The RDA of Vitamin D is based on bad statistics

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. 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. They claim that by supplementing with 600 IU of vitamin D per day, 97.5% of people will achieve adequate levels of vitamin D.

FIGURE 5-3 Response of serum 25OHD level to total intake of vitamin D in northern latitudes in Europe and Antarctica during their respective winter seasons
Figure 5-3 from the IOM report: each circle/diamond/square represents a different study.

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, titled “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.

I will explain what this means below. But the punchline is, that after correcting for this error, the authors suggest that the IOM study should have actually concluded that the RDA of vitamin D be somewhere in the neighbourhood of 8895 IU per day.

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Figure 2 from the Veugelers and Ekwaru paper.

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 their serum 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: it confuses a group average with an average individual.

So while 600 IU per day may be what it would take for an average group of people to have in at least 50 nmol/L, this does not imply that the average person needs only 600 IU per day. This distinction is subtle (after all, it tricked many government scientists), so it’s worth spending some time understanding it.

An Analogy

To explain this problem, consider the following analogy:

Imagine a town administers a standardized test to every teacher. There are 40 schools, and each school has 40 teachers—giving a total of 1600 teachers. 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 school is given a certain number of bonus marks to add to the test scores of all the teachers in that school: some schools are given 1 extra point, others are given 2, some are given 5, and so on. Then we calculate that when a school adds exactly 6 bonus points to every teacher’s test, 39 out of 40 schools will have an average score of at least 50 out of 100.

However, from this we mistakenly conclude that giving an individual student 6 bonus points means 1560 out of 1600 students (97.5%) will have an minimum score of 50%. But this does not follow!

Kid's brilliant answer to exam question that asked "show your thinking" is  too hilarious to be wrong - Mirror Online

To see why, imagine that the distribution of grades is skewed such that most students earn very low marks but there are a few extra high performers in each school.

For example, in one school, before the bonus is awarded, 10 teachers earned an 90%, but 30 scored a mere 30%. This is comes out to an average of 45% for the class. ([10*90%+30*30%]/40=45%.) But note that 75% of the teachers scored below average.

Now let’s see what happens after we give everyone the six bonus points (so that 10 teachers end up with 96% and 30 students get 36%). The class average jumps up to 51%, which is a passing grade. But we still have three-quarters of all the teachers in that school with failing grades!

If this trend is typical among different schools, then it becomes extremely unlikely that a 6 mark bonus will mean 97.5% of teachers will earn at least a 50%. It could very well be that almost three quarters of all teachers continue to fail in all 39 out of 40 schools with a passing school-average score!

Summary and Conclusion

The IOM made a serious statistical mistake in calculating its RDA for vitamin D: it mistook the average of averages for what’s typical across individuals. This has serious impacts on what the RDA should be: using the IOM’s own chart, Veugelers and Ekwaru estimate that the RDA should be closer to 9000 IU. However, they point out, this result is way outside of the data range. So a completely different analysis is required.

So what’s typical? In this Google Doc, I review many scholarly sources that suggest that the typical individual requires much more than 600 IU. Like our imaginary schools with teachers with inadequate training, most individuals around the world are found to have inadequate vitamin D levels. In some studies, the suggestions are for individuals to take 4,000 to 10,000 IU per day.

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.