INTRODUCTION

The prevalence of iron deficiency anemia in preschoolers is one of the concerns in
public health. A study conducted in daycare centers with children under five years of
age in the city of Rio de Janeiro presented a prevalence of 47.3%^{1}.

The Ministry of Health^{2} has implemented, among others, the National Program for Iron Supplementation,
along with the mandatory fortification of wheat and corn flour with Iron and Folic Acid,
and nutritional orientation, which constitute the set of strategies that aim at
controlling and reducing iron deficiency anemia in the country. The main point of this
nutritional orientation is the concern with the bioavailability of Iron from vegetables,
as its absorption is favored in the presence of Vitamin C and hindered in dairy foods
due to the presence of Calcium, and also in foods that are rich in phytates^{3}. The Ministry of Health^{4} also recommends that children be breastfed at least until six months of age.

Data from the 2002 - 2003 Family Budget Survey (FBS) point to an increase in the
consumption of industrialized products, which are rich in saturated fat and
monosaccharaides, and to a decrease in the intake of greens, fruits, legumes and
cereals. Legumes, a source of Iron from vegetables, need to be ingested with Vitamin C
in order to make Iron bioavailable^{3}. However, upon observing the consumption of black beans in the FBSs, a reduction
of 30% was verified between the periods of 1974 - 1975 and 2002 - 2003^{5}
^{,}
^{6}.

Evaluating food consumption among children is a fundamental tool to plan initiatives of health promotion and prevention of iron deficiency anemia in groups at risk.

A document of the Institute of Medicine^{7} presents two methods to apply the DRI (Dietary Reference Intake) in dietary
assessments, with calculations of the probability of adequacy/inadequacy for groups in
Appendix E, and also for individuals. However, there is a more marked scarcity of works
produced with the purpose of showing the distribution curves of these nutrients with
gross and adjusted data, thus indicating the probability of adequacy/inadequacy in
population groups. The purpose of this study was to determine the prevalence of adequate
ingestion of Iron and Vitamin C in the diets of preschoolers by considering both methods
described above.

METHODOLOGY

This study is part of a project linked to the line of research Nutrition and Life
Quality, conducted at Universidade do Estado do Rio de Janeiro. It was approved by the
Ethics Committee of Pedro Ernesto University Hospital (794-CEP/HUPE), and it complies
with Resolution 196/96 of the National Health Council^{8}. The participants were children whose legal guardians signed the informed
consent form.

This is a cross-sectional study carried out in 2009. We included in the sample 238
children from 2 to 3 years of age, enrolled for the same school period in 25 full-time
daycare centers - 21 private and 4 public - in the city of Rio de Janeiro. The inclusion
criterion was the absence of chronic diseases that could interfere with their
nutritional status. The initial proposal was to include all the children enrolled in the
daycare centers. However, this was not possible due to the refusal of some legal
guardians to keep a food journal that would complement the dietary survey. For this
reason, the participants composed a pilot sample for which we calculated precision by
considering the average of Iron and Vitamin C intake^{9}. Figure 1 displays our methodological
procedures.

During phase 1, the food consumption of the preschoolers while at the daycare centers was obtained by means of directly weighing their food on three nonconsecutive days and analyzing the nutritional composition of the meals.

In order to quantify the foods and preparations consumed at the daycare centers, the solids were weighed with a digital scale that had a maximum capacity of 2 kg, graduation of 1 g, tare function, and automatic actuation. The liquids were measured with the aid of graded containers and registered on a specific form before being offered to the children. The foods that had their quantity or volume stated on their labels/packages were not weighed.

In case the child asked for a second serving, the same portion given in the first serving was provided, and the same procedure described above was followed.

When there were leftovers at the end of each meal, we weighed what was left on the plate or cup of each child. To obtain the amount of each component of the meals offered, we considered the weight of the leftovers in proportion to the weight of the foods initially portioned and included in the meal. In case the children selected which components were part of the meal offered, the leftovers were calculated by the difference between the total weight of the meal and the foods selected. Next, we calculated the percentage of each component's participation in the mix. The individual food ingestion of each preparation was obtained through the formula:

Individual food ingestion = portion offered - leftovers

With the purpose of complementing the assessment of the children's daily ingestion, their legal guardians kept a food journal. They were oriented to write down the foods and beverages ingested by the children before and after daycare. These foods were described in household measurements and later converted into grams and milliliters. The parents or legal guardians were contacted whenever we had doubts about the foods recorded.

A quantitative evaluation of the nutritional composition of the children's diets was
conducted with the aid of the program Diet Pro version 4.0^{10}, information displayed on labels, and the Brazilian Food Composition Table^{11}.

Phase 2 comprised the verification of the possibility of using the procedures listed on
the *Estimated Average Requirements* (EAR) as a cut-off point of adequacy
of Iron and Vitamin C in the group of children, according to the presuppositions
displayed on Figure 1. In case all the
presuppositions were confirmed, the EAR method would be used as a cut-off point for the
groups. Otherwise, we would opt for the "EAR as the cut-off point for individuals".

With the purpose of verifying whether the nutrients' consumption and requirements were
independent statistically, we opted for the graphic method proposed by Bland &
Altman^{12}. This method is based on the premise that there is no obvious relation between
the differences of values obtained from two matrices yielded by the application of
different procedures. Under these circumstances, a lack of concordance can be identified
by calculating potential biases estimated through the average of the differences and
their respective standard deviation. The authors argue that what is sought is a
concordance between the matrices, and not an association. According to this proposal,
the difference between the matrices' values show the distance between the latter, which
represent concordance or independence^{13}.

The symmetry in the distribution of requirements was verified by asymmetry coefficient
percentiles^{14}. Regarding the last premise - namely that variances in the distribution of
requirements would be small in relation to consumption distribution - our point of
departure was the coefficient of variation (CV) established for the age range from 1 to
8 years^{15} at 40% and 10% for Iron and Vitamin C, respectively. Next, we calculated the
standard deviation using the EAR and the variances.

The use of the EAR method as a cut-off point for the groups followed the sequence
explained below^{16}:

a) We verified the Gaussian behavior of the consumption distribution of the nutrients in question using Kolmogorov-Smirnov's test (K test). If normal, we carried on the procedure; if not, the variables were transformed into Napierian logarithms. The K test was again applied to the converted variables. The gross values of the variables with normal distribution were used; for those with normal distribution after the aforementioned transformation, we used logs;

b) Estimates of intrapersonal (S^{2}w) and interpersonal (S^{2}b) variances, calculated through the analysis of the variance (one-way ANOVA) of
consumption per individual during three days.

Ratios:

Intrapersonal variance: S^{2}
_{W} = QM_{w }

Interpersonal variance: QM_{b} = S^{2}
_{b} = (QM_{b }- S^{2}
_{W}) / K

In which:

QM_{w}: Intrapersonal quadratic mean

S^{2}
_{W}: Intrapersonal variance

QM_{b}: Interpersonal quadratic mean

S^{2}
_{b}: Interpersonal variance

K: number of days of dietary survey of each individual;

c) Calculation of the ratio between interpersonal and observed standard deviations:

S_{b }/ S_{obs} = 1 / [(1 + S^{2}
_{W }/ K * S^{2}
_{b})]^{1/2};

d) Calculation of the mean ingestion of the nutrients, considering the K days of survey for each individual;

e) Adjustment of the observed mean ingestion of the nutrients for each individual:

Adjusted variable of the nutrient = mean + (x_{i} - mean) * S_{b }/
S_{obs}

In which:

Mean: represents the group's consumption average

X_{i}: the value observed for each individual.

This adjustment in the observed consumption distribution was necessary so as to remove day-to-day consumption variability (intrapersonal variability). The results estimated the habitual consumption distribution, thus better reflecting interindividual variability within the group;

f) Reconversion of log variables into original units;

g) Adjusted distribution of the nutrients;

h) Calculation of the prevalence of inadequacy in the population group: proportion of individuals in the group whose habitual intake was below the EAR established for the nutrient;

i) Calculation of the probability of inadequacy given by the area under the normal curve, which corresponds to the proportion of individuals with consumption adequacy/inadequacy12:

Z = (mean - EAR) / sd; in which sd: standard deviation.

When using the EAR method as the cut-off point, our point of departure was the premise
that the best estimate of an individual's necessities is given by the EAR (estimated
average nutritional needs), since the true necessity of each individual assessed is
unknown^{12}
^{,}
^{17}.

The needs varied among the individuals, even when they were in the same stage of life
and were of the same gender. Therefore, it is important to take this variability into
account, given by the nutrient's CV. For analytical purposes, in the present study we
opted for using a CV of 10% for the nutrients, as suggested by the Food and Nutrition
Board of the Institute of Medicine (IOM/DRI)^{16}
^{,}
^{17}.

In order to calculate the "apparent adequacy"^{18} of the nutrients, we used a statistical approach that enables estimates of the
degree of confidence at which the intake of nutrients fulfills the individual's needs.
With this approach, we compared the difference between the average of "n" days of
consumption (the best estimate of habitual intake) and the EAR. The equation devised
also takes into account the variability of the individuals' necessities (Vnec) and
day-to-day intrapersonal variation (Vint). The result is a Z score through which the
probability that a diet is adequate is determined. We considered an individual "apparent
ingestion"^{18} adequate when the probability was higher than 0.7^{17}.

Z= D / DPp = Mean of "n" days of consumption - EAR / root (Vnec + Vint / n)

In which:

Vnec: variability of the individuals' necessities;

Vint: interpersonal variance, obtained from North American population studies^{7};

n: number of days in which the individual's ingestion was assessed.

In the third phase, we used the method of probabilistic approximation only for Iron, since the requirements for Vitamin C distribution were unavailable. The statistical method of probabilistic approximation (risk curve) combines the requirements for distribution and the individual's ingestion in order to verify the probability of risk for iron deficiency anemia.

In the construction of the risk curve, the requirements for Iron were given by the
ordinate, and the probability of risk for iron deficiency anemia by the abscissa. Iron
deficiency anemia was outlined here based on the estimated percentiles of distribution
of the requirements for iron (mg/d) for children, adolescents and adults, available in
Appendix I, table I-3^{15}, where the estimated percentiles are P_{2,5;} P_{5,0;}
P_{10;} P_{20;} P_{30;} P_{40;} P_{50
}(EAR)_{;} P_{60;} P_{70;} P_{80;}
P_{90;} P_{95} (*Recommended Dietary Allowance* -
RDA), and the intervals follow a succession in tens. The last two percentiles are
allocated at 95 and 97.5. Each percentage point is followed by the required amount of
Iron in milligrams. The risk expressed on the abscissa created in the present study
corresponds to each percentile cut-off point divided by 100, as the probability of
occurrence had to be described between 0.00 and 1.00.

RESULTS

The profile of the dietary consumption of the nutrients in question during the three days of observation is presented on Table 1.

Nutrients | Statistics | Minimum – Maximum | Median | Mean (SD) | Variance | Coefficient of variance | 95%CI |
---|---|---|---|---|---|---|---|

Iron | Intake 1 | 0.70 – 13.63 | 6.86 | 6.23 (2.15) | 4.64 | 34.56 | 0.27 |

Intake 2 | 0.60 – 16.61 | 7.10 | 6.20 (2.28) | 5.19 | 36.72 | 0.29 | |

Intake 3 | 0.80 – 15.95 | 6.95 | 6.30 (2.20) | 4.86 | 35.00 | 0.28 | |

Mean of the 3 days | 0.70 – 15.39 | 6.73 | 6.25 (2.15) | 4.62 | 34.43 | 0.27 | |

Vitamin C | Intake 1 | 3.80 – 78.31 | 15.04 | 17.33 (9.88) | 97.71 | 57.03 | 1.26 |

Intake 2 | 2.80 – 128.09 | 15.12 | 18.46 (15.18) | 230.34 | 82.22 | 1.93 | |

Intake 3 | 3.10 – 155.17 | 14.96 | 19.76 (17.38) | 302.05 | 87.96 | 2.21 | |

Mean of the 3 days | 3.23 – 106.36 | 15.00 | 18.52 (12.59) | 158.51 | 67.99 | 1.60 |

^{SD}: standard deviation

The mean amount of Iron and Vitamin C consumed during the three days of observation was 6.25 mg and 18.52 mg, respectively. The relative error of the estimates of mean Iron consumption reached 4.37% (CV = 34.43%); for Vitamin C, it reached 8.64% (CV = 67.99%). These findings denote a high variability for both nutrients, more expressively for Vitamin C.

It was only possible to verify the presupposition about the independence between
consumption and requirements in the case of Iron^{15}
^{,}
^{19}, as there were no available data regarding Vitamin C. For this purpose, we used
the children's mean Iron intake.

As displayed on Figure 2 - Bland and Altman's
dispersion diagram^{12} - we verified that all differences rested below -1, with an expressive distance
from 0, thus indicating dependence between consumption and daily requirements.

Upon verification of the symmetry of Iron requirements, the percentile coefficient of
asimmetry^{14} reached 0.22, which indicates that its distribution is approximately
symmetrical.

The variance of the distribution of Iron requirements (1.44 mg) was small in relation to the distribution of consumption (4.20 mg). The only presupposition that was rigorously met pertained to the variance of the distributions.

We initiated the procedure of applying the EAR as a cut-off point for groups by verifying the Gaussian behavior of the distribution of Iron intake (Table 2). The results show that the intake distribution during the three days of observation did not meet the requirements of the method, even though we attempted to convert the distributions into logarithms.

Normality Test | ||||||
---|---|---|---|---|---|---|

Iron | ||||||

I1 | I2 | I3 | Decision | |||

KS Distance | p-value | KS Distance | p-value | KS Distance | p-value | |

Gross values | ||||||

0.1657* | < 0.0001 | 0.1664* | < 0.0001 | 0.1633* | < 0.0001 | no |

Logarithmized values | ||||||

0.1827* | < 0.0001 | 0.2040* | < 0.0001 | 0.1889* | < 0.0001 | no |

^{*}significant

^{KS}: Kolmogorov-Smirnov.

In light of this, we proceeded to establish adequacy individually. Considering a cut-off
point higher than 0.70 as the probability of adequacy^{17}, we found that 70.0% and 7.9% of the children had adequate intakes of Iron and
Vitamin C, respectively.

Table 3 presents the prevalence of adequacy and inadequacy according to the EAR and the RDA. Considering the latter, the prevalence of adequacy was expressively low both for Vitamin C and Iron.

Probability of adequacy | Discrimination | Nutrients % | |
---|---|---|---|

Vitamin C | Iron | ||

Recommended Dietary Allowances (p ≥ 0.98) | Adequate | 0.4 | 2.5 |

Estimated Average Requirements (p = 0.50 to p < 0.98) | 61.8 | 88.7 | |

Figure 3 displays the risk curve for Iron. To verify this probability of risk, the intake was placed on the ordinate that expresses requirements, and a perpendicular line was traced until it touched the curve. At this point, a line was traced in parallel to the ordinate. The point that touches the abscissa indicates the probability of risk.

Drawing on the graphic (Figure 3), it was possible to estimate the risk for Iron consumption by tracing up a perpendicular line that started at the abscissa until it touched the curve and a parallel line was drawn from this intersection point to the ordinate. For instance, a child in the group studied who presented a mean Iron consumption of 2.73 mg in three days of observation had a probability of inadequacy of 0.625.

DISCUSSION

In the present study, the mean Iron and Vitamin C intake in the three days of
observation was 6.25 mg (CV = 34.43) and 18.52 mg (67.66), respectively. In an
interventional study carried out with data from a large transversal survey in the city
of São Paulo between September 1995 and September 1996, the authors found an Iron intake
of 7.7 mg in the control group and of 7.6 mg in the intervention group before the
intervention, as recorded on food journals, both with CV = 5%^{20}. Comparing these findings, it is possible to verify a high variability in
Vitamin C consumption^{17}. In another study, of a longitudinal nature, in which the participants were 35
children between 2 and 3 years of age of both sexes, enrolled in a philanthropic daycare
center in Ilha de Paquetá, Rio de Janeiro from 2003 to 2004, the authors found an Iron
intake of 5.1 ^{±} 1.7 mg (p < 0.001; CV = 33%) and a Vitamin C intake of
31.5 ^{±} 25.5 mg (p < 0.001; CV = 81%)^{21}. These values are approximate to the ones found in the present study, and
reaffirm the variability in the consumption of both nutrients.

The guidelines of the Subcommittee for DRI Interpretation and Use alert that the RDA
should not be used as a cut-off point to assess nutrient intake in groups, as this level
of consumption exceeds the requirements of 97 to 98% for all individuals whenever the
requirements within a group have normal distribution. This recommendation aims at
avoiding overestimates of the proportions in groups at risk for inadequacy^{19}.

In this sense, it is necessary to use the methods in question, probabilistic approximations, and the EAR as cut-off points to assess the prevalence of inadequacy of nutrient intake.

Both methods demand independence between daily ingestion and requirements. In order to
evaluate this premise, in the case of Iron, we used Bland & Altman's method^{12}, as its advantage is that the matrices of the data are exempt from Gaussian
behavior, and a minimum of 10 measurements in pairs can be used^{22}. The requirement measurements obtained through the reference percentiles for
Iron totalized 13.

It is observable that all differences are within the interval ranging from -4.59 to
-0.89, which is quite distant from a null difference, thus indicating independence
between requirement and ingestion (Figure 1).
However, using the deviation ratio proposed by Delcourt^{13}, we cannot affirm this independence.

The percentile coefficient of asymmetry for Iron points to an approximately symmetrical
distribution of Iron requirement (0.22), inferred from its position in relation to the
EAR. The daily requirements for Iron include the necessary amounts to replace fecal and
dermatologic elimination, and this aspect might have symmetrically affected Iron
distribution in the population of reference. In case of lack of additional information
about the requirement distribution of a given nutrient, it is implicitly assumed on DRI
reports that the unknown distribution is considered symmetrical, based on median
requirements - EAR. Thus, when the fact that a certain requirement distribution is
asymmetrical comes to light, a probabilistic approach can be used to compute a risk
curve that reflects an asymmetrical requirement. The guidelines of the Subcommittee for
DRI Interpretation and Use reveal that moderate asymmetry values in requirement
distribution can result in noticeable biases when estimating prevalences by means of
cut-off point methods^{7}.

Although presuppositions of symmetry in the requirement distribution of a given nutrient
and the independence between consumption and necessity are assumed in the DRI's
document^{7}, we verified all presuppositions. It is worth highlighting that this premise
originated from population studies with larger samples than the one presented here. In
the case of Iron, the EAR is determined by a factor model based on median components of
its requirement for men and women. In the case of children, gender is ignored, as the
differences are small. Taking Vitamin C into account, the RDA was established with a
coefficient of variation of 10%. The EAR can be estimated by dividing the RDA by
1.20^{18}. Both were established based on the recommendations for adults, according to
body weight.

In this study we also took care of verifying the Gaussian behavior of the distributions of the ingestion observed; when it was absent, we adopted logarithmic normal distribution, which was the particular case of Vitamin C. However, the normality test did not allow for considerations of the Gaussian behavior of the consumption curves, preventing us from using the method for groups which enables the displaying of the gross and adjusted distributions of a nutrient's intake.

Although daycare centers offer institutionalized meal services, the variance in Iron
consumption, considering the three days of ingestion, was 4.62 mg (Table 1). The variance of distribution to determine
Iron requirements is 1.44 mg. Situations in which the variance of distribution to
determine Iron requirements is higher than the variance of its consumption - which is
not the case in this study - are related to the monotony of the menus, since the
portions served are controlled^{7}. It is important to highlight that the mean Iron consumption, considering the
three days of ingestion, was between the values of the EAR (4.1 mg) and of the RDA (7
mg)^{15}, which ensures at least 50% of the nutritional recommendations for the
population of interest.

With the information obtained, we constructed the risk curve for Iron. However, it was
not possible to construct it for Vitamin C, in view of the lack of available research
data that could be the basis for establishing the EAR for the 1 to 18-year age range.
Consequently, the requirement distribution is also not available for this population.
The EAR for children and adolescents was estimated by adjusting the data for adults and
based on differences in reference weights^{7}.

The EAR method as a cut-off point is valid when the prevalence of inadequacy in a given
population is higher than 8 to 10%, or lower than 90 to 92%^{7}. In this study, we verified a prevalence of inadequacy of 37.8% and 8.8% (Table 3) for Vitamin C and Iron, respectively.
These findings suggest validity only in the case of Iron.

In regards to the quality of the data on dietary consumption, we must point out some
obstacles, as tables that display food composition do not include Iron and Vitamin C in
a large number of fortified industrialized foods, wheat flour, and cornmeal^{23}. This problem is aggravated by the non-regulated addition of these nutrients to
food products, especially those directed to children. Possible interferences with the
calculations of the adequacy of Iron and Vitamin C are due to overestimates of
consumption.

Information on the food ingestion that occurred at the daycare centers was obtained by
means of direct weighing, complemented by food journals in which the foods consumed at
home or out were registered using household measures. In Brazil, there are no norms that
determine the standardization of utensils, which may have contributed to biases in the
intake observed. Fisberg et al.^{18} highlight that, despite the complexity of assessing diets, and keeping in mind
the recognized imperfection of dietary surveys, this method can provide data that are
indispensable in pinpointing dietary conducts. On the other hand, we did not investigate
the consumption of vitamin and mineral supplements that were potentially included in the
diets^{24}.

CONCLUSION

The use of EAR as a cut-off point applied to individuals identified that 62.2% and 91.2% of the children have adequate amounts of Vitamin C and Iron in their diets, respectively. According to the EAR, this is an expected result. In relation to the RDA, the percentages reached 0.4 and 2.5.

The DRI represent the most thorough set of nutrient reference values developed for planning and assessing habitual food intake. Considering that we used the methods suggested by the Subcommittee for DRI Interpretation and Use, this study contributes in assisting professionals who work in the field of Public Health Policies.

Studying the prevalence of adequacy of Iron and Vitamin C in children's diets enables the tracking of nutritional factors that might impact interventions in populations at risk. The application of DRI allows for evaluations of causal processes and risks in nutritional safety, thus contributing towards the primary prevention of nutritional deficiencies.

In a relation of causality, the sufficient cause - that is, nutritional deficiencies - will be present when an illness occurs. In this sense, the nutrients Iron and Vitamin C were privileged here, in view of the scenario of iron deficiency anemia in Brazil, and considering that Vitamin C stimulates the absorption of heme and non-heme Iron. However, if the food intake of Iron is inadequate (necessary cause), serum concentrations are compromised even when iron deficiency anemia does not occur (hidden hunger).

Studies on the probability of diet adequacy by means of nutritional markers can reduce the probability of occurrence of nutritional deficiencies in children in comparison to others with adequate diets.