Predicting Drug-Resistant Tuberculosis Treatment Outcomes: A Leakage-Controlled Evaluation of Topological Data Analysis Augmentation

Technical Summary: Predicting Drug-Resistant Tuberculosis Treatment Outcomes with Topological Data Analysis

Problem Statement
The study addresses the challenge of predicting treatment outcomes for drug-resistant tuberculosis (DR-TB), a condition with high morbidity and mortality where global treatment success rates remain below 0.6. While clinical prediction models using demographic, clinical, and radiological variables typically achieve Area Under the Receiver Operating Characteristic Curve (AUROC) values between 0.71 and 0.74, there is a need to determine if Topological Data Analysis (TDA) can provide incremental predictive value. The specific research question is whether topological features, which capture the geometric shape of the data distribution, add discriminative signal beyond a well-specified clinical baseline when evaluated under rigorous conditions that prevent data leakage.

Methodology
The authors utilized a cross-sectional dataset of 9,210 patients from the NIAID TB Portals programme. The methodology was designed to eliminate common pitfalls in TDA evaluation, specifically data leakage and weak baselines.

• Data Preprocessing: Longitudinal records were aggregated to a single row per patient using "worst-case" aggregation for binary, ordinal, and outcome variables. This resulted in a 99-feature clinical schema after feature engineering and selection.
• Leakage-Controlled Pipeline: A strict pipeline order was enforced where every topological step (dissimilarity matrix, UMAP embedding, Mapper cover, and local persistence computation) was fitted exclusively on the training partition. A sealed "lockbox" of 1,776 patients was held out and opened only once for final evaluation.
• Topological Representations:
  • Mapper Graph: Built on a UMAP lens over a Gower dissimilarity matrix (suitable for mixed-type clinical data). This generated four "D+" features per patient: topological risk score, topological success score, topological stability index, and topological Fiedler value.
  • Persistent Homology (PH): Local Vietoris–Rips persistent homology was computed on a 26-point neighborhood (the patient plus 25 nearest neighbors in the training PCA space) for each patient. This yielded degree-0 (connected components) and degree-1 (loops) summaries. Thirteen vectorization methods were ablated, with "Persistence Statistics" selected as the optimal representation.
• Evaluation Design: Five feature configurations were compared across four classifiers (Logistic Regression, Random Forest, SVM, XGBoost):
  1. Clinical only (Baseline).
  2. Clinical + Mapper D+.
  3. Clinical + PH.
  4. Clinical + Mapper + PH.
  5. Clinical + Mapper + Compressed PH.
     Discrimination was assessed using paired DeLong tests with Bonferroni correction (threshold 0.0125) on the lockbox.

Key Results

• Null Discriminative Result: No topologically augmented configuration meaningfully improved the lockbox AUROC over the clinical-only baseline under any classifier. The best performance was achieved by the baseline model using XGBoost (AUROC 0.7548).
• Bounded Confidence: Across 16 paired comparisons, the upper 95% confidence limit for the improvement in AUROC never exceeded +0.014. In four comparisons (three under Logistic Regression, one under XGBoost), the topological augmentation significantly reduced performance compared to the baseline.
• Marginal Exceptions: One comparison (SVM with Mapper augmentation) met the corrected significance threshold in favor of the augmented model, but the effect size was negligible (+0.0005 AUROC) with a near-zero confidence interval width, rendering it practically meaningless.
• Structural Insights: While topological features did not improve global rank discrimination, they revealed structural heterogeneity. Mapper nodes showed variation in adverse-outcome purity ranging from 5.9% to 30.5% across the largest nodes, suggesting that topological analysis can identify subgroups with distinct risk compositions that a single dominant-class label might obscure.
• Feature Attribution: SHAP analysis indicated that clinical features remained the dominant source of attribution (87–89% in single-augmentation models), with topological features providing a complementary, non-redundant signal (11–13% contribution) rather than replacing clinical predictors.

Significance and Claims
The paper claims a "bounded null result," arguing that the study successfully rules out a useful discrimination gain from TDA augmentation in this specific setting. The authors posit that the lack of improvement is likely due to the nature of the input data: the 99-feature clinical schema was already highly informative and curated, leaving little "noise" or unstructured geometric signal for topology to recover.

The primary contribution is methodological: the paper establishes a rigorous evaluation framework for TDA in clinical prediction that prevents data leakage and uses a well-tuned baseline. The authors conclude that TDA should be framed as a complementary analytical lens for revealing geometric structure and patient subgroups, rather than as a direct replacement for clinical predictors to boost AUROC. They suggest that TDA may yield greater predictive gains in settings with unstructured data (e.g., raw medical imaging) where geometric content has not yet been extracted via feature engineering.

The study explicitly states that its findings do not contradict previous TDA literature focused on subgroup discovery (e.g., identifying distinct survival profiles) but rather challenge the claim that topological features inherently improve the discrimination of tuned prediction models over strong clinical baselines.