{imp}$: Imputes raw data before splitting into modalities using k-Nearest Neighbors (kNN).
   • MSB: Performs imputation on the aggregated survival risk scores (lower-dimensional space) before the stacking step.
   • MSB$_{MIA}$: Uses "Missing Incorporated in Attributes" (MIA) directly within tree-based meta-learners (specifically RSF), treating missingness as a distinct category without imputation.

3. Validation: The framework was validated using 5-fold cross-validation (repeated 3 times) on the PIONeeR dataset. Performance was measured using the C-index (discrimination) and Integrated Brier Score (iBS) for calibration, with statistical significance assessed via paired Wilcoxon signed-rank tests corrected for False Discovery Rate (FDR).

Key Results
The study utilized the PIONeeR dataset ($n=443$ patients, 378 biomarkers across 8 heterogeneous sources) to predict Progression-Free Survival (PFS) in advanced non-small cell lung cancer (NSCLC) patients receiving immunotherapy.

• Predictive Performance: MSB consistently outperformed baseline algorithms trained on the same data (with kNN imputation).
  • Linear Models: MSB-CoxNet showed a 15.9% increase in C-index (from 0.572 to 0.663, $p < 0.001$).
  • Random Forests: MSB-RSF showed a 5.4% increase (from 0.647 to 0.682, $p = 0.002$).
  • Gradient Boosting: MSB-CWXGB showed a 2.1% increase (from 0.678 to 0.692, $p = 0.030$).
• Generalization: A critical finding was the reduction in the generalization gap (the difference between training and test performance). For linear models, the gap decreased from 0.380 (baseline) to 0.055 (MSB), indicating MSB acts as an effective regularizer against overfitting.
• Modality Importance: Permutation importance analysis identified routine clinical features (Source A), medical biology/blood markers (Source B), and PD-L1 expression (Source E) as the primary predictive drivers.
• Missingness Bias: The missing block indicators showed negligible importance. This suggests the model learns from the actual biomarker values rather than data availability patterns, alleviating concerns that the model is merely distinguishing between patients from different clinical centers (e.g., APHM vs. others) based on missing data.

Significance and Claims
The authors claim that MSB provides a statistically validated framework for multimodal survival prediction in the presence of blockwise missingness. Its primary significance lies in:

1. Handling Structural Sparsity: It enables systematic biomarker evaluation without requiring complete data across all modalities, avoiding the sample size reduction associated with listwise deletion.
2. Robustness in Small Cohorts: By decomposing the high-dimensional feature space into modality-specific sub-problems and aggregating risk scores, MSB mitigates the "curse of dimensionality" and overfitting, making it suitable for clinical cohorts where $n \ll p$.
3. Practical Applicability: The framework offers a tool for predictive modeling in multi-center studies where data availability varies by site or protocol.

Limitations and Scope
The paper maintains a modest stance regarding its claims:

• Lack of External Validation: All results are derived from a single cohort (PIONeeR, 17 French centers). The authors explicitly state that MSB should be considered a methodological framework for biomarker research pending external validation in independent international cohorts.
• Endpoint Specificity: The study focused on Progression-Free Survival (PFS) and did not extend to competing risks or cure fraction models, though they note these as potential future directions.
• Imputation Strategy: While kNN imputation was used for its computational efficiency and stability, the authors acknowledge that more complex imputation strategies might exist but were not pursued due to the minimal performance differences observed between MSB variants ($\Delta$C-index < 0.01).

The implementation of the MSB framework is made available under an Inria license.