Vitamin D has been in the news lately, especially for its beneficial effects on immunity (as well as other benefits), and its potentially beneficial effects in preventing the development of COVID-19.

So how much vitamin D should a person be getting every day? The “recommended daily allowance” suggested by the Canadian and American nutrition authorities is 600 “international units” (equivalent to 15 micrograms).

**A Brief History of the Modern RDA**

Where did those RDAs come from? The answer is a 2011 report published by the Institute of Medicine (IOM), called the *Dietary Reference Intakes for Calcium and Vitamin D*. Of particular note, it determined that Americans and Canadians require a daily vitamin D intake of about 600 IU per day by analyzing 32 studies of vitamin D supplmentation.

Their findings are explained and graphed in Chapter 5 of their report, pages 380-383 and figure 5-3: by supplementing with 600 IU of vitamin D per day, 97.5% of people will achieve adequate levels of vitamin D.

A lot of public health policy rests on this report. It’s not just Canada and the US that base their official recommendations on it; other countries such as the UK rely on the IOM data to inform their own research and perspectives.

Yet the IOM report was met with criticism almost immediately after being published. Harvard scientists said that 600 IU is too low to attain optimal bone health. Former IOM panelists complained about a number of inconsistencies, which biased the recommendation to be much too low.

**Bad Stats**

The most devastating criticism, however, comes from a 2014 paper by Paul J. Veugelers and John Paul Ekwaru: that there is “A Statistical Error in the Estimation of the Recommended Dietary Allowance for Vitamin D“. According to the paper, the IOM made a mistake in interpreting their own graph. What the IOM graph *actually* shows is in fact a supplementation of 600 IU results in 97.5% of *study averages* to achieve adequate levels of vitamin D in their blood, measured in nanomols per litre.

Correcting for this error, the authors conclude that the actual RDA should be somewhere in the neighbourhood of 8895 IU per day. (Note that this number is extrapolated well outside the original data set, and thus needs to be taken with a grain of salt.)

Let me explain this difference.

Imagine there are 40 studies, each with 40 people. Each study gave some dose of vitamin D supplements to the individuals, and measured the blood vitamin D levels later. The IOM took the dosage given in each study, and the average serum vitamin D outcome of each study. It then calculated that in 39 out 40 (97.5%) *studies*, 600 IU was sufficient such that the serum vitamin D outcome of study was 50 nmol/L.

However, it *wrongly *interpreted this result as being 600 IU is sufficient for an *individual person* to attain 50 nmol/L. These two interpretations are not the same. Here’s why: although the studies measured serum levels of people, the outcomes represent an average of each study, where each study involved numerous people.

Thus, 600 IU is what it would take for a study average to result in at least 50 nmol/L, but for an individual this may not hold true.

**An Analogy**

This is a very nuanced, difficult to understand point, so an analogy will help to clarify.

Consider a situation with where we want to improve the average test scores (out of 100) of 40 different classrooms, each with 40 students, for a total of 1600 students. As it was a very hard test, the average scores were very low. The administrators decide to bump up everyone’s grades with bonus marks.

Each classroom is given a certain number of bonus marks to add to the test scores of all the students in the class: some classes are given 1 extra point, others are given 2, some are given 5, etc. Then we calculate that for when a class adds exactly 6 bonus points to every student’s test, 39 out of 40 *classes* will have a **class average** of at least 50 out of 100.

However, from this we mistakenly conclude that giving an **individual student** 6 bonus points means 156 out of 160 students (97.5%) will have an minimum score of 50%. To see why this is a problem, consider the fact that the “average” for each classroom may also be their median, meaning that half the class scored lower than the class average.

Thus, if 39 out of 40 classes had a median score of exactly 50%, then we can deduce exactly half of those students will have even lower grades.

As another example, if we assume the distribution of grades for a class follows exactly like the distribution of IQ, then for a class with an average score of exactly 50% after the bonus, 6 students (15 percent of the class) will have scored **at most** 42%; if the average is bumped up to 60%, then only 24 students (85% of the class, not the alleged 97.5%) will have scored above 50%.

Moreover, if the distribution is skewed such that most students earn very low marks but the average is pulled up by a few extra high performers, then the error is even worse.

Consider a class where after the bonus is awarded, 10 students earned an 95%, but 30 earned a mere 35%. This is still an average of 50% for the class, even though 75% of the students are still below the average. If this trend is typical among classes, then it becomes extremely unlikely that a 6 mark bonus will mean 97.5% of students will earn at least a 50. It could very well be that almost three quarters of all students continue to score below the average of 39 out of 40 classes!

**Summary and** **Conclusion**

The IOM made a serious statistical mistake in calculating its RDA for vitamin D: it mistook the average of averages for the average across individuals. This has serious impacts on what the RDA should be: using the IOM’s own data, Veugelers and Ekwaru estimate that the RDA should be closer to 9000 IU.

The conclusion to draw from this episode is to remain vigilant about statistical claims, even if they are from elite sources. It took 3 years for the first published result on this error, and another 3 years for another study to independently rediscover this error (and without citing Veugelers and Ekwaru). Today, there have been no changes or corrections to the nutritional guides with respect to vitamin D for either the US or Canada. It’s time for the numbers to be revisited—lives are at stake.