Analysis of Exposure–Biomarker Relationships with the Johnson <italic>S</italic>_BB Distribution

Application of the Johnson bivariate S(B) distribution, or alternatively the S(BB) 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 S(B) distributions are enhanced by maximizing the Shapiro-Wilk W statistic. The subsequent goodness of fit for the S(BB) 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 S(BB) 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 S(BB) distribution may offer advantages.