title: Model averaging quantiles from data censored by a limit of detection.
abstract: In chemical risk assessment, it is important to determine the quantiles of the distribution of concentration data. The selection of an appropriate distribution and the estimation of particular quantiles of interest are largely hindered by the omnipresence of observations below the limit of detection, leading to left-censored data. The log-normal distribution is a common choice, but this distribution is not the only possibility and alternatives should be considered as well. Here, we focus on several distributions that are related to the log-normal distribution or that are seminonparametric extensions of the log-normal distribution. Whereas previous work focused on the estimation of the cumulative distribution function, our interest here goes to the estimation of quantiles, particularly in the left tail of the distribution where most of the left-censored data are located. Two different model averaged quantile estimators are defined and compared for different families of candidate models. The models and methods of selection and averaging are further investigated through simulations and illustrated on data of cadmium concentration in food products. The approach is extended to include covariates and to deal with uncertainty about the values of the limit of detection. These extensions are illustrated with (134) cesium measurements from Fukushima Prefecture, Japan. We can conclude that averaged models do achieve good performance characteristics in case no useful prior knowledge about the true distribution is available; that there is no structural difference in the performance of the direct and indirect method; and that, not surprisingly, only the true or closely approximating model can deal with extremely high percentages of censoring.
authors.affiliation: Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Hasselt University, Martelarenlaan 42, 3500 Hasselt, Belgium.
authors.forename: Ruth
authors.initials: R
authors.lastname: Nysen
authors.affiliation: Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Hasselt University, Martelarenlaan 42, 3500 Hasselt, Belgium.
authors.forename: Christel
authors.initials: C
authors.lastname: Faes
authors.affiliation: Nutrition and Metabolism Unit, International Agency for Research on Cancer (IARC). 150 Cours Albert Thomas, 69372 Lyon Cedex 08, France.
authors.forename: Pietro
authors.initials: P
authors.lastname: Ferrari
authors.affiliation: Department of Food Safety and Zoonoses, World Health Organization, 20, Avenue Appia, 1211 Geneva 27, Switzerland.
authors.forename: Philippe
authors.initials: P
authors.lastname: Verger
authors.affiliation: Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Hasselt University, Martelarenlaan 42, 3500 Hasselt, Belgium.
authors.forename: Marc
authors.initials: M
authors.lastname: Aerts
mesh_terms: D002104:Cadmium / Q000032:analysis; D002588:Cesium Radioisotopes / Q000032:analysis; D005506:Food Contamination / Q000032:analysis; D059022:Food Safety; D057230:Limit of Detection; D015233:Models, Statistical; D018570:Risk Assessment
chemical_list: D002588:Cesium Radioisotopes; D002104:Cadmium
keywords: Left-censoring; Limit of detection; Model averaging; Quantiles