Deriving D3 supplemental ratios of bodyweight from Ekwaru et al. 2014

Robin Whittle  6 November 2020

This page explains how I derived the ratios referred to in the 01-supp/ page.   Be sure to read that page fully for the context of all that follows - and the disclaimer at ../../about/ .

I chose a target, long-term, 25OHD level of 50ng/ml (125nmol/L) because it is in the middle of the 40 to 60ng/ml range cited by research articles, the D*Action team etc. as mentioned in the the 01-supp/ page.  

My aim is to propose a base ratio of bodyweight as a daily average vitamin D intake which, for people of any given bodyweight, will cause - over the course of several months and thereafter indefinitely - that set of people to have 25OHD blood vitamin D levels averaging about 50ng/ml.  I also chose an upper ratio which, without any risk of toxicity (for people not suffering any acute medical condition which might precipitate this, again see the 01-supp/ page) of, arbitrarily, twice this amount.   This will raise the average 25OHD level to about 60ng/ml and so bring an even greater proportion of the population above some lower threshold, such as 40ng/ml.

There are a number of approximations in this process.   We are not designing rocket ships or microprocessors here.  Vitamin D has a wide margin of safety, between the intake levels which provide good health for most people (and above which little further benefit would be gained) and the much higher intake levels which would cause some people to suffer significant ill-effects.

In principle one can imagine research projects to finesse some of the necessary approximations, but they would take years, involve large numbers of people from countries all over the world, and in the end might improve the accuracy of some values by a few percent - when such precision it not required.

The 2:1 range of the two ratios also demonstrates that there is a broad range of intake values which satisfactorily provide health benefits for most people.  At the same time, some people with particular health problems such as multiple sclerosis (MS) may benefit from much higher intakes and 25OHD levels.

I would appreciate suggestions and critiques from MDs and researchers!

My calculations are based on the graph I adapted  


The Importance of Body Weight for the Dose Response Relationship of Oral Vitamin D Supplementation and Serum 25-Hydroxyvitamin D in Healthy Volunteers
John Paul Ekwaru, Jennifer D. Zwicker, Michael F. Holick, Edward Giovannucci and Paul J. Veugelers.. PLoS One 2014-11-05

These four curves are averages from 22,214 25OHD readings of 17,614 healthy North American adults participating in a preventive health program.  So this is a self-selected sample of the population.  I have assumed a normal bodyweight of 70kg (154lb), while recognising that normal bodyweights (not average - normal, healthy, non-overweight, non-obese) bodyweights for Asians are somewhat less than this.

I used the intercepts of curves and the 50ng/ml 25OHD level directly.  I am not trying to develop an RDA.  See the end of the 01-supp/ page for my reasoning.

My aim is to get a population of people - whether infants, children, adolescents or adults - supplementing D3 so the average of their 25OHD levels is, for the  base ratio about 50ng/ml.

Sidebar on RDAs:

This is a completely different approach than trying to derive an RDA to achieve any given 25OHD in a specific subset of people, such as those with a particular bodyweight.  To do that we would firstly need to know the distribution of individual readings, ideally for a given supplementation amount, and secondly to add a correction for the fact that all subjects must have gained significant D3 from food, UVB skin exposure and perhaps uncounted multivitamins.

If the subjects had zero such inputs, the curves would all intersect with both axes.  

So the ratios I derive assume some level of D3 intake from food and/or multivitamins and some level of cutaneous CD production from UVB exposure.   Some people's situations do not fit the pattern of these study subjects, such as newborns, infants, women who rarely if ever go outside without full coverage clothing and the patients, residents and inmates of hospitals, care homes and prisons.   However, the difference between the very low D3 supplies of these people and those of the study subjects is not particularly significant in the context of the robust D3 supplementation quantities the chosen ratios will provide.   So we don't need to derive a formal RDA, or estimate the ex-supplementation D3 supplies of study subjects with any certainty.

To aim for 50ng/ml, according to the Normal Weight curve, 0.125mg (5000IU) is needed, on average.  Assuming 70kg body weight this is ratio of 1.8ug/kg body weight.   Then there could be different ratios for overweight and obesity.

Ekwaru et al. state (I assume* "1.5 times higher" means the original weight * 1.5, rather than * 2.5):

We recommend vitamin D supplementation be 2 to 3 times higher for obese subjects and 1.5 times higher for overweight subjects relative to normal weight subjects.

They mention "two to three times more" in their abstract, citing the Endocrine Society*, and note that their article is intended to provide a research basis to justify this, which the Society acknowledged was lacking. 

* They are referring to this article, which remains to this day (Nov 2020) the Endocrine Society's clinical guideline for vitamin D, and which Google reports has been cited 8,505 times:

Evaluation, Treatment, and Prevention of Vitamin D Deficiency: an Endocrine Society Clinical Practice Guideline
Michael F. Holick, Neil C. Binkley, Heike A. Bischoff-Ferrari, Catherine M. Gordon, David A. Hanley, Robert P. Heaney, M. Hassan Murad, Connie M. Weaver
The Journal of Clinical Endocrinology & Metabolism, Volume 96, Issue 7, 2011-07-01

This article recommends the IOM's mistaken 600IU RDA for all but those with obesity and those on particular medications.  Their terminology regarding higher intakes for those with obesity with is messy too:

We suggest that obese children and adults and children and adults on anticonvulsant medications, glucocorticoids, antifungals such as ketoconazole, and medications for AIDS be given at least two to three times more vitamin D for their age group . . .

[Normal weight] . . . maintenance therapy of 1500 2000 IU/d.  

From their page 1924 restatement of rec. 3.5:

3.5 In obese patients, patients with malabsorption syndromes, and patients on medications affecting vitamin D metabolism, we suggest a higher dose (two to three times higher; at least 6000 –10,000 IU/d) of vitamin D to treat vitamin D deficiency to maintain a 25(OH)D level above 30 ng/ml, followed by maintenance therapy of at least 30006000 IU/d.

They clearly mean 2 * to 3 *.

Table 3 shows in the right two columns the Endocrine Society recommendations alongside the sliced and diced arrangement of the IOM, and for adults 19 years and above the daily requirement is 1500 to 2000 IU/d, with 10,000 IU being the "upper level", with nothing about obesity, since this is not an element of the IOM's recommendations.

The 1133 page IOM report can be found via .  Page 9 (PDF page 26) has their table of recommendations, here as a PNG.  An early critique is by Robert Heaney and Michael Holick is at: .

"Average weight" means a BMI of 18.5 to 20 - so I assume an average BMI of 19.25

The average BMI of overweight people is 25 to 30 = an average of 27.5, which is 19.25 * 1.425 .  So on this basis, we don't need a ratio different from the normal 1.8 ug/kg for the overweight to achieve their goal of 1.5 times the D3 intake of average weight non-overweight people.

Obesity is open ended: BMI > 30.  If we take the mid-point of another step of 5 upwards, this is 32.5 as the low end of obesity =  19.25 1.69 .   To match this with their low end target of 2 times the average weight D3 intake, we need a ratio (2.0 / 1.69) = 1.1834 * the base ratio of 1.8ug/kg = 2.13g/kg .

I guess that the average high end of obesity is another 5 above this: 37.5 = 19.25 * 1.948.   Ekwaru et al. suggest these people need 3 times the average weight D3 intake, so we need a ratio (3.0 / 1.948) = 1,54 * 1.8ug/kg = 2.77ug/kg.

So I chose 1.8ug/kg for normal and overweight people, with 2.5ug/kg for those with obesity, with a note that those suffering from morbid obesity require medical care and probably still higher ratios of D3 per kg body weight.

Since there is such a high safety margin, since some people may benefit from higher intakes and since aiming for 50ng/ml means half the people will have less than this, I suggest that these two ratios: 1.8ug/kg and 2.5ug/kg be the base recommendation, with upper ratios being twice these.  

There's no research justification for this - but it is convenient, and has the property of adding about another 10ng/ml to the resulting average 25OHD levels, as you can see from the curves.

That would match with the widely stated belief - backed up by all observations - that for average weight adults, 0.25mg (10,000IU) is well below an intake where toxicity might be a concern.

I have not mentioned vitamin D2.   It is generally regarded as being a poor substitute for D3, with a shorter half-life of its type of 25OHD in the bloodstream.   This article makes me think it is a poor cousin to D3: .  This one makes me think that UVB exposed mushrooms are a not particularly stable source of this second-rate alternative to D3.

With the possible exception of millions of strict vegetarian Hindus avoiding D3, I think that the recommendations should assume that there are no objections or other difficulties obtaining and ingesting D3.

© 2020 Robin Whittle   Daylesford, Victoria, Australia