7. Does more tissue mean more infiltration? — hunting a confounder · Dr. Seok's Tumour-Infiltrating Lymphocytes, First Steps

In lesson 2 we settled on tissue tiles as the denominator. But one worry remains.

A slide with a lot of tissue contains that many more different regions — tumour margin, normal tissue, maybe a lymph node. So might a larger tissue area give a higher infiltration rate? And if it did, "high infiltration" might really be reporting "a lot of tissue was sectioned".

That is called confounding. Let us measure it.

This error is on purpose — import pandas as pd is missing. It is practice at reading an error message.

Python Runs in your browser

import til
import numpy as np
from scipy import stats

d = til.slides()
rho, p = stats.spearmanr(np.log10(d.tissue_patches), d.til_pct)
print("rank correlation of tissue size (log) with TIL:  rho = %.3f   p = %.2e" % (rho, p))
print("%s slides" % format(len(d), ","))
print()
print("Median TIL across eight bins of tissue size")
bins = pd.qcut(np.log10(d.tissue_patches), 8)
for k, g in d.groupby(bins, observed=True):
    print("  10^%.2f ~ 10^%.2f  %4d slides  median %5.2f%%"
          % (k.left, k.right, len(g), g.til_pct.median()))

rho = 0.047. The p-value is a small 0.0007, but the per-bin medians run almost flat between 4.1% and 5.5%.

Python Runs in your browser

import til
import pandas as pd
import numpy as np
from scipy import stats

d = til.slides()
rho, p = stats.spearmanr(np.log10(d.tissue_patches), d.til_pct)
print("rank correlation rho = %.3f   p = %.2e   (n = %s)" % (rho, p, format(len(d), ",")))
print()
bins = pd.qcut(np.log10(d.tissue_patches), 8)
for k, g in d.groupby(bins, observed=True):
    bar = "#" * int(g.til_pct.median() * 3)
    print("  10^%.2f~%.2f %4d slides  %5.2f%%  %s"
          % (k.left, k.right, len(g), g.til_pct.median(), bar))

There is something to learn here.

a small p ≠ a large effect

With 5,201 slides, even a tiny correlation becomes "statistically significant". But the actual size is rho = 0.047 — near enough to nothing. The median gap between the smallest and largest tissue bins is 1.4 pp, and the measurement error we meet in lesson 11 is 1.8 pp. The difference is smaller than the error.

So the conclusion is "tissue size is not a confounder worth worrying about in this data". We looked, and it was not there. That is a result too.

Check it per cancer type as well. A flat red line (the per-bin median) means no confounding.

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🤔 Check yourself

At n = 5,201 you get rho = 0.047 with p = 0.0007. What is the right reading?

🤔 Check yourself

You checked for a confounder and there was none. What belongs in the paper?