Statistical Models in Toxicology

Description

Statistical Models in Toxicology presents an up-to-date and comprehensive account of statistical theory topics that occur in toxicology. The attention given by statisticians to the problem of health risk estimation for environmental and occupational exposures in the last few decades has created excitement and optimism among both statisticians and toxicologists. The development of modern statistical techniques with solid mathematical foundations in the twentieth century and the advent of modern computers in the latter part of the century gave way to the development of many statistical models and methods to describe toxicological processes and attempts to solve the associated problems. Not only have the models enjoyed a high level of elegance and sophistication mathematically, but they are widely used by industry and government regulatory agencies. Features: Focuses on describing the statistical models in environmental toxicology that facilitate the assessment of risk mainly in humans. The properties and shortfalls of each model are discussed, and its impact in the process of risk assessment is examined. Discusses models that assess the risk of mixtures of chemicals. Presents statistical models that are developed for risk estimation in different aspects of environmental toxicology including cancer and carcinogenic substances. Includes models for developmental and reproductive toxicity risk assessment, risk assessment in continuous outcomes, and developmental neurotoxicity. Contains numerous examples and exercises. Statistical Models in Toxicology introduces a wide variety of statistical models that are currently utilized for dose-response modeling and risk analysis. These models are often developed based on design and regulatory guidelines of toxicological experiments. The book is suitable for practitioners or it can be used as a textbook for advanced undergraduate or graduate students of mathematics and statistics. Cover Half Title Title Page Copyright Page Dedication Table of Contents Preface Author Bio 1 Introduction 1.1 Background 1.2 Branches of Toxicology 1.3 Basic Elements of Toxicology 1.4 Emergence of Statistical Models 1.5 Scope of This Book References 2 Quantitative Risk Assessment 2.1 Introduction 2.2 Process of Quantitative Risk Assessment 2.3 Methods of Risk Assessment 2.4 Quantitative Definitions of Risk 2.5 Risk Assessment for Quantal Responses 2.6 Risk Assessment for Quantitative Responses 2.7 Multivariate Responses 2.8 Benchmark Dose Software Exercises References 3 Statistical Models for Chemical Mixtures 3.1 Introduction 3.2 Additivity Models for Noninteractive Chemicals 3.3 Mixture of Interactive Chemicals 3.3.1 Characterizing Interactions of Two Chemicals (Binary Mixtures) 3.3.2 Statistical Methods for Departure from Linearity of Two Chemicals 3.3.3 Mixtures of More Than Two Chemicals 3.3.4 Application of 2k Factorial Experiments 3.3.5 Fixed-Ratio Ray Mixtures 3.3.6 Test of Additivity for Fixed-Ratio Ray Mixtures 3.3.7 Test of Additivity When a Single Chemical Data Are Not Available 3.4 Additional Topics Exercises References 4 Models for Carcinogenesis 4.1 Tolerance Distribution Models 4.2 Mechanistic Models 4.2.1 One-Hit Model 4.2.2 Multi-Hit (k-Hit) Model 4.2.3 Weibull Model 4.2.4 Linearized Multistage Model 4.2.5 Multistage Models of Carcinogenesis 4.2.5.1 Solution of the Armitage–Doll Model 4.2.6 Two-Stage Clonal Expansion Model 4.2.6.1 Exact Hazard for Piecewise Constant Rate Parameters 4.3 Discussion Exercises References 5 Models in Reproductive and Developmental Toxicology 5.1 Introduction 5.2 Design of Reproductive and Developmental Toxicity Experiments 5.3 Models for Incorporating the Litter Effect 5.3.1 The Beta-Binomial Model and Likelihood Models 5.3.2 The Quasi-Likelihood Models 5.3.3 Generalized Estimating Equations 5.4 Dose-Response Models 5.5 Risk Assessment for Developmental Toxicity Experiments 5.6 Application of Model Averaging 5.7 Statistical Models for Fetal Weight and Continuous Outcomes 5.8 Modeling Count 5.9 Statistical Models for Trinomial Outcomes 5.10 Statistical Models for Multiple Binary and Continuous Outcomes 5.11 Bayesian Approaches Exercises References 6 Analysis of Quantitative Data and Responses from Neurotoxicity Experiments 6.1 Introduction 6.2 Defining an Abnormal Response 6.3 Risk Assessment for Continuous Responses 6.4 Common Dose-Response Models 6.4.1 Normal Distribution 6.4.2 Skewed Distributions 6.5 Characterization of Dose-Response Models 6.5.1 Mixture of Two Normal Distributions 6.5.2 Risk Assessment for the Mixture Dose-Response Model 6.5.3 Maximum Likelihood Estimation 6.5.4 Risk Estimation 6.6 A More General Mixture Model 6.6.1 Risk Assessment with the Beta-Normal Model 6.7 A Semi-Parametric Approach 6.8.1 Defining Adverse Effect for Neurotoxicants 6.8.2 Dose-Response Model 6.8.3 A Saturated Model for Neurotoxic Effect 6.8.4 Modeling Time to Response Exercise References 7 Developmental Neurotoxicity Modeling and Risk Assessment 7.1 Introduction 7.2 Bioassay Design of Developmental Neurotoxicity Experiments 7.3 Data Analysis 7.4 Dose-Response Modeling 7.4.1 Intralitter Correlation 7.4.2 Maximum Likelihood Estimation 7.5 Risk Assessment 7.6 Modeling DNT Responses with Repeated Measures 7.7 Generalization to Non-Symmetric Distributions 7.7.1 Skew-Normal Distributions 7.7.2 Unconditional Distribution of Litter Means 7.7.3 Intralitter Correlation Exercises References Appendix 1: Data Generation for Mixture of Five Chemicals (Example 3.3) Appendix 2: Data Generation for a Mixture of Four Metals (Example 3.5) Appendix 3: Model Final Exam Questions Index