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OCR for page 196
Act justment of Observec!
Intake Data to Estimate the
Distribution of Usual Intakes
in a Group
An incliviclual's actual intake varies considerably from one clay to
the next, but it is usual or long-term average intakes that are of
interest in assessing and planning clietary intakes to ensure nutrient
acloquacy for inclivicluals or groups. As explained in a previous re-
port (IOM, 2000a), serious error in the assessment of nutrient inaci-
equacy or excess can occur if the clietary intake ciata examined do
not reflect usual intakes. This poses a major obstacle to the assess-
ment of an incliviclual's nutrient intake because his or her usual
intake is generally poorly estimated from only a few clays of observa-
tion, yet more extensive ciata collection is rarely feasible. Assess-
ments of nutrient acloquacy among groups are facilitated by the
availability of statistical adjustment procedures to estimate the clis-
tribution of usual intakes from observed intakes, as long as more
than one clay of intake ciata has been collected for at least a repre-
sentative subsample of the group. These procedures do not yield
estimates of usual intake for particular inclivicluals in the group, but
the acljusteci distribution of intakes is appropriate for use in analy-
ses of the prevalence of inacloquate or excess intakes in the group.
In recent years a number of different statistical procedures have
been clevelopeci to estimate the distribution of usual intakes from
repeated short-term measurements (Hoffmann et al., 2002~. Two
commonly used adjustment procedures are clescribeci here: the Na-
tional Research Council (NRC) method and the Iowa State Univer-
sity (ISU) method. Both procedures are based on a common con-
ceptual foundation, but the ISU method includes a number of
statistical enhancements that make it more appropriate for use with
196
OCR for page 197
APPENDIX E
197
large population surveys. The NRC method is simpler and may be
more appropriate than the ISU method for use with small samples
(those with less than 40 to 50 inclivicluals). However, neither meth-
oci is without limitations.
THE NATIONAL RESEARCH COUNCIL METHOD
Conceptual Underpinnings
In assessing nutrient acloquacy it is necessary to estimate usual
intake. However, usual intake cannot be inferred from measures of
observed intake without error. For any one incliviclual,
Observed intake = usual intake + measurement error
The observe ci variance ~ V0bserved) of a clistribu tion of in take s for a
group baseci on one or more clays of intake ciata per incliviclual is
the sum of the variance in true usual intakes of the inclivicluals who
comprise the group (e.g., the between-person or interindividual
variance, Vbetween) and the error in the measurement of inclivicluals'
true usual intakes. Error arises both because of the normal variation
in inclivicluals' intakes from one clay to the next and because of
random error in the measurement of intake on any one clay. It is
referred to as the within-person, ciay-to-ciay, or intraincliviclual vari-
ance ~ Vwithin) (NRC, 1986) ~
Vobserved Vbetween + Vwithin + Vunderreporting
The observed distribution of intakes will be wider and flatter than
the true distribution of usual intakes as a result of the presence of
within-person variance. However, assuming that the within-person
variation is random in nature, the estimate of mean intake for the
group will not be influenced by this variance.
If multiple days of intake data per individual are averaged, and
the distribution of intakes in the group is constructed from the
means of each incliviclual's multiple intakes, then the error variance
(e.g., within-person variance) diminishes as a function of the num-
ber of clays of intake ciata per person. Thus, as the number of clays
of ciata per person increases, the distribution of observed intakes
Expressed as the inclivicluals' observed mean intakes over the clays
of ciata collection) becomes a better and better approximation of
the true distribution of usual intakes in the group.
The NRC method (NRC, 1986) is typically applied to a data set
OCR for page 198
198
DIETARY REFERENCE INTAKES
comprising multiple clays of intake ciata for a sample of inclivicluals,
ideally with an equal number of observations per incliviclual. This
method of estimating the distribution of usual intakes works by first
partitioning the observed variance into its between- and within-per-
son components, and then shifting each point in the observed clis-
tribution closer to the mean by a function of the ratio of the square
roots of the between-person variance (VbeGween) and observed vari-
ance (VObs~e~) In this way, the method attempts to remove the ef-
fect of within-person variation on the observed distribution. The
variance of the acljusteci distribution should represent VbeGween.
Application
The steps in the NRC method are outlined below. The method is
illustrated using ciata on the zinc intakes of 46 women recorcleci
over three, nonconsecutive, 24-hour clietary intake recalls (a sub-
sample of women drawn from a earlier study by Tarasuk and Beat-
on t19991~.
Step I. Examine normality of distribution and transform data if
necessary.
This adjustment procedure clepencis on the properties of a nor-
mal distribution, yet the observed distribution of intakes for most
nutrients is likely to be positively skewoci. This is because the clistri-
bution is naturally truncated at 0 (i.e., reported intakes cannot fall
below this value) but has no limit at the upper encl. Thus it is imper-
ative that the normality of the 1-clay intake ciata be assessed. (This
can be accomplished through the NORMAL option in PROC
UNIVARIATE in SAS.) If departures from normality are cletecteci,
the ciata should be transformed to approximate a normal clistribu-
tion. The most appropriate transformation will clepenci on the shape
of the original distributions it may have a logarithm, square root, or
cubed root relationship.
Note that for this example, the assessment of normality is con-
ducted on all 138 days of recall data (e.g., 46 women multiplied by 3
clays). The Shapiro-Wilk statistic, W. provides one measure of the
normality of the ciata (Tarasuk and Beaton, 1999~. For the raw ciata,
W= 0.85 (versus a value of 1 for normally clistributeci ciata), and the
distribution departs significantly from normality (p < 0.0001~. A vi-
sual inspection of the plotted ciata reveals that they are right-skewoci.
Through a process of trial and error, a more normal distribution is
achieved by applying a cubed root transformation to these ciata.
OCR for page 199
APPENDIX E
199
The W of the transformed ciata is 0.99 (p = 0.1812) . The next two
steps in this adjustment procedure are conclucteci using the trans-
formeci ciata.
Step 2. Estimate the within- and between Person variance.
Some statistical packages have procedures for partitioning the vari-
ance of the observed ciata into the within- and between-person vari-
ance components (e.g., PROC VARCOMP in SAS). This can also be
easily accomplished using the analysis of variance procedures avail-
able in most statistical packages by conducting a simple one-way
AN OVA with subject ID inclucleci as a categorical or class variable. A
sample program for SAS is presented at the end of this appendix.
When the raw ciata are transformed to better resemble a normal
distribution, this step is conclucteci on the transformed ciata.
Two values are extracted from the AN OVA output. The mean
square error or unexplained variance (e.g., the variance in the ob-
serveci ciaily intakes that is not accounted for by between-subject
clifferences) represents the within-subject variance in the 1-clay ciata.
The mean square model (e.g., the mean square associated with the
subject ID variable entered into the AN OVA) represents the ob-
serveci variance of the 1-clay ciata. Because the adjustment proce-
clure is applied to an incliviclual subject's mean intakes over the
period of observation, both the mean square model and mean
square error neeci to be clivicleci by the mean number of clays of
intake data per subject to obtain the Vobserved and VwiGhin for this ciistri-
bution (e.g., Vobserve`] = mean square moclel/n and VwiGhin = mean
square error/e). VbeGween can be estimated by subtracting VwiGhin from
Unobserved, as follows:
VbeGween = (mean square model - mean square error)/n
where n is the mean number of clays of intake ciata per subject in
the sample. VbeGween represents the "true" variance of the distribution
of usual intakes. Each of these variance estimates can be expressed
as a stanciarci deviation by simply taking the square root of the vari-
ance.
Table E-1 presents the output for the AN OVA procedure as ap-
plieci to this example. The mean number of clays of intake ciata per
subject is three. In this example, VObserve`' = 0~24633584/3, VwiGhin =
0.13375542/3 and VbeGween = (0.24633584—0.13375542) /3.
OCR for page 200
200
DIETARY REFERENCE INTAKES
TABLE E-1 AN OVA of Zinc Intake of 46 Adult Women,
Shown for Data Transformed Using Cubed Roots
Source
Degrees of Sum of
Freedom Squares
Mean
Square F Value Pr > F
Model
Error
Corrected total
45
92
137
11.08511265
12.30549834
23.39061099
0.24633584 1.84 < 0.0069
0.13375542
Step 3. Adjust individual subjects' mean intakes to estimate the
distribution of usual intakes.
Each subject's mean intake is now acljusteci by applying the follow-
ing formula:
Acljusteci intake = Subject's mean - group mean) x (~DbeGween/
~Dobserved) ~ + group mean
where between iS the square root of VbeGween and Unobserved iS the square
root of Vobserve~ This equation effectively moves each point in the
distribution of observed intakes closer to the group mean, but it
floes not shift the group mean. If the distribution of 1-clay ciata was
transformed prior to partitioning the variance (Step 2), the equa-
tion is applied to the individual subject and group means calculated
from the transformed ciata (Step 3), and the resultant distribution
neecis to be transformed back prior to use (see Step 4~. If the ciata
were not transformed, however, the acljusteci intakes calculated from
this equation now represent the estimated distribution of usual
intakes.
Step 4. If the original data have been transformed, transform the
adjusted intake back to the original units.
If the original ciata were transformed in order to satisfy the neces-
sary assumption of normality, the adjusted data need to be trans-
formeci back into the original units prior to their use for nutrient
assessment. Back-transforming refers to the application of the inverse
function of the original transformation. In this example, the original
ciata were transformed using cubed roots; the back transformation
raises subject's acljusteci intakes to the power of three. The process
of transforming data, adjusting it, and then back-transforming it is
OCR for page 201
APPENDIX E
201
TABLE E-2 Observed Distribution of 3-clay Mean Zinc Intakes
(mg) and Estimated (Acljusteci) Distribution of Usual Intakes
for a Sample of 46 Women
Standard 25th 50th 75th
Zinc Intake Mean Deviation Percentile Percentile Percentile
Observed 3-day means 8.84 3.58 6.11 8.49 10.97
Adjusted intake 8.03 2.20 6.58 8.15 9.33
necessary to preserve the shape of the original distribution for anal-
ysis purposes while removing the within-person variance.
Table E-2 presents a comparison of the distribution of the
observed subjects' 3-clay means to the acljusteci intake. The variance
of the acljusteci intake distribution is substantially less than the vari-
ance of the distribution of the observed 3-clay means, as eviclenceci
by the acljusteci intake's lower stanciarci deviation. In aciclition, the
distance between the 25th and 75th percentiles of the acljusteci
intake distribution is closer to its mean than that of the observed
3-day mean.
If the Estimated Average Requirement (EAR) cut-point method is
applied to the acljusteci distribution to assess the prevalence of
inacloquate zinc intakes among this sample, an estimated 26 per-
cent of women (12/46) appear to have inacloquate intakes (12 of
the 46 acljusteci means were below the EAR for zinc for women of
6.8 mg/ciay). This is lower than the 28 percent prevalence of inacle-
quacy that would be estimated from the unacljusteci ciata.
Special Considerations
Two features of the NRC method deserve special note because
they pose challenges to analysts wanting to use this approach. First
is the requirement for normally clistributeci ciata, and the second is
the handling of incomplete data.
Normality
As noted earlier, the NRC method hinges on having normally
clistributeci intake ciata or being able to transform the observed ciata
into a normal distribution. If nonnormal data are not transformed
prior to adjustment, or if the applied transformation fails to correct
for the nonnormality of the ciata, then assessments of the preva-
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202
DIETARY REFERENCE INTAKES
fence of inacloquacy or excess using the acljusteci distribution will be
inaccurate. Some inclication of the importance of this step comes
from a closer look at the results of the adjustment procedure applied
in the example presented above. Both the mean and the meclian of
the acljusteci distribution are slightly lower than the mean and meclian
of the women's 3-clay means (Table E-2), suggesting that the acljust-
ment procedure has shifted the original distribution toward 0. This
shift is a function of the transformation. Haci the transformation
more completely achieved the properties of a normal distribution,
the observed mean and the acljusteci mean would be equivalent.
It may be difficult, if not impossible, to normalize some observed
nutrient intake distributions with simple power transformations.
Observed distributions of vitamin A, in particular, are notorious for
this problem (Aickin and Ritenbaugh, 1991; Beaton et al., 1983) . In
cases where the ciata fail to satisfy the assumptions of a normal
distribution even when transformed, application of the NRC method
and use of the resultant acljusteci distribution for nutrient assess-
ment is problematic (Beaton et al., 1997~. Depending on the extent
of the departure from normality, it may be preferable to not use the
ciata for nutrient assessment. If assessments are conclucteci on ciata
acljusteci without fully satisfying the normality assumption, at mini-
mum, the problem should be noted so that reaclers can interpret
prevalence estimates with greater caution.
Hand;ting Incomp;tete Data
The NRC method was originally developed for application to data
sets with more than one clay of intake ciata per subject. In clescrib-
ing the NRC method here, it has been assumed that an equal
number of replicate observations are available for each member of
the sample. If there are subjects missing one or more clays of intake
ciata, this can be factored into the calculation of VbeGween, reducing
the denominator of that equation. Nonetheless, it is assumed that
few subjects fall into this category.
In large dietary intake surveys it is increasingly common to collect
two or more clays of intake ciata on a subsample of the larger sample
and use the unclerstancling of within- and between-person variance
cleriveci from this subsample to adjust the intake ciata of the entire
sample. (The ISU method Fusser et al., 1996] is well suited to
handling such ciata.) In surveys involving smaller samples, however,
this practice is much less common. The application of estimates of
within- and between-person variance from a subsample to the larger
sample obviously presumes that the subsample is representative of
OCR for page 203
APPENDIX E
203
the larger sample with respect to all characteristics that affect these
variance estimates. If starting with a smaller sample, this representa-
tiveness may be more difficult to achieve through random sampling.
With minor mollifications to the NRC method outlined here it is
possible to derive variance estimates from a subsample and apply
this information to adjust the 1-clay intake ciata for a larger sample.
However, given the issue of representativeness, it is preferable to
obtain two or more clays of intake ciata on all subjects in a small
sample and use all subjects' ciata in the adjustment procedure.
THE IOWA STATE UNIVERSITY METHOD
Working in conjunction with the U.S. Department of Agriculture,
a group of statisticians at ISU clevelopeci a method to estimate usual
intake distributions from large clietary surveys (Nusser et al., 1996~.
The method is implemented through a software package called
SIDE (Software for Intake Distribution Estimation). It can be used
to adjust observed intakes in large clietary surveys as long as two
nonconsecutive or three consecutive clays of intake ciata have been
collected for a representative subsample of the group. For a full
discussion of the ISU method of adjustment, see Guenther and
colleagues (1997~.
Baseci on the NRC method, the ISU approach includes a number
of statistical enhancements (Guenther et al., 1997) . Specifically, the
ISU method is clesigneci to transform the intakes for a nutrient to
the standard normal distribution, applying procedures that go
beyond the simple transformations that analysts can apply in the
NRC method. The distribution of usual intakes is then estimated
from this distribution of transformed intake values and the esti-
mates are mapped back to the original scale through a bias-acljusteci
back transformation.
The procedures represent a major advance over the NRC method
and a number of other more complicated adjustment procedures
that have been proposed (Hoffmann et al., 2002~. In addition, the
ISU method is clesigneci to take into account other factors such as
day of week, time of year, and training or conditioning effects
(apparent in patterns of reported intake in relation to the sequence
of observations) that may exert systematic effects on the observed
distribution of intakes. The ISU method can also account for corre-
lation between observations on consecutive days and for heteroge-
neous within-person variances (e.g., in cases where the observed
level of ciay-to-ciay variability in inclivicluals' intakes is directly associ-
ated with their mean intake levels). While these refinements could
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204
DIETARY REFERENCE INTAKES
be built into the NRC method, in its simplest form the method floes
not account for autocorrelation or other systematic effects on
within-person variation.
Another particularly valuable feature of the ISU method is its
ability to apply sample weighting factors, common in large popula-
tion surveys, so that the acljusteci distribution of intakes truly esti-
mates the distribution of usual intakes in the target population, not
just the sample. Thus the ISU method is well suited for use with
large survey samples. In a recent evaluation of six different methods,
Hoffmann and colleagues (2002) conclucleci that the ISU method
haci distinct advantages over the others. Most importantly, the method
was applicable across a broaci range of normally and nonnormally
clistributeci intakes of food groups and nutrients.
Despite its strengths, however, the ISU method may not be as
appropriate as the NRC method for use with small samples. The
greater complexity of the ISU method requires a larger sample to
ensure that the various steps in the adjustment procedure retain
acceptable levels of reliability. A smaller sample can be used with
the NRC method because the adjustment procedure is more sim-
plistic (e.g., applying simpler methods of transformation and back-
transformation and not accounting for heterogeneity of within-
person variance).
OTHER CONSIDERATIONS IN THE APPLICATION OF
ADJUSTMENT PROCEDURES
Defining Groups for Data Adjustment
Because nutrient requirements vary by life stage and gentler group,
assessments of nutrient adequacy are usually conducted separately
for particular subgroups of the population. The statistical adjust-
ment of intake ciata whether clone by the NRC or ISU methoci-
shoulci therefore also be conclucteci separately for each group for
which the nutrient assessment will be conclucteci. If intake ciata have
been collected across more than one life stage and gender group, it
is not appropriate to combine subgroups for the purpose of adjust-
ment and then later subclivicle the acljusteci ciata for separate analy-
ses. Similarly, if the intencleci analysis of nutrient inacloquacy is by
stratum within a single life stage or gentler group (e.g., the assess-
ment of nutrient inadequacy for particular population subgroups
clefineci by income or education levels), then the adjustment of
intake ciata should be conclucteci separately for each stratum.
OCR for page 205
APPENDIX E
Adjusting Intake Variables Expressed as Ratios
205
To assess the macronutrient composition of cliets and examine,
for example, the proportion of energy cleriveci from saturated fatty
acicis, it is necessary to examine the distribution of usual intakes for
macronutrients expressed as ratios of total energy intake. The
adjustment procedures clescribeci here can be applied to intakes
expressed as nutrient:energy ratios or as nutrient:nutrient ratios.
However, the ratio of interest should be computed for each clay of
intake ciata first; the observed intakes are then acljusteci to estimate
the distribution of usual intakes as ratios. For example, it is not
appropriate to compute the acljusteci distribution of energy and fat
separately and then combine these distributions for analytic purposes.
Underlying Assumptions and [imitations of Adjustment Methods
One important difference in application of the two methods
clescribeci here is that the ISU method of adjustment is typically
applied to the distribution of intakes on clay one of ciata collection,
whereas the NRC method is applied to multiple-clay means. In the
design of large clietary surveys it is becoming increasingly common
to collect a second clay of intake ciata on only a subsample of the
group. The ISU method is then applied to adjust the entire clistri-
bution of intakes on clay one using the information about within-
person variation that is gleaned from the subsample.
In the application of the NRC method to smaller ciata sets, typically
comprising multiple clays of intake ciata for each member of the
sample, multiple-clay means are used as the basis for adjustment
with the underlying assumption that all clays have equivalent validity.
In ciata sets where a sequence effect is observed, with reported
energy and nutrient intakes declining systematically across multiple
clays of ciata collection (Guenther et al., 1997), the adjustment of
intakes to clay-one ciata will result in a higher estimate of usual intake
than an adjustment baseci on inclivicluals' multiple-clay means. If it
can be assumed that intake on day one has been more accurately
reported than on subsequent clays, then clearly the adjustment to
day-one data will yield a less biased estimate of the distribution of
usual intakes. Because good methods to establish the validity of self-
reporteci intakes on particular clays of ciata collection are lacking, it
is difficult to determine whether day-one data or multiple-day means
are better estimates of true intake. Incleeci, the answer may differ
clepencling on the particular group uncler study and the conditions
of data collection.
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206
DIETARY REFERENCE INTAKES
Neither the NRC nor the ISU method of adjustment is capable of
aciciressing problems of systematic bias clue to underreporting of
intakes. The approaches must assume that inclivicluals have reported
their food intake without systematic bias on clay one, at least, for
the ISU method, and across all clays of ciata collection for the NRC
method. If intakes have been unclerreporteci, the acljusteci clistribu-
tion of intakes will be biased by this underreporting.
Irrespective of the method of adjustment applied, it must also be
assumed that reported food intakes have been correctly linked to a
food composition database that accurately reflects the energy and
nutrient content of the food. Systematic errors in the estimation of
nutrient levels in foocis consumed will bias the estimated clistribu-
tion of usual intakes. In the case of nutrients for which food compo-
sition ciata are known to be incomplete, analysts must gauge the
extent to which reported intakes will be biased. If intake cannot be
estimated without substantial error, it is not appropriate to proceed
with nutrient assessment.
Despite these limitations, the adjustment of observed distributions
of intake for within-person variance to better estimate the clistribu-
tion of usual intakes in a group represents a critical step in the
assessment of nutrient acloquacy or excess. In applying the steps in
planning cliets for groups, as clescribeci in this report, the focus is
on planning for usual intakes. The assessments of nutrient acloquacy
and excess that are required to inform the planning process should
be conclucteci on intake ciata that have been acljusteci to provide the
best possible estimate of the distribution of usual intakes in the
group.
OCR for page 207
APPENDIX E
207
SAMPLE SAS PROGRAM FOR THE NRC METHOD
(Written by G.H. Beaton, University of Toronto, in December 1988 and
modified in January 2002j
This program runs an ANOVA, estimates the partitioning of variance, and
calculates the between-person, within-person, and total standard deviations
(e.g., SDINTER, SDINTRA, and SDTOTAL, respectively) for the data set at
hand with these estimates. The program then adjusts the observed distribu-
tion of mean intakes to remove remaining effects of within-person variation
in intakes. The adjusted data can then be used as input data for the EAR cut-
point or full probability assessment (IOM, 2000a). If the original data are
transformed to better approximate a normal distribution, this program
should be run on the transformed data and the final adjusted data back-
transformed prior to the assessment of nutrient adequacy or excess. Note
that the adjustments should be made independently for each stratification
(e.g., males and females) and should be run on ratios after the ratio has
been calculated.
** NOTE: THIS PROGRAM, AS WRITTEN, ASSUMES THAT THE **
** INPUT DATA SET HAS ONE RECORD FOR EACH DAY OF **
** INTAKE. IF MORE THAN ONE DAY OF INTAKE FOR EACH **
** SUBJECT APPEARS IN A SINGLE RECORD, THE DATA SET **
** WILL NEED TO BE REORGANIZED BEFORE THE PROGRAM **
** IS RUN. **
PROC ANOVA DATA=YOURDATA OUTSTAT=ANOVSTAT;
CLASS SUBIID;
MODEL NUTFUENT=SUBJID;
interest;
DATA PARTIT1:
SET ANOVSTAT;
MS= SS/DF;
MSERROR= MS; MSMODEL= MS;
DFERROR= DF; DFMODEL= DF;
IF_TYPE_= 'ERROR' THEN MSMODEL = .;
IF TYPE = 'ANOVA' THEN MSERROR= .
_ _ ,
IF_TYPE_ = 'ERROR' THEN DFMODEL = .;
IF TYPE = 'ANOVA' THEN DFERROR= .
_ _ ,
KEEP MSMODEL DFMODEL MSERROR DFERROR;
PROC UNIVARIATE NOPRINT;
a<< Change variable name to nutrient of
continued
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208
DIETARY REFERENCE INTAKES
VAR MSMODEL DFMODEL MSERROR DFERROR;
OUTPUT OUT=PARTIT2 MEAN = MSMO DEL DEMO DEL MSERRO R
DFERROR;
DATA PARTIT3;
SET PARTIT2;
MEANREPL = (DFMODEL+DFERROR+1 ) / (DFMODEL+1 );
ERRORDIF = MSMODEL - MSERROR;
IF ERRORDIF LT 0 THEN ERRORDIF = 0;
SDINTRA= MSERROR*~0.5;
SDINTER = (ERRORDIF / MEANREPL) *~0.5;
SDTOTAL= (SDINTER*~2 +(SDINTRA*~2/MEANREPL))~0.5;
INDEX=1;
KEEP SDINTER SDTOTAL INDEX;
PROC MEANS NOPRINT DATA=YOURDATA;
VAR NUTRIENT; BY SUBJID;
OUTPUT OUT= SU BJMEAN MEAN= SMEAN ;
DATA SUBJMEAN; SET SUBJMEAN; INDEX=1;
PROC UNIVARIATE NOPRINT; VAR SMEAN;
OUTPUT OUT=MEANS MEAN = GMEAN;
DATA MEANS; SET MEANS; INDEX=1;
DATA ADJUST;
MERGE SUBJMEAN PARTIT3 MEANS;
BY INDEX;
NRCADJ = GMEAN + (SMEAN- GMEAN) ~ SDINTER/SDTOTAL;
KEEP SUBJID NRCADJ;
RUN;
** THIS IS NOW THE ADJUSTED **
** DATA TO BE USED IN ANALYSIS **
** NEED TO DO FOR EACH OF THE **
** INTAKE VARIABLES IF THIS **
** PROCEDURE IS TO BE EMPLOYED **
DATA FINAL; MERGE YOURDATA ADJUST; BY SUBJID;
PROC PRINT;
TITLE 'NUTRIENT DATA SHOWING INDIVIDUAL OBS, MEAN, NRC
ADJUSTED':
RUN;
Representative terms from entire chapter:
usual intakes
