Module 8: Machine Learning for Biomarker Panels: PLS-DA, Random Forests & Overfitting Prevention

1. Why Single Biomarkers Fail in Complex Cancers

Due to profound tumor clonal heterogeneity, single biomarkers (like PSA in prostate cancer or CA-125 in ovarian cancer) suffer from unacceptable false-positive and false-negative rates in broad screening populations. Multiplexed biomarker panels (combining 5 to 10 complementary proteins and metabolites) capture orthogonal biological pathways, drastically improving diagnostic specificity and positive predictive value (PPV).

2. Tackling the Curse of Dimensionality ($p \gg n$)

When measuring $p = 10,000$ omics features across $n = 100$ patients, standard regression models suffer catastrophic overfitting—memorizing sample noise rather than learning genuine cancer pathology. Supervised machine learning requires rigorous dimensionality reduction and feature selection:

• Partial Least Squares Discriminant Analysis (PLS-DA): Rotates multidimensional variance into latent components that specifically maximize covariance with clinical class labels. Features are ranked by Variable Importance in Projection (VIP) scores; features with $\text{VIP} > 1.5$ represent primary discriminatory drivers.
• Random Forest & Boruta Feature Selection: Ensembles of decision trees compute Mean Decrease Accuracy (MDA) when features are permuted. The Boruta algorithm compares real feature importance against synthetic shuffled "shadow" features to select only statistically confirmed cancer biomarkers.
• Nested Cross-Validation: Hyperparameter tuning and feature selection must occur strictly inside an inner cross-validation loop ($k=5$), while diagnostic performance is scored on an entirely unseen outer test fold ($k=10$) to prevent data leakage.

# Machine Learning Biomarker Panel Selection in Python
import numpy as np
from sklearn.ensemble import RandomForestClassifier
from sklearn.model_selection import StratifiedKFold, cross_val_score
from sklearn.metrics import roc_auc_score

# Simulated cancer discovery feature matrix: 100 patients, 500 candidate markers
np.random.seed(42)
X = np.random.randn(100, 500)
# Inject true biological signal into top 5 features
y = np.array([0]*50 + [1]*50)
X[y == 1, 0:5] += 1.8

# Outer cross-validation to prevent leakage
cv_outer = StratifiedKFold(n_splits=5, shuffle=True, random_state=42)
rf = RandomForestClassifier(n_estimators=200, max_depth=4, random_state=42)

scores = cross_val_score(rf, X[:, 0:5], y, cv=cv_outer, scoring='roc_auc')
print(f"5-Marker Panel Mean Validation AUC: {scores.mean():.3f} +/- {scores.std():.3f}")

# Extract Gini Feature Importances
rf.fit(X[:, 0:5], y)
for i, imp in enumerate(rf.feature_importances_):
    print(f"  Biomarker Candidate {i+1} Feature Weight: {imp:.4f}")