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Poverty Related Infection Oriented Research
Department of Internal Medicine
University Medical Centre
Radboud University
PO Box 9101
6500 HB Nijmegen
Netherlands
University Padjajaran
Sub-bagian Infeksi
Department of Internal Medicine
Jl Pasirkaliki 190
40161 Bandung
Indonesia
E-mail: wieringa{at}tiscali.nl
Dear Sir:
We would like to respond to the article by Verhoef et al (1) on the validity of the dose-response tests for the determination of vitamin A status. Unfortunately, the basic assumptions of the authors are incorrect, which invalidate the main results of the article. For example, plasma retinol concentrations are equated with vitamin A status, even though plasma retinol concentrations give only a rough indication of vitamin A status. To illustrate this point, if a subject with a vitamin A status of X is sampled several times, plasma retinol concentrations will vary around a certain value (eg, 0.80 ± 0.10 µmol/L) and, similarly, modified-relative-dose-response (MRDR) values will vary around a certain value (eg, 0.09 ± 0.01 µmol/L). The questions are not how well these MRDR values correlate with plasma retinol concentrations, but how well the MRDR values correspond to the vitamin A status X and whether, after supplementation, changes in plasma retinol or MRDR more closely relate to changes in vitamin A status X. Verhoef and West missed this point; therefore, their article addresses the wrong issue [the relation between plasma retinol and the MRDR or relative dose response (RDR)]. Mathematical models based on plasma retinol concentrations cannot be used to assess the validity of the dose-response tests. Isotope techniques in humans or animal studies with direct assessment of liver stores are needed (2, 3). Hence, the conclusion by Verhoef and West that the MRDR and RDR tests provide no additional information to plasma retinol concentrations cannot be addressed by their study.
Furthermore, Verhoef and West state that "if serum retinol concentration reflects vitamin A status ... then estimators, such as the MRDR, that incorporate the reciprocal of serum retinol concentration will, by definition, be biased." This is not true. The MRDR will be biased toward measuring plasma retinol concentrations, but not toward vitamin A status. If the statement by Verhoef and West were true, many indicators currently in use would be invalid. For example, Cook et al (4) showed that the ratio of serum transferrin receptor to serum ferritin is a sensitive indicator of iron status. Is this ratio biased because ferritin is directly related to iron status? Of course not. However, if we were to repeat the modeling by Verhoef and West and plot this ratio against ferritin concentrations, we would see a wider spread at higher ferritin concentrations, similar to that in Figure 1 in the article by Verhoef and West. This does not invalidate the ratio for the determination of iron status, it merely shows the relation with ferritin.
Verhoef and West also failed to appreciate that the dose-response tests are functional measurements, which yield a proportional response regulated by homeostasis. Instead, they use a fixed effect after a fixed dose as a basic assumption in all their models and in their subsequent interpretation. Hence, the basic assumption used in the model, ie, that there is no relation between the plasma retinol concentration at baseline (R0) and that 5 h after dosing (R5), is also incorrect. In their model, the authors randomly assigned retinol values of R0 to (slightly) higher retinol values of R5. However, this approach ignores the underlying physiology of the RDR, in which the values at R5 are related to the values at R0. Therefore, the results shown in Figures 1 and 2 in the article by Verhoef and West are due to regression to the mean: higher than average values at R0 are less likely to be high again and are more likely to be closer or below the average at R5 (and hence have a lower response). Therefore this model does not reflect the relation between the RDR and vitamin A status, in reality, and thus invalidates the simulation model and hence the results and conclusions.
Finally, Verhoef and West misinterpreted the results of our study (5). We reported lower plasma retinol concentrations, but also lower MRDR values (ie, better liver stores), in infants supplemented with iron. According to Verhoef and West, if mathematical artifacts underlie the relation between the MRDR and vitamin A status, lower plasma retinol concentrations should be associated with higher, not lower, MRDR values. Correlation coefficients were only added to show that there was no correlation between the MRDR and plasma retinol concentrations in infants supplemented with iron.
Furthermore, although Verhoef and West repeatedly referred to the article by Wieringa et al (5) as being from "our group," only one author (CEW) of the first article is also a coauthor of the article by Wieringa et al (which consisted of 6 authors from 5 different departments); therefore, the 2 articles should not be considered to be from the same group. Verhoef and West had no access to the original data of Wieringa et al, and, therefore, have no basis for their statement that "the statistical analysis in the article was wrong because the MRDR was not normally distributed." (In fact, the distribution was borderline normal.) More importantly, however, "heteroscedasticity of data does not produce any bias in the coefficient estimates, but will produce biased standard errors" (6). Hence, even if there is heteroscedasticity in the data, the correlation coefficients will still be reliable.
The discussion of normal distribution is beside the point, however. Although one does not need statistics to see the difference between the infants who received iron and the infants who did not receive iron (as depicted in Figure 3 of Wieringa et al's article), robust, nonparametric chi-square testing identified a highly significant difference between the infants who did and did not receive iron.
ACKNOWLEDGMENTS
Neither author had a conflict of interest.
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