A Predictive Equation to Guide Vitamin D Replacement Dose in Patients

Gurmukh Singh, MD, PhD, MBA; Aaron J. Bonham, MS


J Am Board Fam Med. 2014;27(4):495-509. 

In This Article

Abstract and Introduction


Background. Vitamin D is essential for bone health and probably the health of most nonskeletal tissues. Vitamin D deficiency is widespread, and recommended doses are usually inadequate to maintain healthy levels. We conducted a retrospective observational study to determine whether the recommended doses of vitamin D are adequate to correct deficiency and maintain normal levels in a population seeking health care. We also sought to develop a predictive equation for replacement doses of vitamin D.

Methods. We reviewed the response to vitamin D supplementation in 1327 patients and 3885 episodes of vitamin D replacement and attempted to discern factors affecting the response to vitamin D replacement by conducting multiple regression analyses.

Results. For the whole population, average daily dose resulting in any increase in serum 25-hydroxyvitamin D level was 4707 IU/day; corresponding values for ambulatory and nursing home patients were 4229 and 6103 IU/day, respectively. Significant factors affecting the change in serum concentrations of 25-hydroxyvitamin D, in addition to the dose administered, are (1) starting serum concentration of 25-hydroxyvitamin D, (2) body mass index (BMI), (3) age, and (f) serum albumin concentration. The following equation predicts the dose of vitamin D needed (in international units per day) to affect a given change in serum concentrations of 25-hydroxyvitamin D: Dose = [(8.52 − Desired change in serum 25-hydroxyvitamin D level) + (0.074 × Age) – (0.20 × BMI) + (1.74 × Albumin concentration) – (0.62 × Starting serum 25-hydroxyvitamin D concentration)]/(−0.002). Analysis of the dose responses among 3 racial groups—white, black, and others—did not reveal clinically meaningful differences between the races. The main limitation of the study is its retrospective observational nature; however, that is also its strength in that we assessed the circumstances seen in usual health care setting.

Conclusions. The recommended daily allowance for vitamin D is grossly inadequate for correcting low serum concentrations of 25-hydroxyvitamin D in many adult patients. About 5000 IU vitamin D3/day is usually needed to correct deficiency, and the maintenance dose should be ≥2000 IU/day. The required dose may be calculated from the predictive equations specific for ambulatory and nursing home patients.


The optimum serum concentration of 25-hydroxyvitamin D and what constitutes vitamin D deficiency is controversial. Serum concentrations of 25-hydroxyvitamin D <10 ng/mL are generally accepted to be deficient; however, 16 to 30 ng/mL or even higher is considered by different organizations and investigators to be the optimum concentration.[1–9] It has been suggested that levels of 40 to 60 ng/mL are ideal and that levels up to 100 ng/mL are safe.[5,7–9] If we accept that serum concentration of 30 ng/mL is optimal for 25-hydroxyvitamin D, then inadequacy of vitamin D may be the commonest nutritional deficiency in the United States.[1–18] Nearly 90% of 703 applicants for life insurance had serum 25-hydroxyvitamin D concentration below 30 ng/mL.[18] The vast majority of these individuals were outwardly healthy and represented the "normal" US adult population. Most of an individual's vitamin D requirement may be met through synthesis of vitamin D from 7-dehydrocholesterol in the skin through exposure to sunlight, yet most people have serum concentration of 25-hydroxyvitamin D in the subnormal range, probably because of inadequate sun exposure, and require treatment with supplemental vitamin D.[17]

Vitamin D deficiency is strongly linked to rickets in children and osteomalacia in adults.[19–21] Other disorders associated with vitamin D deficiency include an increase in all-cause mortality, risk of falls, fractures, muscle weakness, pain and arthritis in the elderly, psoriasis, infections, poor oral health, cardiovascular disease, diabetes, multiple sclerosis, and cancers.[22–55] The findings regarding nonskeletal issues are based mostly on observational studies, and the validity of observational studies has been questioned because of a lack of confirmation by randomized controlled trials.[56,57]

There is universal consensus about the role of vitamin D in preventing rickets and osteomalacia, and vitamin D intake of 800 IU/day may be sufficient to protect bone health in healthy subjects. In a meta-analysis of 40 studies, Bolland et al[58] concluded that vitamin D and calcium administration reduced the incidence of hip fractures among institutionalized individuals but did not find any other beneficial effect from vitamin D supplementation. However, the average and median doses analyzed in the studies were 1060 and 800 IU/day, respectively, and serum concentrations of 25-hydroxyvitamin D of 20 ng/mL were considered sufficient. Only one of the 40 trials used a dose of >2000 IU/day. It could be argued that the subjects were deficient in vitamin D and received inadequate supplementation. Proponents of nonbone benefits of vitamin D supplementation recommend much higher doses; for example, Garland et al[4] stated that a serum concentration of 25-hydroxyvitamin D of 60 to 80 ng/mL may be needed to reduce cancer risk. Similarly, Ginde et al[59] reported protective effect of vitamin D from upper respiratory infections at 25-hydroxyvitamin D serum concentrations of >30 ng/mL.

The recommended daily allowance (RDA) for vitamin D was revised from 400 IU/day to 600 to 800 IU/day. Given the high prevalence of vitamin D deficiency, however, it is likely that the revised recommendation is insufficient for the general population, let alone patients.[5,18,32,60–68] Vitamin D need among healthy people for bone health is likely to be different from that of the population seeking health care, particularly if the role of vitamin D in nonskeletal health is accepted.[5,64–68]

Given the level of uncertainty about the recommended dose of vitamin D, we examined the responses of patients to vitamin D replacement under the usual circumstances of health care and analyzed factors affecting the response to treatment using changes in serum concentrations of 25-hydroxyvitamin D as the indicator of response. In 3885 pairs of observations, 25-hydroxyvitamin D concentrations before and after treatment and the average daily dose of vitamin D administered were analyzed. We analyzed averages, medians, and multiple linear regressions to ascertain statistically significant factors affecting the response to treatment. We arrived at a robust predictive equation for estimating the daily dose of vitamin D needed to effect a given change in serum concentrations of 25-hydroxyvitamin D.