If you have a patient with amenorrhea, one possible cause is hyperthyroidism. Thyroid hormones will increase the expression of SHBG, thus enhancing estradiol, then estradiol increases LH (and disturbs its cyclical pattern) and produce amenorrhea.
However, if a patient has polycystic ovary syndrome, levels of SHBG are lower (because of high insulin) and free testosterone is higher, leading to hirsutism and anovulatory cycles.
So, if the free hormone is the active hormone, how it comes that higher SHBG levels increase estradiol activity but lower SHBH levels increase androgen activity? Shouldn't they vary in the same direction?