Implementing food-based dietary guidelines for - United Nations ...

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FIG. 2. Situation in which the ANR cannot be used to estimate
prevalence of inadequacy. When the variability in the
usual intakes of a group is less than the variability in requirements
for a nutrient, the cut-point method, using the ANR
to estimate the prevalence of inadequacy, cannot be applied.
Other methods to estimate prevalence of inadequacy can
be employed [5]. In order to detect rare but widely diverse
requirements in a given population, much larger sample sizes
are needed. (ANR, average nutrient requirement)
intake is greater than the variation in requirements (see
Murphy and Vorster [2] in this issue). Low variability
in intake therefore leads to the need for a larger sample
size [16] in order to obtain good estimates of the true
variation that exists within the population.
This need for very large sample sizes to determine
normal small variation in responses and to differentiate
normal variation from abnormal deviation due to differences
in intake may be demonstrated when diet and
disease relationships are observed in large population
groups but are not subsequently statistically supported
in clinical trials. Frequently such trials are said to be
“underpowered,” since the sample size is not adequate
to demonstrate a relatively rare effect that, although it
may occur, will not show up in a random selection of a
small group of individuals (the group sampled) to the
extent that it would be considered as not occurring
by chance. This has been given as a major reason that
relationships evaluated in intervention trials of different
dietary patterns and the subsequent incidence of
cancers are less than conclusive, although large sets of
observational data from population groups appear to
demonstrate significant associations [13].
When epidemiologic information is used as the
basis for determination of nutrient adequacy, the
data or criteria chosen must be representative of the
group of interest and adequately powered (by a large
enough sample size) to detect relatively small differences
in response (table 3). In order to have adequate
power (1 − β) when small changes in chronic disease
outcomes due to diet are evaluated, sample sizes need
to be large.
Values based on clinical trials or intervention studies.
Statistics are available to estimate the sample size necessary
to determine the ANR as well as the SD ANR in a
population group of interest. Such methods require
» Specifying the minimum difference needed for a
clinically relevant or important indicator of adequacy
(µ 1 – µ 0 );
» Determining the level of confidence (1 − α) that the
difference should represent between the response
due to the variable tested versus a random occurrence;
» The probability (1 − β) that if the specified minimum
difference is not attained, then there truly is not a
meaningful difference in response; and
» An estimate of the probable variance (σ T ) in the
overall population.
If all these are determined, are available, or can be
estimated, then this general formula can be applied to
obtain the relevant sample size:
n = [2 (t α + t β ) σ/(µ 1 – µ 0 )] 2 .
Although components such as (µ 1 – µ 0 ), α, and β can
be set or defined by the researcher, the expected variance
(σ) of the population can only be estimated, and
this is not always possible to do well. A possible source
of estimation is from other similar studies or previous
work.
Given the typical lack of data on human nutrient
requirements that include usable estimates of variation,
pilot studies or validation studies are frequently
conducted prior to initiating expensive larger studies
to get an idea of the variation in response present, thus
providing an estimate of σ T . The costs of such pilot
studies may make it impossible, though, to get estimates
of the variation expected for use in determining
the needed sample size. However, without determining
the size of the sample needed to adequately evaluate a
requirement, the study may be underpowered and not
provide meaningful conclusions.
Many studies of nutrient requirements must limit
the number of subjects studied because of limitations
in space, the number of samples, and the measurements
that can be analyzed with available funds. The
goal when testing multiple levels of intake is to see a
nutritionally relevant difference in response; often this
is not specifically set in advance, with the assumption
that the statistical tests performed will indicate what is
statistically significant. It is then up to the researcher
TABLE 3. Resulting β values for various sample sizesa N 100 200 300 400 500 600 700
β 0.71 0.48 0.31 0.19 0.11 0.06 0.04
a. Example for a given value of α (0.05), predicted mean (0.2), and clinically significant difference of 50%
(0.10), β values are the probability of making a false negative conclusion (type II error).
Source: Matthews and Farewell [17].
A. A. Yates