A treatment can look better in every subgroup—and still look worse when all patients are pooled.
This is Simpson’s paradox. Imagine one hospital treats many straightforward cases and another receives mostly severe ones. A treatment can have a higher success rate within both severity groups, yet a lower overall rate if it was used disproportionately on the hardest cases.
The arithmetic has not broken. The groups contribute different numbers of people, so their averages carry different weights. Pooling can conceal that mix and even reverse the comparison. Which number matters depends on the question and on what variables shape who received each treatment; subgroup rates alone do not automatically establish cause.