What 569 Tumor Data Reveal About Detecting Breast Cancer

Photo by National Cancer Institute on Unsplash

I analyzed the Breast Cancer dataset. Two measurements predicted malignancy with 94% accuracy.

Breast cancer is the most common cancer among women worldwide. Early detection dramatically improves survival rates but what actually distinguishes a malignant tumor from a benign one?

The dataset contains measurements from 569 tumor samples (212 malignant and 357 benign). What I found was striking: among 30 different measurements, a handful of features do almost all the predictive work. And some features that sound important? Completely useless.

Full Report:

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The Two Features That Matter Most

If you could only measure two things about a tumor, these would be your best bets:

Concave Points (correlation with malignancy: r = 0.78) Concavity (correlation with malignancy: r = 0.70)

M = Malignant, B = Benign

Both describe the same thing: how irregular the tumor’s surface is. Malignant tumors have surfaces with more indentations and irregularities. Benign tumors tend to be smoother. Comparison:

• Malignant tumors have approximately 3.5x higher concavity_mean than benign tumors
• Malignant tumors have approximately 3.4x higher concave points_mean than benign tumors
• Both features are strong predictors of malignancy and could be valuable for diagnostic models

Size Matters — A Lot

The second major pattern: malignant tumors are significantly larger.

M = Malignant, B = Benign

Malignant tumors are more than twice the size of benign ones on average.

This led to a practical finding: tumors with radius ≥ 15.1 AND area ≥ 705 are malignant 94% of the time.

M = Malignant, B = Benign

Of 168 tumors meeting both thresholds, 158 were malignant. That’s a simple rule with high predictive power.

The Best Single Predictor

If I had to pick one measurement to distinguish tumor types, it would be area_worst — the largest area measurement across all cells in the sample.

Statistical separation (Cohen’s d): 2.29

For context, a Cohen’s d above 0.8 is considered “large.” At 2.29, we’re seeing near-complete separation between groups:

• Malignant average: 1,422
• Benign average: 559

The “worst” measurements (largest values in each sample) consistently outperform “mean” measurements for classification. This makes intuitive sense — cancer is characterized by abnormal cells, and the most abnormal cells in a sample are the most telling.

Malignant Tumors Are More Variable

Here’s a pattern I didn’t expect: malignant tumors show much higher variability in their measurements.

M = Malignant, B = Benign

Standard error comparison:

This means malignant tumor cells are less uniform. They vary more in size and shape — a hallmark of cancer’s chaotic growth patterns.

This variability itself becomes a diagnostic signal.

The Feature That Might Be Useless

Not every measurement helps. Fractal dimension, a measure of boundary complexity — provides almost zero diagnostic value.

The statistics:

• Malignant average: 0.0627
• Benign average: 0.0629
• P-value: 0.76 (not significant)
• Cohen’s d: -0.027 (negligible)

The values are virtually identical. If you built a model using fractal dimension, it would perform no better than random guessing.

This matters because fractal dimension sounds sophisticated. It appears in the dataset alongside genuinely predictive features. Without analysis, you might assume it’s useful.

It isn’t.

Compactness: The Shape Signature

Compactness measures how circular a tumor is (calculated as perimeter² / area). Malignant tumors are 81% more compact than benign ones:

• Malignant: 0.145
• Benign: 0.080

M = Malignant, B = Benign

M = Malignant, B = Benign

Combined with higher concavity, this paints a picture: malignant tumors are denser and more irregular, while benign tumors are larger relative to their perimeter and smoother.

The Texture Difference

Texture measures variation in grayscale values in the cell image — essentially, how uniform the tumor appears under imaging.

Malignant tumors show 21% higher texture values:

• Malignant: 21.6
• Benign: 17.9
• P-value: 4.06e-25 (extremely significant)
• Cohen’s d: 0.95 (large effect)

M = Malignant, B = Benign

Higher texture = more internal variation = more chaotic cellular structure.

What This Means for Diagnosis

The data reveals a clear diagnostic profile:

Malignant tumors tend to be:

• Larger (2x area on average)
• More irregular surfaces (3.5x more concavity)
• More variable cell sizes (2–3x higher standard error)
• More compact shape
• Higher internal texture variation

Benign tumors tend to be:

• Smaller
• Smoother surfaces
• More uniform cell sizes
• Less compact
• More uniform internal texture

A simple two-threshold rule (radius ≥ 15.1 AND area ≥ 705) correctly identifies 94% of malignant cases.

The Correlation Structure

Within malignant tumors, certain features move together:

Highly correlated (r > 0.9):

• Radius, perimeter, and area (all size-related)
• Concavity and concave points

Moderately correlated (r = 0.7–0.85):

• Size features with concavity features
• Compactness with concavity

This means many features are redundant. A model using radius, concavity, and texture would capture most of the diagnostic information without needing all 30 features.

Practical Thresholds

Based on the analysis, here are approximate thresholds where malignancy becomes likely:

When multiple thresholds are exceeded simultaneously, malignancy probability increases substantially.

Limitations

This analysis is exploratory, not diagnostic. Important caveats:

1. This is one dataset. The Wisconsin dataset is well-studied but represents a specific population and imaging methodology.
2. Correlation isn’t causation. These features predict malignancy but don’t explain why tumors become malignant.
3. Clinical diagnosis is complex. Real diagnosis involves pathology, patient history, imaging, and clinical judgment — not just measurements.
4. The 94% threshold has false negatives. 6% of malignant tumors fall below the thresholds. No simple rule catches everything.

This analysis shows what’s possible with data. Actual clinical tools require rigorous validation, regulatory approval, and integration with medical workflows.

What I Learned

Three insights stood out:

1. A few features do most of the work. Of 30 measurements, concavity, size, and texture carry most of the predictive signal. Many features are redundant or useless (like fractal dimension).

2. Variability is informative. Malignant tumors aren’t just bigger — they’re more chaotic. Cell-to-cell variation within a sample is itself a diagnostic signal.

3. Simple rules can be powerful. A two-variable threshold (radius + area) achieves 94% accuracy. Complexity isn’t always necessary.

Explore Full Report:

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Data Source:

[embed]Breast Cancer Dataset ⚕️ Clinical Breast Cancer Data for Predictive Analyticswww.kaggle.com

Note: This is exploratory data analysis, not medical advice. Clinical diagnosis requires professional medical evaluation.

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