How does a does a change in thyroid binding globulin (TBG) alter free T3, free T4 levels?

in a patient who is already hypothyroid and is taking levothyroxine supplementation, increase the dose of levothyroxine if TBG increases and decrease levothyroxine dose if TBG decreases
What are drugs that increase TBG?: Estrogen containing pill, Tamoxifen, Raloxifene, methadone
what are drugs that decrease TBG?: Glucocorticoid, androgens, anabolic steroid, slow release nicotinic acid