There are two findings here and they deserve opposite treatment. One is a real null worth knowing. The other is a percentage attached to a cohort a thousand times larger than the group it was actually measured in — the arithmetic a reader has to do before any published figure means anything.
The good finding
Polycystic ovary syndrome makes weight loss harder, which is well established, and there was a reasonable worry that it would blunt the response to these drugs. [1] It did not. At ten months, women with PCOS had lost a mean 19.40%, 95% CI 16.42% to 22.38%, against 18.74% for women without it, 95% CI 17.81% to 19.67%. The intervals overlap almost completely.
57.66% of the PCOS group reached 20% total body weight loss, 95% CI 47.44% to 68.29%. On the question the study set out to ask, the answer looks clean.
The denominator
The cohort is 54,114 women. The PCOS group is 4,241. The ten-month weight figure is calculated in 40 of them, against 397 without PCOS.
Forty. That is where −19.40% comes from, and it is why the interval around it runs six percentage points wide while the comparison group’s runs under two.
The engagement result
Among women with PCOS, those who engaged with the app lost 3.42% more in absolute terms, 95% CI 1.71% to 5.12%, p < 0.001.
Read that as a description of who engages, not as a benefit of engaging. Whoever is still logging into a weight-management app at ten months is already someone who is still taking the drug, still weighing themselves and still paying — the same selection that produced the coaching result on this site, which had the same unrandomized shape.
What a buyer takes from it
If you have PCOS, nothing in this suggests the drug works less well for you, and that is worth having. PCOS here is self-reported to a commercial service rather than verified, so it is a large sample of people who say they have it rather than a clinical cohort.
And when a study quotes an enormous headline sample, find the number under the specific figure you care about before you price anything on it — the habit that reading any commercial comparison requires.