Master of Science / Department of Statistics / Christopher I. Vahl / Chemicals and drugs applied to animals used in meat production often have the potential to cause adverse effects on human consumers. To ensure safety, a withdrawal period, i.e. the minimum time allowed between application of the drug and entry of the animal into the food supply, must be determined for each drug used on food-producing animals. The withdrawal period is based on an upper tolerance limit at a given time point. It is not uncommon that the concentration of the drug in some tissue samples to be measured at a level below the limit of quantitation (LOQ). Because the measurement of the tissue concentration cannot be confidently determined with enough precision, these types of observations are often treated as if they were left censored where the censoring value is equal to the limit of quantitation. Several methods are commonly used in practice to deal with this situation. The simplest methods are either to exclude observations below the limit of quantitation or to replace those values with zero, LOQ or ½ LOQ. Previous studies have shown that these methods result in biased in estimation of the population mean and population variance. Alternatively, one could incorporate censoring into the likelihood and compute the maximum likelihood estimate (MLE) for the population mean and variance assuming a normal or lognormal distribution. These estimates are also biased but it has been shown that they are asymptotically unbiased. However, it is not clear yet how these various methods affect estimation of the upper tolerance limit, especially when the sample size is small, e.g. less than 35. In this report, we will examine the effects of substituting the LOQ or ½ LOQ for censored values as well as using the MLEs of the mean and variance in the construction of an upper tolerance limit for a normal population through simulation. Additionally, we propose a modified substitution method where observations below the LOQ are replaced by functions of the order statistics of non-censored observations under an assumption of symmetry. Its performance relative to the above methods will also be evaluated in the simulation study. In the end, the results from this study will be applied to an environmental study.

De nombreuses études de biométrologie sont menées à l’INRS, pour évaluer l’exposition professionnelle à des substances chimiques, en France, et pour compléter les connaissances en proposant des valeurs de références destinées à protéger des salariés exposés à ces substances. Ces études consistent à mesurer simultanément l’imprégnation biologique et l’exposition atmosphérique à une substance, chez des salariés exposés à celle-ci. La relation entre ces mesures biologiques et atmosphériques est ensuite estimée à travers un modèle de régression linéaire. Lorsque que cette relation existe et que la voie d’absorption du toxique est essentiellement inhalatoire, il est ensuite possible de dériver une Valeur Limite Biologique (VLB) à partir de la Valeur Limite d’Exposition Professionnelle (VLEP-8h) du toxique. Deux aspects de ces données ont été identifiés, qui ne sont pas ou seulement partiellement prises en compte dans les modélisations statistiques courantes : la censure due aux limites de détection (LD)/quantification (LQ) des mesures biologiques et atmosphériques et la variabilité inter-individuelle. Ignorer ces deux particularités lors de la modélisation mène à une perte de puissance statistique et à de potentielles conclusions biaisées. Les travaux menés dans le cadre de cette thèse ont permis d’adapter le modèle de régression à ces deux caractéristiques, dans un cadre bayésien. L’approche proposée repose sur la modélisation des mesures atmosphériques à l’aide de modèles à effets aléatoires prenant en compte les valeurs inférieures à la LD/LQ, et sur la modélisation simultanée des mesures biologiques, supposée être linéairement dépendantes sur une échelle logarithmique, de l'exposition atmosphérique, tout en tenant compte de la variabilité inter-individuelle. Ce travail a donné lieu à une publication scientifique dans une revue à comité de lecture. L’application de cette méthodologie a été réalisée sur des jeux d’exposition professionnelle au béryllium et au chrome, après avoir été cependant adaptée aux caractéristiques toxicocinétiques de ces deux substances. Il a ainsi été possible de proposer une VLB pour le béryllium (0,06 µg/g créatinine). L’exploitation de mesures de chrome dans deux secteurs d’activités différents (exposition professionnelle aux peintures de chromates, et exposition professionnelle dans le secteur du chromage électrolytique) a permis de mettre en évidence que le chrome urinaire dépend essentiellement de l’exposition au chrome VI, le chrome non VI ayant moins d’impact. Nous n’avons pas pu montrer de relation entre la solubilité du CrVI et le chrome urinaire. Une VLB de 0,41 µg/g créatinine, de l’ordre de la Valeur Biologique de Référence (VBR) proposée par l’ANSES (0,54 µg/g créatinine), a été estimée pour l’exposition professionnelle aux peintures de chromates, et une VLB de 1,85 µg/g créatinine a été estimée pour l’exposition professionnelle dans le secteur du chromage électrolytique, qui est en cohérence avec la VLB proposée par l’ANSES dans ce secteur, à savoir 1,8 µg/g créatinine / Many biomonitoring studies are conducted at INRS, in order to assess occupational exposure to chemicals in France, and to propose reference values to protect workers exposed to these substances. These studies consist in measuring simultaneously biological and airborne exposure of workers exposed to a toxic substance. The relationship between these biological and airborne measurements is then estimated through a linear regression model. When this relationship exists and the route of absorption of the toxic is essentially inhalatory, it is possible to derive a Biological Limit Value (BLV) from the Occupational Exposure Limit Value (OEL) of the toxic substance. However, two characteristics of these data have been identified, which are not or only partially taken into account in the current statistical modelling: the left-censoring due to limits of detection (LoD)/quantification (LoQ) of biological and airborne measurements, and the between-individual variability. Ignoring both of these features in modelling leads to a loss of statistical power and potentially biased conclusions. The work carried out in this thesis allowed us to adapt the regression model to these two characteristics, in a Bayesian framework. The proposed approach is based on the modelling of airborne measurements using random effects models adapted for values below the LoD / LoQ, and on the simultaneous modelling of biological measurements, assumed to depend linearly on a logarithmic scale, on the airborne exposure, while taking into account between-subject variability. This work resulted in a scientific publication in a peer-reviewed journal. This methodology has been applied on beryllium and chromium occupational exposure datasets, after adaptation to the toxicokinetic characteristics of these two substances. It has thus been possible to propose a BLV for beryllium (0.06 μg / g creatinine). The analysis of chromium measurements in two different sectors of activity (occupational exposure to chromate paints, and occupational exposure in the electroplating sector) made it possible to show that urinary chromium depends mainly on airborne exposure to VI chromium, non-VI chromium having less impact. We were not able to show a relationship between the solubility of airborne VI chromium and urinary chromium. A BLV of 0.41 μg / g creatinine, close to the Biological Guidance Value (BGV) proposed by ANSES (0.54 μg / g creatinine), was estimated for occupational exposure to chromate paints, and a BLV of 1.85 μg/g creatinine was obtained for occupational exposure in the electrolytic chromium plating sector, which is consistent with the ANSES proposed BLV in this sector, i-e 1.8 μg / g creatinine

Made available in DSpace on 2016-06-02T20:06:01Z (GMT). No. of bitstreams: 1 2197.pdf: 1979337 bytes, checksum: 0091ce4138b8a98277d9af0d5d2aa788 (MD5) Previous issue date: 2008-11-13 / Universidade Federal de Sao Carlos / In this dissertation we present a regression modelling proposal for modelling the market prices of urban batches at São Carlos city (SP), over the year of 2005. Usual regression modelling and survival techniques, with left censoring, are considered. A simulation study exames the coverage probabilities the asymptotic confidence for the parameters of the considered modelling. / Nesta disertação apresentaremos uma proposta de um modelo de equação de regressão representativa para a formação do valor de mercado dos lotes urbanos do município de São Carlos, SP, ano de 2005, visando à criação de Plantas de Valores Genéricos (PVG) utilizando as técnicas de: Modelos Lineares Usuais (erros normais e variância constante), estes amplamente utilizados, e a Análise de Sobrevivência com censura à esquerda. Após o ajuste, as duas metodologias são comparadas e testadas num estudo de simulação onde examinamos a probabilidade de cobertura de alguns parâmetros envolvidos na regressão.

O principal objetivo desse trabalho é introduzir um modelo geral bayesiano Weibull hierárquico para dados censurados que estima a função de confiabilidade de cada componente para sistemas de confiabilidade coerentes. São introduzidos formas de estimação mais sólidas, sem a inserção de estimativas médias nas funções de confiabilidade (estimador plug-in). Através desse modelo, são expostos e solucionados exemplos na área de confiabilidade como sistemas em série, sistemas em paralelo, sistemas k-de-n, sistemas bridge e um estudo clínico com dados censurados intervalares. As soluções consideram que as componentes tem diferentes distribuições, e nesse caso, o sistema bridge ainda não havia solução na literatura. O modelo construído é geral e pode ser utilizado para qualquer sistema coerente e não apenas para dados da área de confiabilidade, como também na área de sobrevivência, dentre outros. Diversas simulações com componentes com diferentes proporções de censura, distintas médias, três tipos de distribuições e tamanhos de amostra foram feitas em todos os sistemas para avaliar a eficácia do modelo. / The main purpose of this work is to introduce a general bayesian Weibull hierarchical model for censored data which estimates each reliability components function from coherent systems. Its introduced estimation procedures which do not consider plug-in estimators. Also, its exposed and solved with this model examples in reliability area such as series systems, parallel systems, k-out-of-n systems, bridge systems and a clinical study with interval censoring data. The problem of bridge system hadnt a solution before for the case of each component with different distribution. Actually, this model is general and can be used to analyse any kind of coherent system and censored data, not only reliability ones, but also survival data and others. Several components simulations with different censored proportions, distinct means, three kinds of distributions and sample size were made in all systems to evaluate model efficiency.

O principal objetivo desse trabalho é introduzir um modelo geral bayesiano Weibull hierárquico para dados censurados que estima a função de confiabilidade de cada componente para sistemas de confiabilidade coerentes. São introduzidos formas de estimação mais sólidas, sem a inserção de estimativas médias nas funções de confiabilidade (estimador plug-in). Através desse modelo, são expostos e solucionados exemplos na área de confiabilidade como sistemas em série, sistemas em paralelo, sistemas k-de-n, sistemas bridge e um estudo clínico com dados censurados intervalares. As soluções consideram que as componentes tem diferentes distribuições, e nesse caso, o sistema bridge ainda não havia solução na literatura. O modelo construído é geral e pode ser utilizado para qualquer sistema coerente e não apenas para dados da área de confiabilidade, como também na área de sobrevivência, dentre outros. Diversas simulações com componentes com diferentes proporções de censura, distintas médias, três tipos de distribuições e tamanhos de amostra foram feitas em todos os sistemas para avaliar a eficácia do modelo. / The main purpose of this work is to introduce a general bayesian Weibull hierarchical model for censored data which estimates each reliability components function from coherent systems. Its introduced estimation procedures which do not consider plug-in estimators. Also, its exposed and solved with this model examples in reliability area such as series systems, parallel systems, k-out-of-n systems, bridge systems and a clinical study with interval censoring data. The problem of bridge system hadnt a solution before for the case of each component with different distribution. Actually, this model is general and can be used to analyse any kind of coherent system and censored data, not only reliability ones, but also survival data and others. Several components simulations with different censored proportions, distinct means, three kinds of distributions and sample size were made in all systems to evaluate model efficiency.