Increase in bone mass after vitamin D replacement: can we ignore regression to the mean?

The growth and maintenance of bone are regulated by a combination of nutritional factors, including vitamins, such as vitamin A, B12, C, D, and K.
Vitamin A
Vitamin A is involved in the process of bone remodeling. Retinoic acid, the active metabolite of Vitamin A, has nuclear receptors in osteoblasts and osteoclasts, which are involved in bone remodeling.
Vitamin B12
Vitamin B12 acts as a cofactor during the formation of osteoblast-related proteins, such as osteocalcin. Vitamin B12 plays a role...

Aging and its effect on bone remodeling is the most common cause of bone disorders. In young and healthy people, bone deposition and resorption happen at an equal rate to maintain optimal bone health.
Bone deposition is also affected by the levels of sex hormones like estrogen and testosterone that promote osteoblast activity and bone matrix synthesis. When the level of these hormones decreases due to aging, it causes a reduction in bone deposition. As a result, bone resorption by osteoclasts...

Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when researchers try to extrapolate results...

Bone remodeling is a continuous and balanced process of bone resorption by osteoclasts and bone formation by osteoblasts. In adults, it helps maintain bone mass and calcium homeostasis. While mechanical stress can stimulate turnover as part of the normal maintenance and reparative process, several hormones also regulate bone remodeling.