BEATON'S FULL PROBABILITY METHOD FOR IRON

The full probability approach is a statistical method that was first described by Beaton in 1972 for finding the proportion of people within a group with inadequate intakes of a nutrient. It involves finding the probability that each observed usual intake of a nutrient will be inadequate, that is, below requirements for that nutrient. This is often done for ranges of intake, as in the examples below. For a population group, the overall proportion of people within the group likely to have inadequate intakes (i.e. prevalence of inadequacy) is calculated as the average probability of inadequacy.^1-3

METHOD DESCRIPTION

Requirements for nutrients vary amongst individuals within any given group. Collectively, the requirements of each individual within a group form the requirements distribution for that group. In Beaton’s probability method, the probability that an individual’s observed usual nutrient intake will be inadequate is determined by comparing it with the requirements distribution for their age and sex group. Therefore for each population group, information on both the usual nutrient intakes distribution and the requirements distribution is required. Additionally, the expected correlation between requirements and intakes must be very low. This is assumed to be the case for iron.^1-3

The full probability approach must be used in place of the simpler EAR cut-point method when the requirements distribution is skewed. This is known to be the case for the iron requirements distributions of the following groups: children aged 1 to 3 years, children aged 4 to 8 years, menstruating adolescent young women aged 14 to 18 years, and menstruating adult women.^1,4

The method works as follows:^1,4

For a given population (age and sex) group and nutrient:
1. The distribution of usual intakes of the nutrient in the group is determined, e.g. via a method such as the NCI method.
2. For each observed range of usual nutrient intake (e.g. 20%⁵ of the women aged 19-30 have a usual intake of 4.18-17.51mg of iron per day), the proportion of the requirements distribution which falls above⁵ this intake is determined (e.g. 55%, as shown in the example in the table below).
3. This proportion is taken to be the probability of inadequacy at that intake. Thus in the example, the 20%⁶ of women who consume 4.18-17.51mg of iron each have a 55% probability of having an inadequate intake of iron.
4. The likely prevalence of inadequacy in the overall group, contributed by those consuming 4.18-17.51mg of iron, is then taken to be 55% of this 20%, i.e. 11%.
5. This procedure is repeated for each observed level of usual intakes within the population group of interest. In the below example this has been simplified to three groups with broad intake ranges, for the purpose of illustration. However, matching each observed level of usual intake against the best available estimate of the probability of inadequacy at that level is desirable, to avoid introducing categorical/rounding error.
6. The total prevalence of inadequacy in the whole group (e.g. women aged 19-30) is then found by adding the likely prevalence of inadequacy at each intake within the group. This is also equal to the average probability of inadequacy in the overall group.

Usual intake (mg per day) (a)	Proportion of population (%)(a)	Probability of inadequacy at this intake (proportion of requirements distribution above this range) (a)(b)	Prevalence of inadequacy (probability of inadequacy multiplied by % with intake in this range) (%)(a)
<4.18	10	1 (100%)	10
4.18 - 17.51	20	0.55 (55%)	11
>17.51	70	0 (0%)	0
			Total prevalence of inadequacy(a)= 10 + 11 + 0 = 21%

(a) Not actual data. For the purpose of illustration only.
(b) In practice, this is in fact the proportion of the requirements distribution above the approximate midpoint of this range.⁴

IMPLEMENTATION WITH 2011-12 NNPAS FOR IRON

The full probability method has been implemented for all age and sex groups for iron. It must be used for those age groups known to have skewed iron requirements distributions (growing children and menstruating women).^1,4 For consistency, it has also been implemented on the remaining groups (adolescent males, adult males, and post-menopausal women). The results of the full probability method should be interpreted considering how the requirements distributions were estimated for each age and sex group. Any error in these distributions will affect the quality of the estimates of the prevalence of inadequate iron intakes.

Estimation of the Requirements Distribution

Information on the distribution of requirements for each relevant population group has been sourced from the United States’ Continuing Survey of Food Intakes by Individuals (CSFII) 1994-1996, as published in appendix I to the relevant Institute of Medicine (IOM) Dietary Reference Intakes (DRI) publication.⁴

The following assumptions, in line with the current NRVs, have been made in using the IOM values (from CSFII) in the Australian Health Survey: Usual Nutrient Intakes, 2011-12:⁷

• females under 14 years do not menstruate and all females from 14 years to 50 years do
• all females 51 years and over are post-menopausal
• some menstruating females use oral contraceptives and some do not (i.e. the ‘ mixed population’ has been used)
• an upper limit of 18% iron absorption for all age groups other than one to three years
• an upper limit of 14% iron absorption for age group one to three years

For the age group one to three years, the IOM values had to be adjusted for use in the NNPAS usual intakes publication, as they were originally calculated assuming 18% iron bioavailability rather than 14% bioavailability. The model underpinning the IOM requirements distribution actually estimated how much iron people in the age sex group need to absorb. These values were then converted to the published requirements for iron intakes based on the estimated bioavailability of iron of 18%.⁴ In the NNPAS usual intakes publication, it was therefore possible to back-calculate values for 14% bioavailability for children aged one to three years as follows:

• Iron intake at 14% absorption = (IOM intake x 0.18) / 0.14
• Because:
  • Absorbed iron = IOM intake x 0.18
  • Iron intake at 14% absorption = Absorbed Iron / 0.14

Further information on how the requirements distributions have been estimated is published in Chapter 9 of the IOM document. Using these published values of risk of inadequacy for intervals of usual iron intakes introduces some rounding error (from categorical rather than continuous estimation), but is the approach used in other publications^1,8 and avoids the need to reproduce the modelling process underpinning the requirements distributions.^4,9 Some minor apparent errors of overlapping or non-contiguous intake ranges in this published document have been corrected according to the logic of their presentation.

Using the outputs of the NCI Method for usual intakes with the probability method

For the 2011-12 NNPAS, the NCI method has been used to estimate percentiles of usual intakes of iron (percentiles 0 – 100). The conservative approach of taking the lower bound of each percentile to represent intake at that percentile has been used, that is, the 0^th percentile of intakes has been used to represent the 1^st percent of the population, and so forth. All percentiles of intake were rounded to two decimal places, as the IOM intervals of probabilities of inadequacy are contiguous only for values rounded to two decimal places.

For the outputs of the NCI method, the simplest approach was to find the probability of inadequacy for each percentile of intake. The probabilities (each representing 1% of the population) were directly summed to give the overall prevalence of inadequacy as follows.

Percentile	Observed level of intake (mg)	Proportion of population (%)	Probability of inadequacy at this level (proportion of requirements distribution above this level)	Prevalence of inadequacy (probability of inadequacy multiplied by % with intake in this range)
0	L1	1	P1	Ri=1 = P1 x 1 = P1
1	L2	1	P2	R2
...	...	...	...	...
99	L100	1	P100	R100
				Total prevalence of inadequacy =

Sampling errors were calculated via group jackknife. The probability method was re-run for each of the replicate weight groups in the 2011-12 NNPAS, and the variability associated with the replicate estimates was then used to calculate standard errors and margins of error. The group jackknife variance estimation method captures sampling error, but will not capture other forms of error, such as error in the requirements distributions or error introduced by the use of the probability method itself. Therefore there is likely to be underestimation of the variance associated with these statistics. However every effort has been made to use the best available information on iron requirements and to ensure that the probability method is sound. For more information on the use of group jackknife with usual nutrient intakes, see Data Quality.

ENDNOTES

1 Gibson, RS and Ferguson, EL. 2008, ‘An interactive 24-hour recall for assessing the adequacy of iron and zinc intakes in developing countries’, HarvestPlus Technical Monograph 8, International Food Policy Research Institute and International Centre for Tropical Agriculture, Harvest Plus, Washington DC and Cali, <http://www.ifpri.org/sites/default/files/publications/tech08.pdf>, last accessed 9/2/2015.
2 National Research Council, 1986, Nutrient adequacy: assessment using food composition surveys, National Academy Press, Washington, D.C., <http://www.nap.edu/catalog/618/nutrient-adequacy-assessment-using-food-consumption-surveys>, last accessed 17/02/2015.
3 Food and Nutrition Board: Institute of Medicine, 2000, Dietary Reference Intakes: Applications in dietary assessment, National Academy Press, Washington, D.C., p.p.73-105, and 203-231.
4 Institute of Medicine, 2001, Dietary reference intakes for vitamin A, vitamin K, arsenic, boron, chromium, copper, iodine, iron, manganese, molybdenum, nickel, silicon, vanadium, and zinc. National Academy Press, Washington, D.C., pp. 697-703 <http://www.iom.edu/Reports/2001/Dietary-Reference-Intakes-for-Vitamin-A-Vitamin-K-Arsenic-Boron-Chromium-Copper-Iodine-Iron-Manganese-Molybdenum-Nickel-Silicon-Vanadium-and-Zinc.aspx>
5 In practice, the proportion of the requirements distribution above the approximate midpoint of the range of usual nutrient intakes is taken to be the probability of inadequacy within that range.⁴
6 Not actual data – for the purpose of illustration only
7 National Health and Medical Research Council and New Zealand Ministry of Health, 2006, Nutrient Reference Values for Australia and New Zealand, <https://www.nrv.gov.au/nutrients/iron>, last accessed 4/2/2015
8 Mulrine, H & Mackerras, D. 2011, ‘Beaton’s probability approach for estimating prevalence of inadequate iron intakes applied to Australian data’, Proceedings of the Nutrition Society of Australia, vol. 35, poster 94.
9 Originally the IOM requirements distributions were derived via Monte Carlo simulation of the requirements distributions for each age-sex group, based on a factorial model, with log-normal estimation of menstrual losses for females, from which percentiles of requirements were empirically estimated.

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