Polycystic ovary syndrome may be a sort of “exception” to the “calories in, calories out” rule. Of course, it will still be true to say that burning more than you supply will make you lose weight, but affected women have their baseline metabolism reduced quite a bit.
https://pubmed.ncbi.nlm.nih.gov/18678372/
The above study looked at what the baseline caloric needs are (before all the exercise, activity and everything else) for women with polycystic ovarian syndrome combined with hyperandrogenism and those of healthy women.
For the “normal” woman, the baseline requirement was 1868 kcal per day. In the syndrome combined with hyperandrogenism, it dropped to 1445, averaging 1590 in the absence of insulin resistance and only 1116 in its presence.
But it’s not that simple, another study assessed baseline caloric requirements in the usual syndrome, without hyperandrogenism:
https://pubmed.ncbi.nlm.nih.gov/30847861/
As it turned out, the syndrome practically did not affect the results at all, sick and healthy women had almost identical requirements.
The question to ask: were the studies done correctly? It often happens that scientists make up their own results, but then we are faced with the mystery of who is writing the truth and who is lying. Perhaps there is a specific connection to hyperandrogenism involved?
It is known that people with diabetes have an increased, not decreased, basal metabolic rate:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3850714/
It is also known that polycystic ovary syndrome does not cause obesity in those countries where there is a culture of healthy eating, such as Japan. There are even suggestions that it is not so much the cause of health problems, but rather the result of poor diet and general lack of taking care of oneself.
Aside from what your doctor recommends, there are a few things you can do “on your own”. One of these is zinc supplementation. In a study, it not only significantly reduced disease symptoms, but also significantly improved insulin resistance parameters in women suffering from the syndrome:
https://pubmed.ncbi.nlm.nih.gov/25868059/
https://pubmed.ncbi.nlm.nih.gov/26315303/
Vitamin D3 helped reduce insulin resistance and reduced hyperandrogenism:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7086222/
No studies have been done on magnesium supplementation, but it is known that low magnesium intake (and low fiber intake) is associated with significantly worse disease parameters:
https://pubmed.ncbi.nlm.nih.gov/31024716/
Proper magnesium supplementation is 200 mg per day, divided into 2 servings, together with selenium, which by the way also had a very beneficial effect on the syndrome:
https://pubmed.ncbi.nlm.nih.gov/25510442/
Myo-inositol supplementation gave very good results, not only did it allow to lose weight, but also restored regular menstruation:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5655679/
https://reproductive-health-journal.biomedcentral.com/articles/10.1186/s12978-021-01073-3
The dose is at least 4 grams per day, 2 in the morning, 2 in the evening.