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1 From the Departments of Nutritional Sciences (SZ), Public Health Sciences (BF, SZ, and GT), and Health Policy, Management and Evaluation (WS, BF, and GT), University of Toronto, Toronto, Canada; the Department of Pediatrics (SZ and BF), the Division of Rheumatology (BF), and the Research Institute (MT, SZ, and BF), The Hospital for Sick Children, University of Toronto, Toronto, Canada; the Department of Medicine, The University Health Network, University of Toronto, Toronto, Canada (GT); The Centre for International Health, University of Toronto, Toronto, Canada (WS and SZ); and the Medical Advisory Secretariat, Ministry of Health and Long-Term Care, Government of Ontario, Toronto, Canada (WS)
2 Supported by the Canadian Institute of Health Research (Program in Metabolism), the Hospital for Sick Children, and the HJ Heinz Co Foundation. 3 Address reprint requests to W Sharieff, Ministry of Health and Long-Term Care, Government of Ontario, 56 Wellesley Street West, 8th floor, Toronto, Ontario M5S 2S, Canada. E-mail: doc.sharieff{at}utoronto.ca.
ABSTRACT
Background: Iron deficiency is the most common preventable nutrition problem in developing countries. Several randomized clinical trials (RCTs) have been conducted to determine the effectiveness of various iron dosing schemes in multiple settings.
Objective: The objective was to determine whether enough is known about iron metabolism to predict hemoglobin and serum ferritin (SF) concentrations with a computer model and whether the model could be used as a substitute for new RCTs.
Design: Guided by the physiology of iron absorption and regulation, we used data from RCTs that tested iron Sprinkles to develop a computer model. Of 2 RCTs in Ghana, we used 1 to compute the amount of iron absorbed from a given dose in anemic and nonanemic children and the other to compute the resulting change in hemoglobin concentrations. We used this model to predict hemoglobin and SF concentrations in a new RCT in China and compared model-predicted values with actual values by using summary statistics (means and medians) and quantile-quantile plots.
Results: The model-predicted hemoglobin means were within ±2 g/L, and SF medians were within ±3 µg/L of the corresponding means and medians of the actual values. On quantile-quantile plots, the predicted hemoglobin quantiles were within ±5 g/L, and SF quantiles were within ±10 µg/L of the corresponding quantiles of the actual values.
Conclusion: Our model of iron metabolism can accurately predict hemoglobin and SF concentrations after iron supplementation with Sprinkles in children; the model can thus obviate the need for repeating RCTs in multiple settings.
Key Words: Markov model • Monte Carlo simulation • clinical trial • iron deficiency
INTRODUCTION
Physiologic needs of iron are high in young children; iron deficiency during these crucial times may impair the cognitive development of growing children (1, 2). It is believed that a feedback mechanism regulates iron absorption from the gut; more iron is absorbed when body iron is low in relation to needs and vice versa (3). Body iron comprises 4 functional compartments: tissue, red blood cell, basal losses of iron, and storage iron (4). The tissue compartment contains 0.7 mg Fe/kg body weight (5). In the red blood cell compartment, 3.4 mg Fe is utilized for the synthesis of each gram of hemoglobin (6); when a person with iron deficiency anemia is supplemented with iron, a curvilinear change in hemoglobin concentration is observed over time (7). This suggests that when the hemoglobin concentration is low, absorbed iron is readily incorporated into red blood cells and when the hemoglobin concentration normalizes, further incorporation slows down. Excess iron is directed to the other 2 compartments. Of these, basal losses constitute a near zero amount of iron excreted in the urine, feces, and sweat, which may be up to 2 mg/d at times of iron overload (8); the rest of absorbed iron is accumulated in the body (storage compartment). Serum ferritin (SF) is an index of storage iron (9); when SF is between 15 and 500 µg/L, each 1 µg SF/L represents 140 µg/kg body weight of storage iron (10). Outside this interval, the relation is less precise; nevertheless, SF concentrations <15 µg/L indicate that iron stores are absent, and SF concentrations >300 µg/L indicate that the stores are increased. Increasing amounts of free iron can be toxic (11); it is not wise to consume too much iron except at crucial times. Therefore, dietary reference intakes (DRIs) were established with the use of Monte Carlo simulations on each body iron compartment to estimate median iron needs (and percentiles) by sex for various age groups in a Western population.
However, these DRIs cannot be applied to about two-thirds of children in developing countries, who, primarily because of insufficient iron intakes, are iron deficient (12, 13); thus, their iron needs are higher. The dose, frequency, and duration (dosing scheme) of iron supplementation for these children remain uncertain (14). With the advent of Sprinkles (Sprinkles Global Health Initiative, Toronto, Canada) as a strategy for home fortification of young children's foods with micronutrients, including iron (15), several randomized clinical trials (RCTs) were planned to find the most appropriate dosing scheme of iron for public health interventions. As data from a few of these RCTs became available (16–18), we could translate the above physiologic processes into a dynamic simulation of growing children subjected to a Sprinkles dosing regimen; the objective was to accurately predict hemoglobin and SF concentrations with the idea that the model may then be used as a substitute for new RCTs.
METHODS
Overview
We built a computer simulation model based on the physiology of iron absorption and regulation in growing children and the observations from an iron-absorption study that used intrinsically labeled stable isotopes (Isotope study) (16). Model development was an iterative process wherein we kept refining some of the model components until its output matched that of an RCT conducted in Ghana (Ghana study) (17). We validated the same model by comparing model-predicted hemoglobin and SF concentrations with those from a new RCT in China (China study) (18). We provide all the details of the model, including estimations of the simulation cohort size and computations of iron absorption and distribution, in an appendix (see Technical Appendix under "Supplemental data" in the current online issue at www.ajcn.org).
Data sources
We used data from multiple sources (Table 1) and have provided specific references where applicable. Of the studies that used encapsulated ferrous fumarate as Sprinkles, the Isotope study measured the percentage of iron absorbed from 30 or 45 mg Fe in anemic and nonanemic children (6–18 mo). The Ghana study evaluated the hematologic response to 80 mg Fe provided daily for 2 mo to anemic children (6–18 mo) in their homes. The China study evaluated the hematologic response to 30 mg Fe provided to children (3–6 y) with sufficient iron stores for 5 d/wk (daily group) or once a week (weekly group) for 3 mo in school.
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TABLE 1. Data sources
Model building
Using means and SDs for age, body weight, and hemoglobin concentrations and the correlation coefficient between age and body weight from the Isotope study, we created a fictitious cohort of 5000 children (6–18 mo) via Monte Carlo simulations. We randomly assigned these children to receive 30 or 45 mg Fe. Next, we used body weight to compute blood volume (19), hemoglobin and blood volume to compute body iron and SF concentrations, and hemoglobin, SF, and iron dose to compute the daily amount of iron absorbed from the given Sprinkles regimen. We compared the medians and interquartile ranges from the model outputs with those from the Isotope study; when the differences were within ±0.3 mg in medians of absorbed iron, we dismissed these differences as clinically unimportant.
Model development
On replicating the results of the Isotope study, we replaced the means and SDs for age, body weight, and hemoglobin with baseline means and SDs from the Ghana study. Thus, at the starting point, we had created a cohort of 5000 children (6–18 mo) in which each child had a unique and related set of values for age, body weight, blood volume, hemoglobin, SF, compliance, and iron absorption. We then assigned the cohort to receive 80 mg Fe/d for 2 mo and subjected it to a Markov process, where the current set of values for each child predicted a new set of values for the next day for the same child, the next day's values predicted for the day after, and so on. In this process, the amount of iron absorbed each day depended on the child's compliance, ie, whether the child took the supplement or not on that day and the current amount of iron in body compartments. We added the amount of iron absorbed each day to body iron and redistributed iron in the 4 functional compartments, updated the values for body weight and blood volume (which change with growth), and used these values to compute new hemoglobin and SF values (20). We terminated this process at day 60 (endpoint of the Ghana study).
We compared the means and medians of the model outputs with those of the Ghana study; we dismissed differences within ±5 g/L in hemoglobin means, within ± 0.5 kg in body weight means, and within ±10 µg/L in SF medians as clinically unimportant. In addition, we examined the distributions of age, hemoglobin, SF, mean compliance (number of supplements taken out of total assigned), absorbed iron, and body weight with histograms and their interrelations with scatter plots in relation to the Ghana study. We examined the histogram of basal loss for similarity with data in the literature (8). When the differences were not dismissible or the graphs were inconsistent with the literature (usually due to incorrect choice of a variable's distribution), we reviewed the underlying assumptions and revised the model until its output was within acceptable limits of values from the literature and from the Ghana study. Of note was the initial dissimilarity between model-generated and actual SF distributions, which resolved after the incorrect distribution of basal losses was revised. Thus, our model specifically assumed that 1) the compliance of each person in a community would vary from 50% to 100% of the total assigned supplements (17), 2) the percentage of iron incorporation into red blood cells out of the total absorbed iron would vary across persons (16), 3) a feedback mechanism regulates the daily amount of iron absorbed from the gut (3), 4) the change in hemoglobin concentrations would be curvilinear over time (7), 5) basal losses would be minimal (in the interval 0–2 mg/d) (8) and would correlate positively with storage iron (21), and 6) leftover iron would be stored after the tissue and red blood cell compartments were filled and after basal losses were accounted for (4). The model is illustrated in Figure 1.
FIGURE 1.. Diagrammatic presentation of the computer simulation model. min, minimum; max, maximum. Sprinkles was developed by the Sprinkles Global Health Initiative (Toronto, Canada).
Model validation
After internal validation of the model with data from the Isotope study and the Ghana study, we replaced the means and SDs for age, body weight, and hemoglobin and values for iron dose and length of intervention in the developed model with those of the China study. Because Sprinkles were provided for either 5 d/wk (daily group) or once a week (weekly group), we modified the model: the iron dose was zero for 2 consecutive days after every fifth day in the daily group and was zero for all days except once after every sixth day in the weekly group. In addition, we changed the means and SDs for compliance, the absorbed iron from food, and the growth rate with those appropriate for a kindergarten population (3–6 y) (22). We ran the simulation on 5000 children per regimen and compared the hemoglobin and SF concentrations of these children on the 97th day (endpoint) with those from the China study.
Uncertainty analyses
There were 2 sources of uncertainty: parameter uncertainty related to the model assumptions and chance variability related to variation in individual responses when a study is repeated (23). We tested model assumptions by substituting these assumptions with their variant forms, ie, by changing the parameter values for mean compliance or by setting fixed values for iron incorporation, iron absorption, change in hemoglobin, and mean basal loss, rather than assuming variability or correlation with other variables. To examine chance variability, we obtained 50 samples from the China study through bootstrapping with replacement and plotted quantiles of each sample against quantiles of the model. Quantiles of a distribution are the distribution's percentage points (eg, the 0.025 quantile = the 2.5th percentage point = the 2.5th percentile, the 0.5 quantile = the 50th percentage point = the median, and the 0.975 quantile = the 97.5th percentage point = 97.5th percentile) (24). Thus, the quantile-quantile (QQ) plot is a graphic data analysis technique used to compare the distributions of 2 data sets; when data from the RCT and the model have the same distribution, the QQ plot will fall on a diagonal line (y = x) on the x-y plane. We examined these 50 QQ plots for hemoglobin and SF concentrations for the daily and weekly regimens, respectively, while scaling the x and y axes to lie between the 2.5th and 97.5th percentiles of the original cohort; thus, in the case of a perfect fit we could say that the model values exactly match 95% of the values of the original cohort. We considered a variation in QQ plots to be within clinical equivalence when hemoglobin quantiles were within ±5 g/L and SF quantiles were within ±10 µg/L.
Approval for the study was granted by the Research Ethics Board at the Hospital for Sick Children, Toronto, Canada. We used the SAS programming language (version 8.2; SAS Institute Inc, Cary, NC) to build the model. The SAS programs are available from the authors on request.
RESULTS
The model output was within the acceptable set of values from the Isotope study (Table 2). In children with hemoglobin concentrations <100 g/L, the median amount of iron absorbed in the model was higher than that in children with a hemoglobin concentration 100 g/L. Also, the model produced hemoglobin and SF concentrations that were similar to those found in the Ghana study (Table 3).
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TABLE 2. Internal validation: iron absorption determined with the computer simulation model and with isotopes (16), stratified by hemoglobin concentration and iron dose
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TABLE 3. Internal validation: body weight and hemoglobin and serum furitin concentrations determined with the computer simulation model and in a study conducted in Ghana (17)
A comparison of the means and medians of the model with those of the China study showed that the hemoglobin means were within ±2 g/L, and the SF medians were within ±3 µg/L at the end of supplementation (Table 4).
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TABLE 4. External validation: body weight and hemoglobin and serum ferritin concentrations determined with the computer simulation model and in a study conducted in China (18)1
Of the assumptions tested (Table 5), the model was sensitive to compliance, the regulatory feedback mechanism of iron absorption, and the curvilinear change in hemoglobin over time.
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TABLE 5. Uncertainty analyses: model assumptions
Overlaid bootstrapped QQ plots for daily and weekly groups are shown in Figure 2. QQ plots show that for 95% of the persons in the China study, the hemoglobin quantiles were within ±5 g/L of the corresponding hemoglobin quantiles in the model, and SF quantiles were within ±10 µg/L of the corresponding SF quantiles in the model.
FIGURE 2.. Overlaid bootstrapped quantile-quantile plots of data from the China study against model data for hemoglobin and log-transformed serum ferritin in the daily group (30 mg Fe provided 5 d/wk for 3 mo) and in the weekly group (30 mg Fe provided 1 d/wk for 3 mo) of children aged 3–6 y. The minimum to maximum values on the x and y axes correspond to the 2.5th and 97.5th percentiles. The variation in quantile-quantile plots is within ±5 g/L for hemoglobin and within ±10 µg/L for serum ferritin.
DISCUSSION
We translated physiologic processes into a computer simulation model that replicated postsupplementation hemoglobin and SF concentrations in the Ghana study, where all children (6–18 mo) had low hemoglobin concentrations (<100 g/L) before they were supplemented daily with 80 mg Fe for 2 mo. The same model could also accurately predict postsupplementation hemoglobin and SF concentrations in the China study, where >90% of the children (3–6 y) had hemoglobin concentrations in the normal range before they were supplemented with 30 mg Fe for 3 mo, either for 5 d/wk or once a week.
This accuracy was achieved despite differences in age, baseline iron status, iron regimen (dose, frequency, and duration), and setting (home compared with school). The variations in QQ plots at any point were not >5 g/L for hemoglobin concentration and 10 µg/L for SF concentration; thus, these variations had minimal clinical relevance. This implies that the model can be used to reliably predict hemoglobin and perhaps SF concentrations.
Certain limitations in computing SF concentrations exist: SF concentrations are inappropriately elevated in the presence of infection or inflammation (25). SF concentrations may transiently rise as iron is mobilized across the body's functional compartments, and the calculation of iron stores from SF and vice versa is less precise when SF is outside the interval of 15–500 µg/L. Thus, SF concentrations are of limited use in estimating cumulative changes in iron stores from long-term supplementation, such as food fortification. Nevertheless, these limitations should not affect the estimation of the proportion of persons with an SF concentration <15 µg/L (iron deficiency) and the proportion with an SF concentration >300 µg/L (increased iron stores) at a certain time after supplementation. Thus, our method could be used to estimate the risk of iron overload in men from food fortification in Western countries, although we have no data to support this contention.
The close agreement between our model and the China study means that our physiologic beliefs about iron metabolism are correct. The following were the key steps that led to this agreement: 1) the Isotope study provided the regression coefficients for computing iron absorption (dependent variable) with the use of the joint distribution of hemoglobin, SF, and iron dose (independent variables); 2) the Ghana study provided the regression coefficients to determine the curvilinear change in hemoglobin; 3) the Markov process simulated day-to-day variation in iron absorption; 4) Monte Carlo simulation described both known relations between physiologic variables (through regression coefficients) and the remaining natural variation (by adding residual errors); 5) we accounted for variation in iron intake due to the variation in compliance in a home or school setting; and 6) we chose appropriate distributions through an extensive literature review. These steps ensured that we captured most of the factors that influence the rate of iron absorption, which include body iron stores, the level of erythropoietic activity in bone marrow, the blood hemoglobin concentration, the blood oxygen content, and the presence or absence of inflammatory cytokines (26). Recently, it was discovered that hepcidin is a major factor in iron regulation; the same factors that regulate iron absorption also regulate the expression of hepcidin by the liver; iron absorption decreases when hepcidin increases and vice versa (27). We therefore believe that the model followed real-life processes to generate output similar to that of an RCT and may be further refined as data on hepcidin become available. With the use of relevant data on iron absorption and incorporation, it should be possible to predict hematologic outcomes for other forms of iron supplements.
To be effective against childhood anemia, iron-supplementation programs must include a universal dosing regimen and cover all young children (whether iron deficient or not). However, a standard regimen is yet to be determined. Although some dosing schemes have been proposed (28, 29), further research is ongoing. Our model can predict the hematologic response in a given population from a selected range of doses, frequencies, and durations of Sprinkles. Thus, the model could prevent the time and resources needed to conduct additional RCTs, each of which may cost $100 000 and require 1–2 y for planning and implementation; these estimates are based on our experiences with the Isotope, Ghana, and China studies. In addition, the use of the model could spare children from undergoing venipunctures for blood sampling and exposure to the other unforeseen risks associated with RCTs.
In conclusion, we believe that our Markov time series model can accurately predict hemoglobin and SF concentrations after supplementation with Sprinkles. The same method could be applied to predict results for other interventions.
ACKNOWLEDGMENTS
We thank George Beaton for his comments on the initial conceptualization of the computer simulation model.
WS conceived the study, acquired the data, developed the model, analyzed the results, and wrote the first draft of the article. MT, SZ, BF, and GT critically reviewed the article for important intellectual content. GT helped develop the simulation model and write the SAS codes. All authors contributed to the preparation of and approved the article. None of the authors had a conflict of interest. The sponsors had no role in study design, data collection, data analysis, data interpretation, or in writing the paper.
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