Adjusting Iron Deficiency for Inflammation in Cuban Children Aged Under Five Years: New Approaches Using Quadratic and Quantile Regression

INTRODUCTION Ferritin is the best biomarker for assessing iron deﬁ ciency, but ferritin concentrations increase with inﬂ ammation. Several adjustment methods have been proposed to account for inﬂ ammation’s eﬀ ect on iron biomarker interpretation. The most recent and highly recommended method uses linear regression models, but more research is needed on other models that may better deﬁ ne iron status in children, particularly when distributions are heterogenous and in contexts where the eﬀ ect of inﬂ ammation on ferritin is not linear. OBJECTIVES Assess the utility and relevance of quadratic regression models and quantile quadratic regression models in adjusting ferritin concentration in the presence of inﬂ ammation. METHODS We used data from children aged under ﬁ ve years, taken from Cuba’s national anemia and iron deﬁ ciency survey, which was carried out from 2015–2018 by the National Hygiene, Epidemiology and Microbiology Institute. We included data from 1375 children aged 6 to 59 months and collected ferritin concentrations and two biomarkers for inﬂ ammation: C-reactive protein and α-1 acid glycoprotein. Quadratic regression and quantile regression models were used to adjust for changes in ferritin concentration in the presence of inﬂ ammation.


INTRODUCTION
Interpreting iron indicators in the presence of infl ammation is a topic of particular interest to public health.[1] Serum ferritin concentration is recognized by WHO as the best indicator of populations' iron defi ciency, [2] but infl ammation can aff ect ferritin concentrations, as it is an acute phase protein (APP).[3] For this reason, WHO suggests accompanying ferritin measurements with measurements of other APPs to confi rm the presence of infl ammation.[1,2] Among the most widely-used infl ammation biomarkers in clinical practice and nutrition research are C-reactive protein (CRP) and Alpha-1-acid glycoprotein (AGP).[4] Several approaches have been proposed which use APPs to adjust for infl ammation's eff ects on ferritin levels and other biomarkers, [5][6][7][8] but there is still no consensus as to a preferred method.[4] In addition to taking the advantages and limitations of each method into account, the choice of method must be weighed against the burden of infection in the country or region where it is applied.[9] Most studies have been conducted in low-to middle-income countries with moderate to high infection burdens.[10][11][12][13][14][15] Cuba is a developing country considered to have a population with a low level of infl ammation.The most recent study on iron defi ciency in children aged under fi ve years supports the hypothesis that ferritin concentrations change in magnitude according to the state of infl ammatory processes in the fi rst fi ve years of life.[16] Iron status in Cuban children aged under fi ve years is modifi ed in the presence of infl ammation.[16] In Pita's study, [16] the ferritin concentrations of 1375 children were adjusted for infl ammation (measured by CRP and AGP), using four of the most well-known approaches in recent literature: a) higher ferritin cut-off point (>30 g/L); b) excluding subjects with infl ammation (CRP >5 mg/L or AGP >1 g/L); c) CRP-or AGP-based arithmetic correction factors; and d) regression correction using the method proposed by the BRINDA group (Biomarkers Refl ecting Infl ammation IMPORTANCE This study demonstrates the usefulness of two new approaches for correcting ferritin concentrations in the presence of infl ammation, which would improve methods for evaluating iron defi ciency in Cuban children aged under fi ve years , and thus provide more reliable data on iron defi ciency prevalence in the country.

Original Research
and Nutritional Determinants of Anemia).[17] The signifi cant disparity between unadjusted ferritin values and those adjusted by some of the above approaches underlines the importance of correcting for infl ammation and the need to develop adequate tools to examine the validity of the methods used for correction.Regression correction (RC) is recommended, [7] but the need for continued investigation into other methods of adjusting ferritin concoentrations is emphasized.[18] The RC approach is based on subtracting infl ammation's eff ects from observed ferritin concentrations.This approach is less subject to bias and allows for continuous correction of ferritin even for lower reference values for infl ammation than those traditionally used.[19] However, it is based on the assumption of a linear eff ect of infl ammation on iron defi ciency indicators; in practice, relationships between iron status biomarkers and APPs (CRP and AGP) are not linear.[4] Additionally, diff erent types of relationships could exist for subpopulations that deviate from average trends for heterogenous distributions.It may therefore be necessary to use more fl exible regression models, like quadratic regression models [20] and quantile regression models.[21][22][23][24] Quantile regression (QR) is considered a natural extension of the standard regression model and allows for separate regression models to be used for diff erent parts of the dependent variable's distribution.QR's additional fl exibility may broaden the description of infl ammation's eff ect on ferritin's conditional distribution.An additional advantage to QR is that it does not depend on normality assumptions or transformations.Some exogenous factors-such as observations below detection limits-can alter parameters of the dependent variable's conditional distribution.It is common practice to fi ll in undetected or censored data with a value equal to or less than the detection limit.However, when there are a considerable number of such replacements, estimates of mean eff ects and standard errors of least-squares regression models will not be reliable, risking erroneous conclusions.QR is more robust against these types of outliers.Therefore, QR models could be used to not only detect heterogenous CRP and AGP eff ects at diff erent quantiles of ferritin values, but also to obtain more precise estimates compared to mean regression when normality assumptions are breached, or when there are outliers and long tails.[24] Taking into account the need for more robust adjustment models that off er more precise measurements, we set out to estimate possible non-linear relationships and the usefulness and relevance of quadratic regression and quadratic regression by quantile models to explain ferritin concentration's relationship with CRP and AGP infl ammation biomarkers in Cuban children aged under fi ve years.

Population, study area and variables
We used data pertaining to population, study area and variables obtained from Cuba's national anemia and iron defi ciency survey, a cross-sectional study carried out by the National Hygiene, Epidemiology and Microbiology Institute (INHEM), from February through April each year from 2015-2018 in four randomly-selected regions of the country.The sample included 1375 presumably healthy children, with no diagnosis of chronic disease, aged 6 to 59 months, and complete serum ferritin, CRP and AGP records.A detailed description of sample selection can be found in the aforementioned article by Pita.[16] Case defi nition Iron defi ciency was defi ned as ferritin concentration <12 μg/L, the cut-off point recommended by WHO.[2] Acute infl ammation was defi ned as CRP ≥5 mg/L and chronic infl ammation as AGP >1 g/L.[2] Statistical analysis Graphs and simple statistics were used to study the distribution of the three biochemical variables.All showed some kind of positive skew and were transformed to their natural logarithms to avoid disproportionate ranges.Once data was transformed, histograms and normal probability plots were constructed to visually judge normality.
To explore the relationship between ferritin and infl ammatory biomarkers, children in the sample were divided into 10 subgroups, determined by intervals of equal length, according to ln(CRP) or ln(AGP) values.Box-and-whisker plots were constructed to observe ferritin concentration patterns in the diff erent ranges of each infl ammation biomarker.
APP's eff ect on ferritin was evaluated using models on a continuous scale.We used linear regression, quadratic regression (R c ) and quantile quadratic regression (QR c ). Models were adjusted considering each biomarker's eff ect (CRP and AGP) both separately and jointly.We constructed scatterplots to show bivariate associations.
To interpret iron stores in the presence of infl ammation, ferritin concentrations were adjusted using two approaches: quadratic regression correction (R c C) and quantile quadratic regression correction (QR c C).These analyses were conducted using the statistical software R, version 3.5.3(Free Software Foundation, USA).[25] We used the The Im function of the Stats statistical package was used to fi t models with the least squares method.Model fi t by quantiles was performed using the rq function of the quantreg package.[26] Estimation of quantile regression's eff ects While ordinary least squares regression (OLS) off ers only information on the conditional mean, QR allows us to estimate conditional quantiles of a response variable's distribution based on a set of p predictor variables.
Analogous to linear regression, where , the QR model for a conditional quantile can be formulated as: where 0 < < 1 and denote the conditional quantile function for the θ-θth quantile.is the response vector, is the explanatory variable matrix and is the vector for unknown parameters for the generic conditional quantile .
Unlike OLS regression, in which a single regression line is fi tted, QR has multiple lines, and therefore, as many coeffi cient vectors as quantiles are considered.
Parameter estimates in linear QR models are interpreted in the same way as any other linear model.Therefore-as in the OLS model-in the case of a multivariate QR with p explanatory variables, the QR model coeffi cient can be interpreted as the rate of change of the Ɵth quantile of the dependent variable distribution by unit change in the jth regressor: A median regression ( = 0.5) of ferritin concentrations on infl ammation biomarkers specifi es changes in median ferritin concentration as a function of predictors.Indicators' eff ects on median ferritin concentration can be compared with their eff ects on other ferritin quantiles.As we increase from 0 to 1, we can determine the full distribution of , conditional on .

Quantile regression correction
Suppose that we have data , and that the parameter of interest is the conditional quantile of , given by .Pairs are assumed to be observations of randomly-selected individuals from a population.
While the eff ects of CRP and AGP are uniquely calculated in linear regression, in quantile regression they vary depending on the desired quantile.It is possible to identify for each individual the QR model that can best predict the response variable to provide a unique vector of coeffi cients.[23] Consider the QR model for a given conditional quantile θ: The generic element of matrix is the dependent variable's estimate corresponding to the ith individual according to the θth quantile.
The best estimate for each individual is the one that minimizes the diff erence between observed and estimated values for each of the k models: [23] (1) Once is identifi ed for each individual i, ferritin concentrations are adjusted by subtracting the estimated eff ects of infl ammation on the corresponding quantile assigned to each individual.Take, as an example, the measurements of ln(ferritin) and ln(CRP) of the random sample of Cuban children aged under fi ve years.The quantile quadratic model used to evaluate the eff ect of each infl ammation biomarker on diff erent parts of ferritin's conditional distribution is expressed as follows: (2) where is the intercept and and are the regression coeffi cients of the θth quantile.
The graphs of each quadratic quantile function are parabolas in the form of , so the vertex is their lowest point.In this study, a threshold for infl ammation was defi ned as the point at which the quadratic quantile function was minimized.This occurs when: Where and are the estimates of the regression coeffi cients of each quantile function in (2).Once identifi ed for each individual according to the criteria in (1), ferritin concentrations were adjusted by performing the following transformation: To avoid overfi tting, the correction was applied according to the following expression: The adj subscript refers to the ferritin concentrations' fi tted values.The ref subscript refers to infl ammation reference values, under the assumption that they mark the cutoff points of infl ammation biomarkers, from which ferritin concentrations increase.
Results on the values of infl ammation-adjusted ferritin concentrations were expressed in the original measurement scale.Iron defi ciency was determined by applying a ferritin cut-off of <12μg/L [2] to infl ammation-corrected ferritin concentrations.

Relationship between infl ammation and iron defi ciency
Figure 1 shows the means and the 0.10, 0.25, 0.50, 0.75 and 0.90 quantiles of ln(ferritin) in each subgroup, of the variables ln(CRP) and ln(AGP), respectively.
The distribution of ln(ferritin) conditioned to ln(CRP) is similar in the fi rst subgroups, but as the magnitude of infl ammation increases, the distribution of ln(ferritin) shifts toward higher values.Moreover, this variability does not seem to be constant (Figure 1a). Figure 1b shows a non-linear pattern in which ferritin concentrations are low when infl ammation is moderate, and are high, for both high and low ln(AGP) values.

Eff ects of CRP and AGP on ferritin estimation
In univariate linear regression models, the eff ect of ln(CRP) on ln(ferritin) was signifi cant (0.105, p <0.000), suggesting that on average, when CRP values increase, ferritin concentrations also increase, but mean ln(ferritin) concentrations did not change signifi cantly (0.066; p = 0.298) with increasing ln(AGP).When both infl ammation biomarkers were included in a model, both eff ects were signifi cant.The estimated eff ect of ln(CRP) was positive (0.128, p = 0.021), but the eff ect of ln(AGP) was negative (-0.162, p = 0.025).
Graphs were used to fi nd inconsistencies as per assumptions of models' normality, linearity and homoscedasticity.Using information from Figure 1 as a guide, we evaluated quadratic functions in order to achieve a better fi t.For illustrative and comparative purposes, Figure 2 shows two graphs that represent the linear and quadratic regression functions for each of the univariate models.
The minimum value of the nonlinear function is reached when ln(CRP) is -1.182, so the CRP value from which infl ammation begins to positively infl uence ferritin values is 0.31 mg/L (Figure 2a), but it is nearly impossible to visually discriminate ferritin values below the vertex of the quadratic function.Inside the range of CRP values defi ned by the segment where linear and quadratic functions intersect, the fi t of the two functions is similar, and ferritin concentrations increase more rapidly as infl ammation increases.
The quadratic model (Figure 2b) shows a U-shaped relationship between ln(ferritin) and ln(AGP), with the vertex at ln(AGP) of -0.397.Thus, infl ammation begins to positively infl uence ferritin from AGP = 0.67 g/L.On average, ferritin concentrations tend to rise in individuals with high AGP values.
Table 1 shows the estimates of the quadratic regression models (R c ) for the conditional means of the combined and individual

Peer Reviewed
Original Research infl ammation biomarkers: R c -(CRP), R c -(AGP) and R c -(CRP, AGP).Estimated coeffi cients were signifi cant (p <0.05).Adjusted R 2 values were small, but higher than those obtained using linear models.Due to the high heterogeneity of the data, the quadratic models can only explain a small portion of ln(ferritin)'s variation around the mean.Associations explaining ferritin's relationship to CRP values may be diff erent in other parts of the conditional ferritin distribution.

Quantile regression feasibility and adequacy
Quantile regression shows variation between ln(ferritin)'s quantile distribution.In diff erent parts of the distribution, proposed models show an infl ammation-iron defi ciency relationship, which, as expected, was not linear and was identifi ed in regression to the mean.Table 1 shows estimated coeffi cients for the 0.10, 0.25, 0.50, 0.75 and 0.90 quantiles of three models: QR c , QR c-(CRP), QR c -(AGP) and QR c -(CRP, AGP).
Quadratic regression models R c -(CRP) and QR c -(AGP) showed a signifi cant parabolic correlation (p <0.05) between ferritin concentrations and infl ammation.In the case of the QR c -(AGP) model, estimated coeffi cients in all quantiles diff er signifi cantly from zero.In the QR c -(CRP), the coeffi cients associated with the linear ln(CRP) at the 0.10 quantile and the quadratic ln 2 (AGP) at the 0.90 quantile were not signifi cant.As in the case of regression to the mean, the QR c models confi rm that the relationship between ferritin and both infl ammation biomarkers is not completely linear.
The graphic versions of the quadratic fi ts of the estimated conditional quantiles in Table 1 (models 4 and 5) can be seen in Figures 2c and 2d.Infl ammation's eff ect on ferritin seems to be accentuated as CRP values increase (Figure 2c), as seen in children in the 0.25 and 0.50 percentiles.In the two highest quantiles, ferritin values also increased due to the eff ect of infl ammation; but the increase is discrete and almost linear.
Figure 2d shows a positive increase of ferritin from each quantile function's vertex.As AGP values increase, the eff ect of infl ammation decreased toward the tail's upper distribution (0.75 and 0.90 percentiles).
When both infl ammation biomarkers were considered in the R c -(CRP, AGP) quadratic regression model, all estimated coeffi cients showed a statistically signifi cant positive eff ect, with non-linear ferritin growth (Table 1).
Estimation by quantiles in the QR c -(CRP, AGP) model suggests a more complex situation (Table 1), since the infl uence of explanatory variables on ferritin varied from one quantile to another, and some were signifi cant in only some quantiles.The ln(CRP)'s eff ect was only statistically signifi cant in the subpopulation of children who had the highest iron reserves.The ln 2 (AGP) variable is the

Original Research
most important in explaining ferritin's variation throughout the conditional distribution.

Statistical signifi cance of OLS and QR estimate diff erence
Within the 0.25 to 0.90 quantiles of the QR c -(CRP) model, estimates of ln(CRP)'s eff ects are within the estimation interval of the OLS regression (Figure 3a), which indicates that in this part of ferritin's conditional distribution, the linear relationships identifi ed by QR c are the same as those suggested by classical regression.However, the eff ect of ln 2 (CRP) at the 0.25 quantile is signifi cantly higher than the OLS estimate, suggesting that in this part of the distribution, CRP's quadratic eff ect is higher than the OLS estimate.
Figure 3b shows that the estimates of the eff ect of ln(AGP) in the QRc-(AGP) model is signifi cantly higher at the 0.50 quantile of the distribution when compared to the mean estimate, indicating that around the median of the conditional distribution of ferritin, the linear eff ect of AGP could be greater than that estimated by regression to the mean.
The estimates of the linear eff ects of the two infl ammation biomarkers on ln(ferritin) at almost all quantiles in the QR c -(CRP, AGP) model are within or very close to the OLS estimate's confi dence interval limits (Figure 3c), while the eff ect of ln 2 (CRP) at the 0.25th percentile is signifi cantly larger than the estimate for the mean, confi rming that CRP's quadratic eff ect is larger than that estimated by classical regression in this part of the distribution.

Statistical signifi cance of diff erences between estimated coeffi cients at conditional quantiles
The analyses of greatest interest focused on the 0.10, 0.25, and 0.50 quantiles, where adjusting for the eff ect of infl ammation on ferritin concentrations was most likely to produce a change in iron deficiency prevalence, since they represent the subpopulation of children with ferritin concentrations around the WHO-recommended cutoff point defi ning iron defi ciency.
The eff ects of CRP (both linear and quadratic) are similar across quantiles in the QR c -(CRP) model.The coeffi cient equality test [27] shows that there are no statistically signifi cant diff erences between estimated values in the 0.10, 0.

Impact of adjustments on estimated iron defi ciency prevalence
Table 2 summarizes the median ferritin estimates and adjusted and non adjusted iron defi ciency prevalences for the two correction approaches.Adjusting ferritin concentrations using internal reference values for infl ammation produced a mean increase in iron defi ciency prevalences of 2.6, 2.

Original Research
(see graph in Table 2), but they could be important from an epidemiological point of view, since the upper limit of the intervals reaches diff erences in prevalence >6% with respect to the unadjusted model.However, their confi dence intervals overlap, so it cannot be ruled out (with an error probability of less than 5%), that the small prevalence diff erences obtained from these models are due to chance.
The diff erences in the prevalence of iron defi ciency estimated before and after adjustment by RcC-(CRP, AGP) and QRcC-(CRP, AGP) models are statistically signifi cant (p <0.05).Estimated prevalence is higher when QRcC-(CRP, AGP) is used.In this case, the confi dence interval's upper limit for the diff erences in prevalence is greater than 9%.

DISCUSSION
Coeffi cients estimated by linear regression for the sample of 1365 children were slightly diff erent than those obtained by Pita, [16] due to the exclusion of the 10 individuals with outliers in AGP and CRP values.
The small values of the R 2 and pseudo R 2 fi t measures [28] and the signifi cant p-values of coeffi cients in the quadratic regression and quantile quadratic regression models indicate that although the data show high variability, there is a non-linear trend to the response which off ers relevant information on the relationship between ferritin and biomarkers for infl ammation.Note that the goal of regression correction methods is not to predict ferritin concentrations, but to remove infl ammation's eff ect on ferritin concentrations.In quantile regression, the best estimate for each individual is the one that minimizes the absolute diff erence between observed values and estimated values for each of the quantile models.
Quantile regression was able to detect that infl ammation may have diff erent eff ects on diff erent parts of iron status' conditional distribution.In agreement with other studies, [6,29] we found that high concentrations of CRP and AGP are associated with high ferritin concentrations, but it would be risky to generalize the eff ect of infl ammation on these values.These results suggest that infl ammation exerts less infl uence on ferritin concentrations in children with the highest iron stores.
Reference values for serum ferritin concentrations fall within the range of 15-300 μg/L, and are lower in children.[9] Apparentlyhealthy children were selected in the current study, so it is expected that in the subpopulation with high ferritin concentrations resulting from high iron stores, physiological homeostasis would be expected to control infl ammation's eff ect on regulating deviations in iron status indicator ranges, thus maintaining a state of balance in the body.
The use of quadratic regression models to estimate infl ammation's infl uence on ferritin allows us to recognize that the mean eff ect of infl ammation on ferritin concentrations in this sample is manifested from AGP and CRP values below the limits WHO designates as clinically relevant (CRP ≥5 and AGP >1).[2]

Original Research
Interest in correcting ferritin focused on the 0.25 quantile, which represents the subpopulation of children with ferritin concentrations close to the cut-off point recommended by WHO to signal iron defi ciency (ferritin <12 μg/L).According to the QR c C-(CRP, AGP) method, 80.8% of children with potentially overestimated ferritin values-who, after applying the infl ammation correction changed their status from adequate iron stores to iron defi ciency-were part of the 0.25 quantile subpopulation.Infl ammation's eff ect on the population of children with the highest (0.75 and 0.90 quantiles) and lowest (0.10 quantile) iron stores also provoked an overestimation of ferritin values.However, while an individual correction for infl ammation would result in a decrease in estimated ferritin concentration values, these changes would not modify the children's iron status classifi cation, or, consequently, iron defi ciency prevalence.
Using QR as a method of estimating the eff ects of infl ammation on ferritin reduces the bias that undetected ferritin values can introduce.In this investigation, the censored data comprise part of the 10% of observations located below the regression line of the 0.10 quantile, so when substituting the unknown value for the minimum detected value, there is no signifi cant change in estimates of the eff ects of infl ammation biomarkers on ferritin at the distribution's lower end.Infl ammation's eff ects may be more important in some subpopulations than in others, but if the eff ects estimated in the conditional quantiles are considered equivalent to the eff ect estimated using only the conditional expectation, the R c C approach may be preferred over the QR c C method, due to its simplicity; especially in population studies.But before making decisions based on these results, the QR c estimate's confi dence intervals should be checked to see whether they include values with important epidemiological implications.
Another aspect to consider is the choice of infl ammation cut-off points, because iron defi ciency estimates depend not only on fi gures of iron reserves in the population, but also on the presence of infl ammation in the population.To avoid overfi tting, corrections of ferritin concentrations are restricted to individuals whose infl ammatory biomarkers exceed reference values.The BRINDA group [7] recommends using the upper limit of the fi rst decile of each biomarker as a reference value.Based on this criteria, Pita [16] obtained a CRP reference value of 0.10 mg/L and an AGP reference value of 0.54 g/L.
In the current study, the non-linear trend between infl ammation and ferritin concentrations obtained with the quadratic regression models R c -(CRP) and R c -(AGP) showed that in a population with low infl ammation levels (such as those in the Cuban population), [16] the threshold from which we can assume that infl ammation begins to exert infl uence on ferritin concentrations may be greater than that determined by the upper limit of the fi rst decile (CRP = 0.31 mg/L and AGP = 0.67 g/L).
The QR c C approach refl ects the underlying relationship between ferritin and infl ammation better than the RC approach, but diff erences in the estimated eff ects along the conditional distribution of ferritin with respect to mean eff ects did not produce important diff erences in iron defi ciency prevalences adjusted by both methods.Infl ammation's eff ect on ferritin may be greater in some subpopulations and therefore the adjusted concentrations in these subpopulations will decrease more compared to adjusted concentrations in other subpopulations.However, these diff erences will only be important to prevalence if they occur in the subpopulation of children whose ferritin values are around the 0.25 quantile, which is the quantile closest to the cut-off point recommended by WHO to defi ne iron defi ciency (ferritin <12 μg/L).[2] In this investigation, the eff ects of infl ammation that were statistically signifi cant at the 0.25 quantile only occurred for CRP's quadratic eff ect in the QR c -(CRP) and QR c -(CRP, AGP) models.
Compared with unadjusted prevalence, the R c C and QR c C approaches led to similar iron prevalence estimates when ferritin concentrations were adjusted for CRP or AGP.
The highest estimates were obtained when ferritin concentrations were adjusted for both biomarkers, particularly when the QR c C approach was used.Developing tools to examine correction method validity is both merited and necessary.
One limitation of this study is that the children selected for the study came from a two-stage cluster sample, [16] so Peer Reviewed the results may not refl ect the diversity of the entire Cuban population.Furthermore, its cross-sectional nature precludes analysis of any seasonal infl uence of infl ammation on ferritin concentrations.

CONCLUSIONS
The combined use of quadratic regression and quantile regression is a useful analytical resource to explain the peculiarities of how ferritin levels change in the presence of infl ammation.Each function's vertex can be a guide suggesting the threshold from which infl ammation begins to infl uence ferritin concentrations.The quantile regression correction allows estimating higher prevalences of iron defi ciency if CRP and AGP values are included at the same time.Correction methods using quadratic regression and quantile quadratic regression models confi rm that infl ammation can lead to underestimating iron defi ciency prevalence in Cuban children aged under fi ve years.
The proposed approach can be used to complement standard correction analysis.Comparisons using diff erent correction methods can reduce discrepancies between statistical estimates, while helping interpret results in both biochemical and epidemiological terms.
7 and 4.5 percentage points according to the R c C-(CRP), R c C-(AGP) and R c C-(CRP, AGP) methods.Iron defi ciency prevalence calculated using the QR c C-(CRP), QR c C-(AGP), and QR c C-(CRP, AGP) methods led to a mean increase of 2.8, 2.8, and 6.3 percentage points (Table2).The diff erences in the estimated prevalence of iron defi ciency before and after adjustment for RcC-(CRP), QRcC-(CRP), RcC-(AGP) and QRcC-(AGP) do not reach statistical signifi cance,

Table 1 :
Parameter estimates (and standard errors) of quadratic OLS and quantile regression models for ln(ferritin) -1-acid glycoprotein; CRP: C-Reactive protein; OLS: Ordinary least squares regression; QR: Quantile regression Standard errors appear in parentheses.The * indicates signifi cant coeffi cients (p <0.05) adjusted R 2 and pseudo represent the capacity of the independent variables to explain the variation of ferritin in the OLS and QR regression models, respectively.

Figure 3 :
Figure 3: Regression coeffi cients estimated by OLS and QR