Dietary Iron Bioavailability: Agreement between Estimation Methods and Association with Serum Ferritin Concentrations in Women of Childbearing Age

Predictive iron bioavailability (FeBio) methods aimed at evaluating the association between diet and body iron have been proposed, but few studies explored their validity and practical usefulness in epidemiological studies. In this cross-sectional study involving 127 women (18–42 years) with presumably steady-state body iron balance, correlations were checked among various FeBio estimates (probabilistic approach and meal-based and diet-based algorithms) and serum ferritin (SF) concentrations. Iron deficiency was defined as SF < 15 µg/L. Pearson correlation, Friedman test, and linear regression were employed. Iron intake and prevalence of iron deficiency were 10.9 mg/day and 12.6%. Algorithm estimates were strongly correlated (0.69≤ r ≥0.85; p < 0.001), although diet-based models (8.5–8.9%) diverged from meal-based models (11.6–12.8%; p < 0.001). Still, all algorithms underestimated the probabilistic approach (17.2%). No significant association was found between SF and FeBio from Monsen (1978), Reddy (2000), and Armah (2013) algorithms. Nevertheless, there was a 30–37% difference in SF concentrations between women stratified at extreme tertiles of FeBio from Hallberg and Hulthén (2000) and Collings’ (2013) models. The results demonstrate discordance of FeBio from probabilistic approach and algorithm methods while suggesting two models with best performances to rank individuals according to their bioavailable iron intakes.


Introduction
While iron deficiency persists as one of the most common nutritional disorders worldwide, which justifies the long-standing international efforts to increase iron intake of high-risk groups, a low dietary iron bioavailability (FeBio) is still presumed as the major cause of anemia (i.e., insufficient hemoglobin levels to meet body tissues demands for oxygenation) in both developed and developing countries [1]. Public health actions to address that issue include iron supplementation programs, food fortification policies, and nutritional counseling, especially targeted to children and women of childbearing age, notwithstanding the high daily iron requirements estimated for these two population groups [1,2].
However, even when an adequate amount of dietary/supplemental iron is provided, a high variability of iron absorption efficiency is expected among normal individuals [3,4]. It occurs mainly that one or more of the algorithm estimates would be associated with women's body iron stores, as measured by SF concentrations. Therefore, we assumed that, after adjustments for physiological losses, variations in steady-state body iron stores are potentially predicted by precise estimates of the usual bioavailable iron intake [25].
To allow comparability of the results, we adopted a definition of dietary FeBio consensually followed by scientific committees reporting reference values of dietary intakes, such as the United Nations Food and Agriculture Organization (FAO) and the Institute of Medicine (IOM) [26,27]. Hence, FeBio was defined as the percentage of the total ingested iron that is absorbed and utilized within the body by individuals with minimal iron stores (SF = 15 µg/L) [16,17].

Participants
This cross-sectional observational study was conducted on the main campus of the University of São Paulo (USP), São Paulo, Brazil, between May 2014 and June 2016. A sample size of 126 women was calculated prior to the start of the study, aiming a test power of 80% and a 2-tailed type I error rate of 5%, to detect significant differences of at least a half standard deviation on log-SF concentration values among women grouped by tertiles of bioavailable iron intake. Recruitment was conducted through posters, flyers, and electronic announcements. Volunteer students were screened using an eligibility questionnaire. If the initial criteria were met, these students were instructed to provide dietary intake information via a web-based system. Then, a blood collection, anthropometry measurements, and responding to general characterization questionnaires were scheduled.
The study protocol was approved by the Research Ethics Committee of the Faculty of Pharmaceutical Sciences from the University of São Paulo (USP) (protocol number: 228.946/03-2013). All volunteers gave their written informed consent prior to participating in the study. Those with any hematological and/or biochemical abnormalities were referred for medical care.

Dietary Data Acquisition
Dietary intake was assessed via three web-based Food Records (FR) and an FFQ, using the online Nutriquanti system [28]. Briefly, the participants used an instruction manual attached to the electronic messages to access the system's webpages and complete FRs on non-consecutive days, including one weekend day. Women were instructed to avoid changing their usual eating habits during the registration period. Moreover, they were encouraged to provide enough details about the types, portions, brands, and preparation modes of all food and beverages, based on a list with more than 3000 items. Meals were self-identified by participants.
Weights and volumes from household measures of all foods and beverages were standardized according to the national reference data [29,30]. Conversions of food into energy, iron, vitamin C, calcium, and alcohol intakes were mostly based on the national food chemical composition tables and [31,32], for few items, on an international database [33]. To add the food components required to estimate FeBio, the analytical data from our laboratory and other independent sources were used to ascribe heme iron [5,[34][35][36], phytate [5,37], and polyphenols (tannic acid equivalents) to foods [5]. Moreover, based on the facts from food labels and standard recipe references [29,30], industrialized foods and composite dishes were broken down into ingredients to estimate the amounts of animal tissues, eggs, soy protein, and iron-fortified flours (corn and wheat). Unit conversions of phytate and raw animal tissue values to phytic acid (3.53 mg = 1 mg phytate phosphorus) and cooked tissue (1 g = 1.3 g raw tissue) were applied when necessary [5,7]. As proposed by Armah et al. (2013), tea and coffee equivalents (cups/day) were calculated by assuming that 1 cup of tea is equivalent to 2 cups (480 mL) of ice tea or 1.5 cup (360 mL) of coffee or herbal tea [13].
Invalid data in FRs were checked using the method proposed by McCrory et al. (2002) [38], assuming a cutoff limit of 2 standard deviations in the ratio between total energy intake (TEI) and total energy expenditure (TEE), as predicted by the equations from Vinken et al. (1999) [39]. Underreports were therefore considered as those whose mean TEI in FRs was lower than 50.8% of their predicted TEE.
All participants with valid FRs were also requested to respond to an online version of a validated FFQ form for adults in São Paulo (SP) [40], which assessed the participants' usual intake frequency of 84 foods, beverages, or food groups in the previous 12 months.

Dietary Data Analysis
Using the online Multiple Source Method (MSM), daily means of all studied dietary variables were adjusted by the intraindividual data variability (deattenuation), to estimate the women's usual intakes [41,42]. Data from the FFQ were used to define true non-consumers and usual consumer of animal tissues and alcoholic beverages, which served in MSM models as adjustment variable of daily heme iron and alcohol intake estimates, respectively. The same strategy was used to estimate the usual tea and coffee intake.
Before being employed in the analysis of correlation or stratification in quantiles, all dietary variables were adjusted by total energy intake values, using the residual method [43].

Probabilistic Approach Estimate
Based on percentiles of iron physiological requirements described by the IOM for healthy adult women users and non-users of hormonal contraceptives [27], we constructed probability distributions of bioavailable dietary iron adequacy, varying in 5% increments, within a range of 0-100%, using the interpolation command of the online R program [44]. Then, these distributions were compared to 40 series of theoretical values of absorptions of the usual iron intake from each woman (range, 1-40%) to identify the probability that those different levels of bioavailable iron intake would meet the reference physiological iron requirements. Finally, the groups' averages of iron inadequacy associated with each of the theoretical dietary iron absorption value was calculated. By approximation, the FeBio of each group was assumed to be the iron absorption value associated with a dietary inadequacy compatible with the prevalence of iron deficiency (SF < 15 µg/L) [45], given the observed usual total iron intake [14]. Finally, the weighted average of the two estimates separately made for user and non-user of hormonal contraceptives was calculated.

Algorithm Estimates
Three meal-based algorithms [Monsen et al. (1978) [7],   [5], and Reddy et al. (2000) [8]] and two diet-based algorithms [Armah et al. (2013) [13], and Collings et al. (2013) [12]] were assessed. Selected characteristics of these five FeBio algorithms are summarized in Table 1. In all calculations, individual's iron status was adjusted to 0 mg body store or a SF concentration equal to 15 µg/L (i.e., absence of iron stores), to estimate the maximum iron absorption from each individual diet and assess the sole influence of dietary factors [16].   calculations. Non-heme iron was calculated as total iron discounted from heme iron. In all algorithms, 50% of the non-heme iron in mandatorily fortified wheat and corn flours from Brazil (4.2 mg of iron/100 g of flour) was not computed [46], since it is presumably not available for intestinal uptake. That assumption is based on the low relative bioavailability of elemental iron and insoluble iron salts [47], mostly employed by Brazilian mills for fortification purposes [46,48].
Previous studies have described some unrealistically non-heme FeBio estimates (>45%) when applying  and Reddy et al.'s (2000) algorithms to meals constituting high amounts of iron absorption enhancers [11,19,49]. Thus, when using these two models, meals with high vitamin C (>85 mg) and animal tissue (>175 g) contents had these values adjusted to 85 mg and 175 g (134.6 g of cooked tissues), respectively. In addition, non-heme FeBio estimates >45% were manually confined to this upper limit [49].
To calculate the dietary intake using Armah et al. (2013) and Collings et al.'s (2013) algorithms, complete diets were assumed as the daily food intake data from each of the women's FRs. For the Collings et al. (2013) model, diets should be classified in three different types: "standard diet", "with inhibitor", and "with enhancer" [12]. Here, two classifications were considered: (1) women self-declared as vegetarians or meat restrictors were considered as having diets poor in iron absorption enhancers and/or rich in inhibitors ("with inhibitor") and (2) omnivorous women was considered as having diets without modification ("standard diet").
Relative FeBio (%) were calculated as the ratio between deattenuated bioavailable iron and total iron intake values (mg/day).

Characterization Questionnaires and Anthropometry
Data regarding women's sociodemographic, lifestyle, and menstrual flow information were collected using a self-administered questionnaire. Self-declared skin color/race was one of the five categories employed in the Brazilian census ("white", "brown/mixed", "black", "yellow/Asian," and "indigenous"). Socioeconomic level was inferred using the national criteria for scoring and stratification of social classes (A-E) [50]. Although vegetarianism or dietary meat restriction was self-declared, we checked the participants' FRs and FFQ data for consistency. The short form of the International Physical Activity Questionnaire version 8 was applied to classify the physical activity levels ("sedentary", "insufficiently active", "active," and "very active") [51].
Based on the usual duration of periods as well as the types and amounts of commonly used tampons and/or pads, we calculated a validated score proposed by Heath et al. (1999) to stratify women according to tertiles of menstrual flow intensity. In addition, due to the great effect of hormonal contraceptives on menstrual iron losses (reduction of~60%) and consequent long-term impact (up to 3 years) on the body iron balance [22,24,27], we carefully investigated the previous use of these medications or devices. Only women reporting no synthetic hormone use for at least 21 months in the last 2 years were considered contraceptive non-users. By contrast, women with a recent abandonment of these medicines were classified as hormonal contraceptive users if reporting a previous treatment of at least 18 months in the last 2 years.
Participants underwent anthropometric measurements three times in light clothing and with no shoes. Height was recorded to the nearest 0.1 cm using a portable stadiometer (Alturexata, Belo Horizonte, Brazil). Weights were recorded to the nearest 0.1 kg using an electronic digital platform scale (Kratos, Embu, Brazil). The mean values of height and weight were then used to calculate the BMI (BMI-kg/m 2 ) and to diagnose undernutrition (<17 kg/m 2 ), low or normal weights (17-24.9 kg/m 2 ), overweight (24.9-29.9 kg/m 2 ), and obesity (≥30 kg/m 2 ) [52]. Moreover, waist circumference (WC) was measured to the nearest 0.1 cm at the midpoint between the lower margin of the last rib and the top of the iliac crest, using a retractable inelastic tape (AvaNutri, Três Rios, Brazil). High WC values served as an indicator of increased risk of cardiovascular and metabolic complications (>80 cm) [53].

Hematological and Biochemical Determinations
Women were requested to fast overnight for at least 8 h before a blood collection (08:00-11:00 a.m.). By venipuncture, blood samples were obtained in vacuum tubes containing EDTA (1.8 mg/µL), for hematological analysis, and in tubes with clot activator gel, for separation of serum by centrifugation at 4.000 RPM for 15 min. All blood analysis was performed by an accredited laboratory from the university hospital.
It has been long recognized that inflammation can increase SF, therefore affecting the assessment of iron status [45,54]. Hence, before any analysis, we corrected the SF concentration values by a possible subclinical infection and/or inflammation, as proposed by Thurnham and McCabe (2012) [54]. CRP > 5 mg/L and AGP > 100 mg/dL indicated the acute phases of incubation (for increased CRP only), early convalescence (for increased AGP and CRP), or late convalescence (for increased AGP only), for which the specific correction factors of 0.77, 0.53, or 0.75 on SF concentration values were applied, respectively [54].

Statistical Analysis
Analysis was performed using IBM SPSS (version 20.0, IBM SPSS Inc., Chicago, IL, USA) and GraphPad Prism (version 5.0, GraphPad Software Inc., San Diego, CA, USA) software. A significance level adopted in all statistical tests was 5%.
The normal distribution of continuous variables was evaluated using Kolmogorov-Smirnov test. When necessary, natural logarithm transformation was applied on variable values to approximate normal distributions. Data are presented as means and standard deviations or geometric means and 95% confidence intervals.
Due to the heteroscedasticity between values distributions, repeated measurements from algorithms (mg/day and %) were compared using the non-parametric Friedman test, followed by Dunn's post hoc test. The linear association between continuous variables was assessed using Pearson's correlation and simple linear regression analysis. To compare the independent groups, chi-square test, likelihood ratio test, or Fisher's tests were used to analyze categorical variables, and Student's t-test or analysis of variance (ANOVA) followed by polynomial contrast for linear trends or Tukey's post hoc test for continuous variables.
Multiple linear regression was used to test the associations between SF and tertiles or combined extreme quartiles of the dietary variables. The covariates included in the multiple models were age (years), BMI (kg/m 2 ), hormonal contraceptive use (yes vs. no), menstrual flow score (tertiles), self-declared skin color/race (white vs. black or brown/mixed; white vs. yellow), and physical activity levels (active vs. insufficiently active; active vs. very active). In sensitive analysis, an additional adjustment for self-declared vegetarianism or dietary meat restriction (yes vs. no) was also tested. In all models, possible interactions between dietary variables and hormonal contraceptive use were evaluated. Residual analysis and collinearity diagnosis were performed to assess the validity of the final regression models.

Participants' Characteristics
The study flow diagram is shown in Figure 1. One hundred and twenty-seven students were included in the final analysis. Mean age was 27 years, and mean body mass index was 22 kg/m 2 . Participants who were considered obese were not recruited; however, 26% of women had high WC and 11% was overweight. According to the national criteria, >80% of the students belonged to upper-middle or upper socioeconomic classes (A-B). About three-quarters of the sample were self-declared as white (74.8%) and two-thirds were classified as physically active or very active (61.4%) ( Table 2). Non-omnivores included 10 lacto-ovo-vegetarians (7.9%), 6 pesco-vegetarians (4.7%), and 2 vegans (1.6%).
None of women reported the use of intrauterine devices. In contrast, 60% of women reported the use of hormonal contraceptives, which was more frequent among women <30 years old (p < 0.05) and those belonging to the upper-middle socioeconomic class (p < 0.05). These women showed significantly lower levels of menstrual flow intensity score (p < 0.01) and, curiously, a higher prevalence of subclinical inflammation (CRP > 5 mg/L) ( Table 2).
Mean total iron intake was estimated to be 10.9 mg/day, which is approximately 6% of heme iron and 29% of iron from fortified corn and wheat flours ( Table 2). Lunch and dinner showed comparable total daily iron amounts (3.71 mg/day and 3.12 mg/day), although differed in almost 50% on their contributions to total daily heme iron intake (62.8% and 33.0%). In turn, breakfast and snacks provided the highest daily amounts of calcium (32.6% and 25.3%) and polyphenols (32.9% and 47.9%) (Table S1).
Geometric mean of SF concentrations was 36.6 µg/L. While no iron overload case was found, iron deficiency was diagnosed in 12.6% of women, one-quarter of whom were also anemic. Even though hormonal contraceptive users had a slightly higher mean total iron intake than non-users (10.3 mg/day vs. 11.2 mg/day, p < 0.05), iron deficiency was three times more prevalent among the latter (6.7% vs. 21.2%, p < 0.05), in accordance with their evident differences in menstrual iron losses (Table 2). evaluated. Residual analysis and collinearity diagnosis were performed to assess the validity of the final regression models.

Participants' Characteristics
The study flow diagram is shown in Figure 1. One hundred and twenty-seven students were included in the final analysis. Mean age was 27 years, and mean body mass index was 22 kg/m 2 . Participants who were considered obese were not recruited; however, 26% of women had high WC and 11% was overweight. According to the national criteria, >80% of the students belonged to uppermiddle or upper socioeconomic classes (A-B). About three-quarters of the sample were self-declared as white (74.8%) and two-thirds were classified as physically active or very active (61.4%) ( Table 2). Non-omnivores included 10 lacto-ovo-vegetarians (7.9%), 6 pesco-vegetarians (4.7%), and 2 vegans (1.6%).
None of women reported the use of intrauterine devices. In contrast, 60% of women reported the use of hormonal contraceptives, which was more frequent among women <30 years old (p < 0.05) and those belonging to the upper-middle socioeconomic class (p < 0.05). These women showed significantly lower levels of menstrual flow intensity score (p < 0.01) and, curiously, a higher prevalence of subclinical inflammation (CRP > 5 mg/L) ( Table 2). Mean total iron intake was estimated to be 10.9 mg/day, which is approximately 6% of heme iron and 29% of iron from fortified corn and wheat flours ( Table 2). Lunch and dinner showed comparable total daily iron amounts (3.71 mg/day and 3.12 mg/day), although differed in almost 50% on their contributions to total daily heme iron intake (62.8% and 33.0%). In turn, breakfast and snacks provided the highest daily amounts of calcium (32.6% and 25.3%) and polyphenols (32.9% and 47.9%)

Dietary Iron Bioavailability Estimates
As illustrated in Figure 2, based on physiologic iron requirement distributions, usual total iron intakes, and prevalence of iron deficiency among hormonal contraceptive users and non-users, their expected dietary FeBio values were of 16% and 19%, respectively ( Figure 2). A weighted average of these two estimates, assumed as a mean for the overall sample, was calculated as 17.2%. No substantial changes in this value were observed after excluding vegetarians or meat restrictors from the analysis.  Upon searching for dietary variables related to each of the tested algorithm estimates, we found all of them were strong negatively associated with heme iron and animal tissue intakes. Only estimates from  and Reddy et al.'s (2000) algorithms were unrelated to non-heme iron, while were negatively correlated with dietary phytate intakes. A negative association was also found between calcium and the former algorithm estimates. In turn, only Reddy et al. (2000) and Collings et al.'s (2013) models provided estimates that independently varied from dietary vitamin C intakes (Table S2).  [14]. Values in boxes are prevalence of iron deficiency (serum ferritin < 15 µg/L). Mean dietary iron bioavailabilities of 16% and 19% were estimated for hormonal contraceptive users and non-users, respectively. Table 3 shows the estimates from the five tested algorithms. Although 1.7% and 4.1% of meals analyzed using Hallberg and Hulthén (2000)   Upon searching for dietary variables related to each of the tested algorithm estimates, we found all of them were strong negatively associated with heme iron and animal tissue intakes. Only estimates from  and Reddy et al.'s (2000) algorithms were unrelated to non-heme iron, while were negatively correlated with dietary phytate intakes. A negative association was also found between calcium and the former algorithm estimates. In turn, only Reddy et al. (2000) and Collings et al.'s (2013) models provided estimates that independently varied from dietary vitamin C intakes (Table S2).

Correlation between Dietary Iron Bioavailability Estimates
Notably, all FeBio algorithms underestimated 25%-50% of the probabilistic model; all algorithm estimates, whether based on meals or complete diets, were strongly correlated. However No slope coefficients from regression equations between algorithm estimates was close to 1 (0.8 ≥ β ≥ 1.2), suggesting a lack of identity between them (Table 4). Table 4. Correlation coefficients and simple linear regression equations of the bivariate relationship between iron bioavailability estimates (mg/day).

Armah et al. (2013) [13]
Hallberg and Hulthén  respectively. Moreover, differences in SF concentration values of approximately 30% was found among women classified based on the median values of these two algorithm measurements (p < 0.05 and p < 0.01, respectively) ( Figure S1). transferrin saturation (Table S3).

Association between Dietary Iron Bioavailability Estimates and Serum Ferritin Concentrations
Besides FeBio measures, quantiles of total iron, non-heme iron, and heme iron intakes were also evaluated in relation to SF, but no significant association was found. Moreover, neither of the tested regression models showed an interactive effect between dietary variables and hormonal contraceptive use on the biomarker concentrations.

Discussion
Using the dietary and biochemical data from a selected group of healthy women of childbearing age and steady-state body iron balance, we demonstrated that FeBio values from a probabilistic approach contradict those from predictive algorithms, especially those complete diet-based models. Still, when searching for estimates that could predict SF concentrations, we found one meal-based   [5]) and one diet-based (Collings et al. (2013) [12]) methods that can better rank individuals according to their bioavailable iron intakes. From our knowledge, this is the first study to compare the different FeBio models and evaluate their practical usefulness using a set of data typically available in cross-sectional epidemiologic surveys.
Aimed at studying heathy women with reliable dietary and biochemical data, extensive selection criteria were used in screening the volunteers, which may have biased the inclusion of a relatively iron-sufficient population (87.4%). This scenario may have increased the degree of uncertainty on the FeBio estimate from the probabilistic model [14], as evidenced by a 3% difference on FeBio estimates for hormonal contraceptive users and non-users. These two groups differed in approximately 1 mg/day on the usual total iron intakes and in almost 10 times on the prevalence of subclinical inflammation, which possibly affected the dietary and biochemical inadequacy estimates. However, it is unlikely that this small iron intake difference has substantially impacted our results, and we corrected the SF to remove the effect of inflammation on this iron biomarker [54]. Additionally, our overall mean FeBio estimated with this model (17.2%) was very close to that assumed for diverse Western diets (18%) [27], providing an initial evidence of good performance to this method. Further studies with populations at higher risk of iron deficiency might result in more accurate FeBio calculations using the probabilistic approach.
To assess the relative validity of different FeBio methods, we then compared the estimates from the five algorithms to each other and with the probabilistic approach, assuming the latter model is the least affected by measurement errors associated with collection and analysis of dietary data [14]. Based on our results, all algorithms underestimated the probabilistic approach; however, the highest discordance from all other tested models were observed for the diet-based algorithms of Collings et To assess a possible mediation effect of the non-omnivorous dietary pattern on the associations between algorithm measurements and SF concentrations values, an additional adjustment for vegetarians or meat restrictors in regression models was tested. In this sense, the association between SF and tertiles of FeBio measured using Collings et al.'s (2013) model, but not with  model, remained statistically significant (p = 0.021 and p = 0.103, respectively). Interestingly, only  algorithm estimates were also associated with transferrin saturation (Table S3).
Besides FeBio measures, quantiles of total iron, non-heme iron, and heme iron intakes were also evaluated in relation to SF, but no significant association was found. Moreover, neither of the tested regression models showed an interactive effect between dietary variables and hormonal contraceptive use on the biomarker concentrations.

Discussion
Using the dietary and biochemical data from a selected group of healthy women of childbearing age and steady-state body iron balance, we demonstrated that FeBio values from a probabilistic approach contradict those from predictive algorithms, especially those complete diet-based models. Still, when searching for estimates that could predict SF concentrations, we found one meal-based   [5]) and one diet-based (Collings et al. (2013) [12]) methods that can better rank individuals according to their bioavailable iron intakes. From our knowledge, this is the first study to compare the different FeBio models and evaluate their practical usefulness using a set of data typically available in cross-sectional epidemiologic surveys.
Aimed at studying heathy women with reliable dietary and biochemical data, extensive selection criteria were used in screening the volunteers, which may have biased the inclusion of a relatively iron-sufficient population (87.4%). This scenario may have increased the degree of uncertainty on the FeBio estimate from the probabilistic model [14], as evidenced by a 3% difference on FeBio estimates for hormonal contraceptive users and non-users. These two groups differed in approximately 1 mg/day on the usual total iron intakes and in almost 10 times on the prevalence of subclinical inflammation, which possibly affected the dietary and biochemical inadequacy estimates. However, it is unlikely that this small iron intake difference has substantially impacted our results, and we corrected the SF to remove the effect of inflammation on this iron biomarker [54]. Additionally, our overall mean FeBio estimated with this model (17.2%) was very close to that assumed for diverse Western diets (18%) [27], providing an initial evidence of good performance to this method. Further studies with populations at higher risk of iron deficiency might result in more accurate FeBio calculations using the probabilistic approach.
To assess the relative validity of different FeBio methods, we then compared the estimates from the five algorithms to each other and with the probabilistic approach, assuming the latter model is the least affected by measurement errors associated with collection and analysis of dietary data [14]. Based on our results, all algorithms underestimated the probabilistic approach; however, the highest discordance from all other tested models were observed for the diet-based algorithms of Collings et al. (2013) and Armah et al. (2013) [12,13]. It surprisingly occurred even though these two models were published as presumably more accurate alternatives to the traditional meal-based algorithms [12,13]. These findings indicate a possible exaggerated effect attributed to SF concentrations or to dietary elements on the non-heme FeBio using these two aforementioned methods.
Our results largely differed from those described by Armah et al. (2015) and Perignon et al. (2018) who, using the algorithm proposed by the former researchers [13], estimated higher FeBio means in the diet of North Americans (15%) and French (13%), respectively [55,56]. Possibly, our assumption of a large unavailability for uptake to the non-heme iron from Brazilian-fortified flours (50%) and dietary dissimilarities of our studied women have contributed to these discordances [46,47]. Nevertheless, the precision and accuracy of all models tested in our study have not yet been extensively explored by external studies. Hence, our results suggest that FeBio values estimated with algorithms must be carefully employed when used as a basis for readjusting dietary references values of iron intake or when applied in public health policies aimed at treating anemia.
In fact, two previous studies that tested the accuracy of FeBio algorithms described similar results [18,19]. In a cohort of religious women from the Philippines, Beard et al. (2007) reported that the algorithms of Monsen et al. (1978), , and Reddy et al. (2000) underestimated 57-66% of the FeBio values objectively predicted from the women's change in body iron stores following the introduction of a high iron rice variety in their diets [19]. In a second study, Zimmermann et al. (2005), also based on an indirect calculation of FeBio from changes in the body iron status of Moroccan children, found a 50% underestimation for measurements obtained with the Reddy et al. (2000) algorithm [18].
Based on our findings,  and Collings et al.'s (2013) models provided FeBio estimates that independently predicted the SF variability among the studied women [5,12]. Moreover, those estimates obtained using Collings et al.'s (2013) algorithm-the simplest of all the tested models-surprisingly had a relatively stronger association with this biomarker. Although non-identical estimates were provided, these two models were strongly correlated, despite their deep methodologic particularities. The  algorithm-the most refined and complex of all published FeBio models-was elaborated from a set of radioisotope assays testing iron absorption from chemical characterized meals. It exhibits enhancing and inhibitory effects on the dietary elements by means of eight equations applicable to the non-heme iron and one to the heme iron intakes. In addition, it includes correction terms for the efficiency of both heme and non-heme iron absorptions by the SF concentrations, using exponential equations [5]. The Collings et al.'s (2013) model, in turn, was generated from a meta-analysis of radioisotope or stable isotope assays testing complete diets (food intake periods ≥ 1 day). It also employs exponential equation for correction of non-heme iron absorption by SF concentrations but lack an adjustment term to heme iron absorption. Exceptionally, this model does not require any quantitative dietary data for its calculations, except the usual non-heme iron intake. Its equation is summarized in three constant bioavailability values applied in function of the diet under analysis, arbitrarily classified according to its overall content of inhibitors or enhancers of iron absorption [12].
Hence, we found significant associations between dietary enhancers and inhibitors of iron absorption with FeBio estimates from Hallberg    algorithm, are not likely the cause of the relatively stronger association between SF and estimates from the first model. Nevertheless, it is reasonable to assume that these two algorithms were the most efficient of the tested models due their relatively more appropriate adjustments terms ascribed to dietary factors on the non-heme iron absorption. In this sense, we found that the Hallberg and Hulthén's (2000) algorithm better discriminated FeBio differences between omnivorous and vegetarian diets and was the unique model significantly associated with women's transferrin saturation values, besides the SF. Taken together, our findings confirm Hunt's (2010) observations that, in an attempt to validate different meal-based FeBio algorithms testing omnivorous and vegetarian diets, showed best results for the  model [17].
The limitation of our study is the small sample size with possible low representativeness of the general population. Moreover, we collected dietary data using FRs, which are subjected to reactivity, leading to changes in food intake or food reporting [57]. In this sense, however, our dietary estimates indicated a mean total iron intake (10.9 mg/day) very close to that described for Brazilian adult women in a national dietary survey (10.1 mg/day) [58]. Similarities were found in the contribution of flour fortification (~30%) to the total iron intake [59], and in the mean values of total animal tissue intake (130.7 g/day of cooked tissues) [60]. The estimated phytate contents in the evaluated meals were also very similar to those found in directly analyzed samples designed to reflect the Brazilian pattern [61], despite the use of international food phytate databases [5,37]. Nevertheless, our findings must be confirmed, especially in larger population-based studies, by using not reactive diet assessment methods (e.g., 24-h food recall) and by employing data from chemical analysis of national foods.
In our experimental conditions, neither total iron, non-heme iron, nor heme intakes were strongly correlated with SF as were FeBio estimates. These observations reinforce the importance of considering the effect of dietary modifiers of iron absorption for a better interpretation of the role of diet on body iron status and its related health or disease outcomes. Taken together, our findings signal the need for validation of currently available FeBio models for use in epidemiological dietary surveys. Based on the data presented herein, the original hypothesis that predictive mathematical algorithms and the probabilistic approach models generate discordant FeBio estimates may be accepted. Also, we highlight that, among women of childbearing age and varied dietary patterns,  and Collings' (2013) algorithms showed the best results at predicting body iron statuses, as measured by SF concentrations.
Supplementary Materials: The following are available online at http://www.mdpi.com/2072-6643/10/5/650/s1, Table S1: Selected dietary characteristics according to meals in the diet of women at presumably steady-state body iron balance; Table S2: Selected dietary characteristics according to quantiles of bioavailable iron intake (mg/day) of women at presumably steady-state body iron balance; Table S3: Selected hematological and biochemical characteristics according to quantiles of bioavailable iron intake (mg/day) of women at presumably steady-state body iron balance. Figure S1. Serum ferritin (µg/L) of women stratified at median of bioavailable iron intake (mg/day).