Analysis of exposure-biomarker relationships with the Johnson S BB distribution

Abstract

Application of the Johnson bivariate SB distribution, or alternatively the SBB distribution, is presented here as a tool for the analysis of concentration data and in particular for characterizing the relationship between exposures and biomarkers. Methods for fitting the marginal SB distributions are enhanced by maximizing the Shapiro-Wilk W statistic. The subsequent goodness of fit for the SBB distribution is evaluated with a multivariate Z statistic. Median regression results are extended here with methods for calculating the mean and standard deviation of the conditional array distributions. Application of these methods to the evaluation of the relationship between exposure to airborne bromopropane and the biomarker of serum bromide concentration suggests that the SBB distribution may be useful in stratifying workers by exposure based on using a biomarker. A comparison with the usual two-parameter log-normal approach shows that in some cases the SBB distribution may offer advantages. © The Author 2007. Published by Oxford University Press on behalf of the British Occupational Hygiene Society.