The interval is the result

A worked interval, on prior_therapy in clinical-trial: 342 of 900 rows, so 38.0%.

The standard error on a proportion is sqrt(p(1-p)/n). Here that is 1.62 percentage points, so the 95% interval runs 34.8% to 41.2% — a width of 6.3 points.

import math

n, k = 900, 342
p = k / n
se = math.sqrt(p * (1 - p) / n)
print(f"{p:.3%}  [{p - 1.96*se:.3%}, {p + 1.96*se:.3%}]")

That interval is wide enough that a change of a point or two means nothing, and it will be reported as a change anyway unless someone puts the bounds next to it.

Getting the interval down to ±0.5 points would need about 36,204 rows. Precision costs sample size quadratically — halving the width costs four times the data — which is the single most useful fact for anyone about to promise a more precise answer next week.

Normal approximation, and it starts lying at small counts or proportions near the boundaries; the Wilson interval behaves there. The pattern has both.