Unsupervised Fit of Distributions for Probabilistic Exposure Factors

Abstract

P-730 Abstract: In 1995 the German Committee for Environmental Hygiene (AUH) published the first German Exposure Factors Handbook (Standards zur Expositionsabschätzung). This handbook compiles many variables influencing the uptake such as inhalation rates, food consumption or anthropometric data. Ten years later the German Federal Environmental Agency (UBA) funded the Xprob-project to evaluate and update these information. One objective was to generate input distributions for use in probabilistic exposure modelling. The project started with the definition of a uniform report format for probabilistic exposure factors. The format will provide the user with all information necessary for choosing the desired exposure factor, for computing a deterministic or probabilistic exposure model, for evaluating the uncertainties and discussing model alternatives. All information are provided in a structured electronic database, which could be extended by the users and/or the funding institution. This form offers clear advantages compared to the actual state where data are presented isolated and in unequal quality. In a second step criteria for the evaluation of empirical data were discussed. The project chose a minimal set of requirements, which is needed for the fit of a distribution to the data. A generalized F-distribution with point mass at zero was estimated using the maximum likelihood principle. For practical reasons a subdistribution with two parameters and point mass at zero was determined by minimising the likelihood ratio. To incorporate additional information on strata, especially on sex and on age, a method was developed, which divides the population in homogeneous subgroups. The F-statistic was used here as criteria for optimisation. The determination of distributions goes on unsupervised and in the same manner for all (continuous, positive) exposure factors. The procedure is transparent; in particular, the achieved goodness of fit is described. The program code will be freely available at the end of the project. The results comply with the proposed report format and are harmonized in the sense that they share the same assumptions. The rationale behind the procedure will be compared with alternative methods. We will discuss the use of the report format and the database, exemplified by some exposure factors. An outlook to further enhancements is given, like fitting of censored and multidimensional data. Approaches for two-dimensional exposure models, which also take the uncertainty of the fit into consideration, will be discussed too. Finally we combine the exposure assessment with a probabilistic effect assessment and discuss the benefit for a transparent and rational regulation.