🧬 biology

Feature Dimensionality Outweighs Model Complexity in Breast Cancer Subtype Classification Using TCGA-BRCA Gene Expression Data

Using TCGA-BRCA gene expression data, this study demonstrates that in breast cancer subtype classification, the choice of feature selection and the use of simpler models like logistic regression are more critical for achieving balanced performance across all subtypes than increasing model complexity.

Original authors: Meena Al Hasani

Published 2026-05-08

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CC BY 4.0

Original authors: Meena Al Hasani

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine you are a detective trying to sort a massive pile of mixed-up puzzle pieces into five different boxes. Each box represents a different "flavor" of breast cancer (like Luminal A, Basal-like, etc.). The catch? You have a huge box of pieces (20,000+ genes), but you only have a small number of people to help you sort them (about 1,000 samples).

This paper is a report on how well different "sorting strategies" (machine learning models) work when faced with this tricky puzzle. The author, Meena Al Hasani, tested three different detectives to see who could sort the pieces most fairly and accurately.

The Three Detectives (The Models)

The Simple Organizer (Logistic Regression): This detective uses a straightforward, linear rulebook. It doesn't try to overthink things; it just looks for the clearest patterns and draws a straight line to separate the groups.
The Team of Experts (Random Forest): This detective is actually a whole committee of 500 decision-makers. They vote on where each piece goes. They are powerful and can spot complex, non-linear patterns, but they can get distracted by the loudest voices in the room.
The High-Tech Scanner (SVM): This detective uses a sophisticated, curved lens to find complex boundaries between groups. It's very sensitive and can find subtle connections, but it gets confused if there are too many pieces to look at at once.

The Trap: "Accuracy" vs. "Fairness"

The biggest problem in this puzzle is that the boxes aren't empty. One box (Luminal A) is huge, containing half the pieces. Another box (Normal-like) is tiny, with only a few pieces.

If you just count how many pieces you got right overall (Accuracy), the "Team of Experts" might look like a genius. Why? Because if they just guessed the big box for everything, they'd get 50% right instantly. They might ignore the tiny box entirely and still have a high score.

The author realized that Accuracy is a trickster. It hides the fact that the detective is failing the people in the small boxes.

Instead, the author used a "Fairness Score" (Macro F1). Imagine a judge who says, "I don't care how many pieces are in the big box. I want to see how well you sorted the tiny box, the medium box, and the big box equally." If you fail the tiny box, your score drops, no matter how well you did on the big one.

The Big Discovery

The author tested these detectives with different numbers of puzzle pieces (genes), ranging from just 50 pieces up to the full 20,000.

Here is what happened:

The Complex Detectors got confused: The "Team of Experts" (Random Forest) and the "High-Tech Scanner" (SVM) struggled when given all 20,000 pieces. The Scanner (SVM) actually got worse as the pile got bigger, like a person trying to read a book by staring at every single letter at once until they went blind. The Team of Experts did okay overall, but they kept ignoring the tiny boxes (minority subtypes).
The Simple Organizer won: The "Simple Organizer" (Logistic Regression) was the most consistent. It didn't get overwhelmed by the huge pile of data. Most importantly, it was the only one that treated the tiny boxes fairly. It didn't just guess the big box; it actually found the patterns in the small groups.

The "Goldilocks" Zone of Genes

The study also found that you don't need all the puzzle pieces to solve the mystery.

Using 50 pieces was too few; the detectives couldn't see the whole picture.
Using 20,000 pieces was too many; it created noise and confusion.
Using about 1,000 pieces (specifically the ones that varied the most) was the "Goldilocks" zone. It was just enough to get the job done without overwhelming the system.

The Takeaway

The paper concludes that in this specific medical puzzle:

Simplicity wins: A simple, linear model (Logistic Regression) was better than complex, fancy models because it didn't get lost in the noise of the massive data.
Don't trust the headline score: If you only look at "Accuracy," you might think a model is great when it's actually ignoring the rare, important cases. You need a "Fairness Score" (Macro F1) to see the truth.
Less is more: You don't need every single gene to classify cancer subtypes; a curated list of the most active genes works best.

In short, the author argues that when dealing with messy, high-stakes biological data, a steady, simple hand often does a better job than a complex, over-enthusiastic one, provided you measure success fairly.

Technical Summary: Feature Dimensionality Outweighs Model Complexity in Breast Cancer Subtype Classification

Problem Statement
Accurate classification of breast cancer molecular subtypes (Luminal A, Luminal B, HER2-enriched, Basal-like, and Normal-like) is critical for clinical decision-making. However, utilizing gene expression data (specifically TCGA-BRCA RNA-seq data) for this task presents a "small $n$ , large $p$ " challenge: the dataset contains 20,518 gene features but only 981 samples. This high dimensionality relative to sample size increases the risk of overfitting, particularly for complex machine learning models. Furthermore, the dataset exhibits significant class imbalance, with Luminal A comprising over half the samples and the Normal-like subtype representing a small minority. Traditional evaluation metrics like accuracy often obscure poor performance on these minority classes, leading to misleading conclusions about model utility.

Methodology
The study systematically evaluates the interaction between model complexity and feature dimensionality using three classifiers of increasing complexity:

Logistic Regression (LR): A linear model with L2 regularization.
Random Forest (RF): An ensemble method using 500 estimators.
Support Vector Machine (SVM): A non-linear model using an RBF kernel.

Experimental Design:

Dataset: 981 TCGA-BRCA samples with 20,518 gene expression features.
Feature Selection: A variance-based heuristic was applied. Genes were ranked by variance within the training fold, and the top $N$ genes were selected, where $N \in \{50, 75, 100, 1000, 20518\}$ . This selection was performed independently within each cross-validation fold to prevent data leakage.
Validation: Stratified 5-fold cross-validation was used to preserve subtype distribution.
Evaluation Metrics: While accuracy was reported, the Macro F1 score was designated as the primary metric to ensure equal weighting of all subtypes, including minority classes. Per-subtype F1 scores were also analyzed to identify specific failure modes.

Key Results

Model Performance: Logistic Regression consistently achieved the highest Macro F1 scores (ranging from 0.65 to 0.80), demonstrating the most balanced performance across all subtypes. Random Forest achieved comparable overall accuracy to LR but significantly lower Macro F1 scores (dropping to ~0.61–0.70), indicating a bias toward dominant classes (Luminal A) and poor performance on minority classes like BRCA Normal (F1 $\approx$ 0.21). SVM showed competitive performance at intermediate feature sizes (1,000 genes) but degraded significantly at full dimensionality (20,518 genes).
Feature Dimensionality: Performance for all models improved as the number of features increased from 50 to 1,000, suggesting that highly variable genes capture the essential subtype-discriminative signal. However, performance gains plateaued beyond 1,000 genes. Notably, SVM performance declined with higher dimensionality, confirming its sensitivity to large feature spaces in small-sample settings.
Subtype-Specific Behavior: BRCA Basal and Luminal A were consistently classified with high F1 scores across all models. In contrast, BRCA Normal and Luminal B showed greater variability and lower performance. Logistic Regression maintained the most consistent performance across these difficult subtypes.
Statistical Significance: Pairwise Wilcoxon signed-rank tests on Macro F1 scores did not reach statistical significance at the 0.05 threshold (e.g., LR vs. RF $p = 0.0625$ ). The authors attribute this to the limited statistical power of 5-fold cross-validation with only five paired observations, suggesting the observed trends are practically meaningful rather than formally significant.

Key Contributions

Re-evaluation of Model Complexity: The study challenges the assumption that complex models (RF, SVM) inherently outperform simpler models (LR) in high-dimensional biological data. It demonstrates that simpler, regularized linear models can provide more balanced and stable classification across imbalanced subtypes.
Metric Sensitivity: The paper highlights that accuracy is an insufficient metric for this domain, as it can mask the failure of models to classify minority subtypes. The use of Macro F1 and per-subtype analysis is shown to be essential for revealing these failure modes.
Feature Selection Impact: The work provides empirical evidence that variance-based feature selection is effective for dimensionality reduction, with 1,000 highly variable genes often sufficient to capture discriminative signal, thereby avoiding the instability associated with using the full gene set.

Significance and Claims
The paper claims that for breast cancer subtype classification using TCGA-BRCA data, feature dimensionality and evaluation strategy outweigh model complexity. Specifically:

Simplicity is Robust: Logistic Regression with L2 regularization trained on the top 1,000 variance-selected genes is identified as the most robust configuration, offering balanced performance and computational efficiency.
Caution with Complex Models: Random Forest is cautioned against as a primary classifier in this specific setting due to its tendency to ignore minority classes despite high overall accuracy.
Evaluation Rigor: The study emphasizes that robust evaluation strategies, including stratified cross-validation and Macro F1 scoring, are critical to avoid misleading conclusions, particularly when dealing with rare biological subtypes.

The authors maintain a modest tone, acknowledging that their findings are specific to the TCGA-BRCA dataset and that the lack of statistical significance in pairwise comparisons limits the ability to make definitive claims about superiority, though the practical trends are clear. They note that variance-based selection is a heuristic and does not guarantee biological interpretability, nor did they perform systematic hyperparameter tuning.