Table of contents
Removing outliers from a dataset is standard statistical practice
However, removing the data IS NOT the same as subracting the data
Download the PDF from VitaminDWiki.
Figure 1 Outliers to be removed
Figure 2 Outliers removed incorrectly by subtraction
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AVERAGE vitamin D responses from 8 studies (Heaney - 2013)
click on chart for details
Figure 2 with overlay of 40 ng response to 1800 IU from 8 studies
Note: In reality 95% of people wll be > 40 ng (a good level) with just 4,000 IU
A Statistical Error in the Estimation of the Recommended Dietary Allowance for Vitamin D
Nutrients. Oct 2014; 6(10): 4472–4475.Published online Oct 20, 2014. doi: 10.3390/nu6104472
Paul J. Veugelers and John Paul Ekwaru
The Institute of Medicine (IOM) issues dietary recommendations on the request of the U.S. and Canadian governments. One of these recommendations is the Recommended Dietary Allowance (RDA). The RDA is the nutrient intake considered to be sufficient to meet the requirements of 97.5% of healthy individuals . The RDA for vitamin D is 600 IU per day for individuals 1 to 70 years of age and is assumed to achieve serum 25-hydroxyvitamin D (25(OH)D) levels of 50 nmol/L or more in 97.5% of healthy individuals . Serum 25(OH)D is the established proxy for vitamin D status and levels of 50 nmol/L or more have been shown to benefit bone health and to prevent disease and injury .
The IOM based their RDA for vitamin D on an aggregation of 10 supplementation studies that were carried out during winter months and at locations with latitudes above the 50th parallel north to minimize the influence of cutaneous vitamin D synthesis [2,3,4,5,6,7,8,9,10,11]. As several of these 10 studies examined more than one supplementation dose, collectively they provided 32 study averages of serum 25(OH)D levels. These are replicated as the green diamonds in Figure 1. The IOM regressed the 32 study averages against vitamin D intake to yield the dose response relationship of vitamin D intake and serum 25(OH)D (green solid line in Figure 1). The IOM further calculated the lower and upper 95% confidence prediction interval based on the 32 study averages and the standard deviation of these 32 study averages (green dashed lines in Figure 1). On the basis of this, the IOM estimated that 600 IU of vitamin D would achieve an average 25(OH)D level of 63 nmol/L and a lower 95% confidence prediction limit (2.5 percentile) of 56 nmol/L. The latter value was rounded downwards to 50 nmol/L to accommodate uncertainty in the estimation . This data point (600 IU vitamin D, 50 nmol/L) is the basis for the current RDA and for the IOM’s conclusion that an intake of 600 IU of vitamin D per day will achieve serum 25(OH)D levels of 50 nmol/L or more in 97.5% of individuals. This conclusion, however, is incorrect.
Figure 1 Dose response relationship of vitamin D intake and serum 25 hydroxyvitamin D.
The correct interpretation of the lower prediction limit is that 97.5% of study averages are predicted to have values exceeding this limit. This is essentially different from the IOM’s conclusion that 97.5% of individuals will have values exceeding the lower prediction limit. To illustrate the difference between the former and latter interpretation, we estimated how much vitamin D is needed to achieve that 97.5% of individuals achieve serum 25(OH)D values of 50 nmol/L or more. For this purpose we reviewed each of the 10 studies used by the IOM. Eight studies reported both the average and standard deviation [2,5,6,7,8,9,10,11]. These eight studies had examined a total of 23 supplementation doses [2,5,6,7,8,9,10,11]. For each of these 23 study averages we calculated the 2.5th percentile by subtracting 2 standard deviations from the average (depicted by yellow dots in Figure 2). Next, we regressed these 23 values against vitamin D intake to yield the lower prediction limit (red line in Figure 2). This regression line revealed that 600 IU of vitamin D per day achieves that 97.5% of individuals will have serum 25(OH)D values above 26.8 nmol/L rather than above 50 nmol/L which is currently assumed.
It also estimated that 8895 IU of vitamin D per day may be needed to accomplish that 97.5% of individuals achieve serum 25(OH)D values of 50 nmol/L or more.
As this dose is far beyond the range of studied doses, caution is warranted when interpreting this estimate. Regardless, the very high estimate illustrates that the dose is well in excess of the current RDA of 600 IU per day and the tolerable upper intake of 4000 IU per day .
Figure 2 Dose response relationship of vitamin D intake and serum 25 hydroxyvitamin D.
The public health and clinical implications of the miscalculated RDA for vitamin D are serious. With the current recommendation of 600 IU, bone health objectives and disease and injury prevention targets will not be met. This became apparent in two studies conducted in Canada where, because of the Northern latitude, cutaneous vitamin D synthesis is limited and where diets contribute an estimated 232 IU of vitamin D per day . One study estimated that despite Vitamin D supplementation with 400 IU or more (including dietary intake that is a total intake of 632 IU or more) 10% of participants had values of less than 50 nmol/L . The second study reported serum 25(OH)D levels of less than 50 nmol/L for 15% of participants who reported supplementation with vitamin D . If the RDA had been adequate, these percentages should not have exceeded 2.5%. Herewith these studies show that the current public health target is not being met.
We recommend that the RDA for vitamin D be reconsidered to allow for appropriate public health and clinical decision-making.
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Heaney (with data from Grassroots Health) estimates 3,800 IU from all sources to most > 20 mg - March 2015
Letter to Veugelers, P.J. and Ekwaru, J.P., A Statistical Error in the Estimation of the Recommended Dietary Allowance for Vitamin D. Nutrients 2014, 6, 4472-4475; doi:10.3390/nu6104472
Nutrients ISSN 2072-6643
Robert Heaney pheaney at creighton.edu, Cedric Garland 2, Carole Baggerly 3, Christine French 3 and Edward Gorham 2
Creighton University, Omaha, NE 68178, USA
Department of Family and Preventive Medicine, University of California, San Diego, La Jolla, CA 92093, USA; E-Mails: cgarland at ucsd.edu (C.G.); Edward.Gorham at med.navy.mil (E.G.)
GrassrootsHealth, Encinitas, CA 92024, USA; E-Mails: carole at grassrootshealth.org (C.B.); french.cmb at gmail.com (C.F.)
Recently Veugelers and Ekwaru published data  indicating that, in its dietary reference intakes for calcium and vitamin D, the Institute of Medicine (IOM) had made a serious calculation error . Using the same data set as had the IOM panel, these investigators showed that the Recommended Dietary Allowance (RDA) for vitamin D had been underestimated by an order of magnitude. Veugelers and Ekwaru, using the IOM’s data, calculated an RDA of 8895 IU per day. They noted that there was some uncertainty in that estimate, inasmuch as this value required an extrapolation from the available data, which did not include individuals receiving daily vitamin D inputs above 2400 IU/day.
In this communication, we present data from a different cohort entirely, including many individuals with vitamin D intakes spanning a range from zero to above 10,000 IU per day. The data presented here are derived from the GrassrootsHealth (GRH) database, which had been characterized elsewhere . Here we examine the probability range for the previously published GRH data at all supplement intakes across the relevant range.
(Text added to graph by VitaminDWiki for clarification)
Figure 1 plots the 25(OH)D values for 3657 individuals as a function of their own intakes of vitamin D, showing both the best fit regression line through the data  and the 95% confidence limits for the total data set. The horizontal dashed lines in the figure are for serum 25(OH)D values of 20, 30, and 40 ng/mL (50, 75, and 100 nmol/L). The points at which these lines intersect the lower bound of the 95% probability band for serum 25(OH)D reflect the inputs necessary to ensure that 97.5% of the cohort would have a vitamin D status value at or above the respective 25(OH)D concentration. These three values represent, respectively, the recommended values of the IOM, the Endocrine Society , and GrassrootsHealth. The precise inputs corresponding to these serum 25(OH)D values are 3875, 6201, and 9122 IU/day.
While the 3875 IU intake value needed to achieve at least 20 ng/mL (50 nmol/L) in 97.5% of the population is lower than the estimate of Veugelers and Ekwaru, it should be noted first that, as Veugelers and Ekwaru had stated, both estimates are roughly an order of magnitude higher than the published IOM value. Also, it must be stressed that this input is explicitly supplemental, i.e., it presumes a daily, basal input from food and sun of some non-zero magnitude.
The best-fit regression line through the data, as can be seen in the figure, intersects the 7-axis at a value of 34 ng/mL (85 nmol/L), reflecting an intake from food and sun amounting to somewhat more than 3000 IU per day (5). Since an RDA, by definition, relates to intake from all sources, it is clear that total intake required to achieve 20 ng/mL in 97.5% of the cohort must be close to 7000 IU per day, not substantially different from that calculated by Veugelers and Ekwaru.
Thus, we confirm the findings of these investigators with regard to the published RDA for vitamin and we call for the IOM and all public health authorities concerned with transmitting accurate nutritional information to the public to designate, as the RDA, a value of approximately 7000 IU per day from all sources. We note that this conclusion applies specifically to the IOM’s designation of 20 ng/mL as the lower bound of adequacy, and that higher values, such as that of the Endocrine Society and GRH, would mandate the higher RDA values cited above.
With regard to possible safety concerns related to such a recommendation, we note that: (a) as the figure shows, the mean 25(OH)D and the upper bound of the 95% probability range for the supplemental intake of 3875 IU/day are less than 50 ng/mL and 100 ng/mL, respectively; (b) the correctly calculated RDA is well below the cutaneous production of vitamin D from summer sun ; and (c) the total, all-source intake of 7000 IU/day is below the no observed adverse effect level (NOAEL) of both the IOM and the Endocrine Society, below the tolerable upper intake level (UL) of the Endocrine Society, and well within the safe range delineated by Hathcock et al. , who had generated that range using the IOM’s method of hazard identification.
Author Contributions RP Heaney performed the analysis and drafted the text. The other authors participated in accumulating the data and contributed to the text.
- Veugelers, P.J.; Ekwaru, J.P. A Statistical Error in the Estimation of the Recommended Dietary Allowance for Vitamin D. Nutrients 2014, 6, 4472-4475.
- Food and Nutrition Board, Institute of Medicine. Dietary Reference Intakes for Calcium and Vitamin D; The National Academic Press: Washington, DC, USA, 2011.
- Garland, C.F.; French, C.B.; Baggerly, L.L.; Heaney, R.P. Vitamin D supplement doses and serum 25-hydroxyvitamin D in the range associated with cancer prevention. Anticancer Res. 2011, 31, 607-612.
- Holick, M.F.; Binkley, N.C.; Bischoff-Ferrari, H.A.; Gordon, C.M.; Hanley, D.A.; Heaney, R.P.; Murad, M.H.; Weaver, C.M. Evaluation, treatment, and prevention of vitamin D deficiency: An Endocrine Society Practice Guideline. J. Clin. Endocrinol. Metab. 2011, 96, 1911-1930.
- Heaney, R.P.; Armas, L.A.G. Quantifying the vitamin D economy. Nutr. Rev. 2015, 73, 51-67.
- Hathcock, J.N.; Shao, A.; Vieth, R.; Heaney, R.P. Risk assessment for vitamin D. Am. J. Clin. Nutr. 2007, 85, 6-18.