On Intra-individual Variations in Hair Minerals in Relation to Epidemiological Risk Assessment of Atopic Dermatitis

We have conducted a cohort study of 834-mother-infant pairs to determine the association between hair minerals at one month and the onset of atopic dermatitis (AD) at ten months after birth. Thirty-two minerals were measured by PIXE (particle induced X-ray emission) method. (Yamada et al., J. Trace Elem. Med. Bio. 27, 126-131, 2013, [11]) described a logistic model with explanatory variables Selenium (Se), Strontium (Sr) and a family history of AD whose performance in predicting the risk of AD was far better than that of any similar study. However, as discussed in (Saunders et al., Biometrie und Medizinische Informatik Greifswalder Seminarberichte, 18, 127-139, 2011, [9]), intra-individual variations in those minerals were large and could have degraded the regression coefficients of Sr and Se in the logistic model. Therefore, (Yamada et al., Biometrie und Medizinische Informatik Greifswalder Seminarberichte, 2013, [12]) examined the intra-individual variations of Sr levels in the mothers (Mother-Sr) assuming log-normality and obtained a regression coefficient of Mother-Sr corrected for the variations. This paper addresses Sr levels in the babies (Baby-Sr) which are not distributed as log-normal and require more sophisticated modeling of the variations. Here we elaborate on the “true-equivalent sample” (TES) method, developed in (Yamada et al., Biometrie und Medizinische Informatik Greifswalder Seminarberichte, 2013, [12]) and determine the distribution of Baby-Sr. The revised TES method presented here will be useful for determining the distribution type for minerals whose distributions are zero-inflated, thereby obtaining a risk estimate corrected for the intra-individual variations. This will allow hair mineral data to play a more important role in medical and epidemiological research.