Modeling the effect of levothyroxine therapy on bone mass density in postmenopausal women: a different approach leads to new inference

BACKGROUND: The diagnosis, treatment and prevention of osteoporosis is a national health emergency. Osteoporosis quietly progresses without symptoms until late stage complications occur. Older patients are more commonly at risk of fractures due to osteoporosis. The fracture risk increases when suppressive doses of levothyroxine are administered especially in postmenopausal women. The question is; "When should bone mass density be tested in postmenopausal women after the initiation of suppressive levothyroxine therapy?". Standard guidelines for the prevention of osteoporosis suggest that follow-up be done in 1 to 2 years. We were interested in predicting the level of bone mass density in postmenopausal women after the initiation of suppressive levothyroxine therapy with a novel approach. METHODS: The study used data from the literature on the influence of exogenous thyroid hormones on bone mass density. Four cubic polynomial equations were obtained by curve fitting for Ward's triangle, trochanter, spine and femoral neck. The behaviors of the models were investigated by statistical and mathematical analyses. RESULTS: There are four points of inflexion on the graphs of the first derivatives of the equations with respect to time at about 6, 5, 7 and 5 months. In other words, there is a maximum speed of bone loss around the 6(th )month after the start of suppressive L-thyroxine therapy in post-menopausal women. CONCLUSION: It seems reasonable to check bone mass density at the 6(th )month of therapy. More research is needed to explain the cause and to confirm the clinical application of this phenomenon for osteoporosis, but such an approach can be used as a guide to future experimentation. The investigation of change over time may lead to more sophisticated decision making in a wide variety of clinical problems.