LAUSR

In the April 2018 issue of the European Journal of Pediatrics, we published results from the nationwide and representative KiGGS study in German adolescents aged 11 to 17 years, showing significant associations between serum 25-hydroxyvitamin D (25[OH]D) concentrations and clinically important hematological markers of red blood cells [2]. In a letter to the editor, Virella and colleagues expressed concerns regarding the statistical methodology used in our paper [4]. We appreciate their well-advised comment on our paper and, indeed, completely agree with their criticism that the proportion of published false-positive findings is expected to increase with decreasing effect sizes, as was reported in our article. Unfortunately, however, Virella et al. did not consider in their comment that there is likewise an increased probability that statistically significant results may, in fact, be false-positive when a study is underpowered due to an unacceptably low sample size [1 ]. In view of the large sample size of the KiGGS cohort, we have clearly acknowledged this methodological limitation in the BDiscussion^ section of our original paper and, in addition, pointed out that due to the cross-sectional analysis, any causal interpretation of our findings is not allowed. Given the sample heterogeneity and the overall small range of hematological measurements, it is not surprising that the reported effect sizes in our analysis were generally small. Our observation of significant and independent associations between serum 25[OH]D levels and numerous red blood cell indices can serve as a basis not only for replicating this research in future trials but also for stimulating further hypothesis testing. Thus, we performed herein an additional analysis of the same KiGGS age cohort to test the research question whether health-related quality of life is mediating these relationships. To this end, we computed a set of mediation models using the bootstrapping method developed by Hayes [3] to test for possible interaction effects of health-related quality of life, as measured by the self-rated KINDL questionnaire, on the associations between serum 25[OH]D and the various red blood cell parameters. In these mediation models, the same set of covariates was used as in the regression analyses, in order to keep the results comparable to our published data [2]. The results from this alternative approach confirmed our main conclusion by showing significant direct effects of serum vitamin D on each red blood cell parameter (p < 0.015), except for the mean corpuscular volume and ferritin. Again, the observed effect sizes were expectedly small. In contrast to these direct effects, the indirect effects failed to reach significance for all parameters tested, except for the mean corpuscular hemoglobin (MCH, lower and upper levels for the confidence interval [LLCI, ULCI] = 0.0005, 0.0077), as judged from their 95th percentile-based confidence intervals exceeding zero. In summary, these novel data from the mediator analysis Communicated by Peter de Winter