Statistical Analysis of Ecotoxicity Studies

A guide to the issues relevant to the design, analysis, and interpretation of toxicity studies that examine chemicals for use in the environment Statistical Analysis of Ecotoxicity Studies offers a guide to the design, analysis, and interpretation of a range of experiments that are used to assess the toxicity of chemicals. While the book highlights ecotoxicity studies, the methods presented are applicable to the broad range of toxicity studies. The text contains myriad datasets (from laboratory and field research) that clearly illustrate the book's topics. The datasets reveal the techniques, pitfalls, and precautions derived from these studies. The text includes information on recently developed methods for the analysis of severity scores and other ordered responses, as well as extensive power studies of competing tests and computer simulation studies of regression models that offer an understanding of the sensitivity (or lack thereof) of various methods and the quality of parameter estimates from regression models. The authors also discuss the regulatory process indicating how test guidelines are developed and review the statistical methodology in current or pending OECD and USEPA ecotoxicity guidelines. This important guide: Offers the information needed for the design and analysis to a wide array of ecotoxicity experiments and to the development of international test guidelines used to assess the toxicity of chemicals Contains a thorough examination of the statistical issues that arise in toxicity studies, especially ecotoxicity Includes an introduction to toxicity experiments and statistical analysis basics Includes programs in R and excel Covers the analysis of continuous and Quantal data, analysis of data as well as Regulatory Issues Presents additional topics (Mesocosm and Microplate experiments, mixtures of chemicals, benchmark dose models, and limit tests) as well as software Written for directors, scientists, regulators, and technicians, Statistical Analysis of Ecotoxicity Studies provides a sound understanding of the technical and practical issues in designing, analyzing, and interpreting toxicity studies to support or challenge chemicals for use in the environment.

Table of Contents:
Preface ix Acknowledgments xi About the Companion Website xiii 1. An Introduction to Toxicity Experiments 1 1.1 Nature and Purpose of Toxicity Experiments 1 1.2 Regulatory Context for Toxicity Experiments 7 1.3 Experimental Design Basics 8 1.4 Hierarchy of Models for Simple Toxicity Experiments 12 1.5 Biological vs. Statistical Significance 13 1.6 Historical Control Information 15 1.7 Sources of Variation and Uncertainty 15 1.8 Models with More Complex Structure 16 1.9 Multiple Tools to Meet a Variety of Needs or Simple Approaches to Capture Broad Strokes? 16 2. Statistical Analysis Basics 19 2.1 Introduction 19 2.2 NOEC/LOEC 19 2.3 Probability Distributions 24 2.4 Assessing Data for Meeting Model Requirements 29 2.5 Bayesian Methodology 30 2.6 Visual Examination of Data 30 2.10 Time‐to‐Event Data 37 2.11 Experiments with Multiple Controls 38 3. Analysis of Continuous Data: NOECs 47 3.1 Introduction 47 3.2 Pairwise Tests 47 3.3 Preliminary Assessment of the Data to Select the Proper Method of Analysis 53 3.4 Pairwise Tests When Data do not Meet Normality or Variance Homogeneity Requirements 62 3.5 Trend Tests 67 3.6 Protocol for NOEC Determination of Continuous Response 75 3.7 Inclusion of Random Effects 75 3.8 Alternative Error Structures 76 3.9 Power Analyses of Models 77 Exercises 81 4. Analysis of Continuous Data: Regression 89 4.1 Introduction 89 4.2 Models in Common Use to Describe Ecotoxicity Dose–Response Data 92 4.3 Model Fitting and Estimation of Parameters 95 4.4 Examples 104 4.5 Summary of Model Assessment Tools for Continuous Responses 112 Exercises 114 5. Analysis of Continuous Data with Additional Factors 123 5.1 Introduction 123 5.2 Analysis of Covariance 123 5.3 Experiments with Multiple Factors 135 Exercises 41 6. Analysis of Quantal Data: NOECs 157 6.1 Introduction 157 6.2 Pairwise Tests 157 6.3 Model Assessment for Quantal Data 160 6.4 Pairwise Models that Accommodate Overdispersion 162 6.5 Trend Tests for Quantal Response 165 6.6 Power Comparisons of Tests for Quantal Responses 168 6.7 Zero‐Inflated Binomial Responses 172 6.8 Survival‐ or Age‐Adjusted Incidence Rates 175 Exercises 179 7. Analysis of Quantal Data: Regression Models 181 7.1 Introduction 181 7.2 Probit Model 181 7.3 Weibull Model 188 7.4 Logistic Model 188 7.5 Abbott’s Formula and Normalization to the Control 190 7.6 Proportions Treated as Continuous Responses 197 7.7 Comparison of Models 198 7.8 Including Time‐Varying  Responses in Models 199 7.9 Up‐and‐Down Methods to Estimate LC50 204 7.10 Methods for ECx Estimation When there is Little or no Partial Mortality 206 Exercises 215 8. Analysis of Count Data: NOEC and Regression 219 8.1 Reproduction and Other Nonquantal Count Data 219 8.2 Transformations to Continuous 219 8.3 GLMM and NLME Models 223 8.4 Analysis of Other Types of Count Data 228 Exercises 237 9. Analysis of Ordinal Data 243 9.1 Introduction 243 9.2 Pathology Severity Scores 243 9.3 Developmental Stage 249 Exercises 255 10. Time‐to‐Event Data 259 10.1 Introduction 259 10.2 Kaplan–Meier  Product‐Limit Estimator 261 10.3 Cox Regression Proportional Hazards Estimator 266 10.4 Survival Analysis of Grouped Data 268 Exercises 271 11. Regulatory Issues 275 11.1 Introduction 275 11.2 Regulatory Tests 275 11.3 Development of International Standardized Test Guidelines 276 11.4 Strategic Approach to International Chemicals Management (SAICM) 279 11.5 The United Nations Globally Harmonized System of Classification and Labelling of Chemicals (GHS) 279 11.6 Statistical Methods in OECD Ecotoxicity Test Guidelines 279 11.7 Regulatory Testing: Structures and Approaches 279 11.8 Testing Strategies 287 11.9 Nonguideline Studies 291 12. Species Sensitivity Distributions 293 12.1 Introduction 293 12.2 Number, Choice, and Type of Species Endpoints to Include 294 12.3 Choice and Evaluation of Distribution to Fit 294 12.4 Variability and Uncertainty 300 12.5 Incorporating Censored Data in an SSD 302 Exercises 307 13. Studies with Greater Complexity 309 13.1 Introduction 309 13.2 Mesocosm and Microcosm Experiments 310 13.3 Microplate Experiments 316 13.4 Errors‐in‐Variables Regression 321 13.5 Analysis of Mixtures of Chemicals 323 13.6 Benchmark Dose Models 326 13.7 Limit Tests 327 13.8 Minimum Safe Dose and Maximum Unsafe Dose 329 13.9 Toxicokinetics and Toxicodynamics 331 Exercises 343 Appendix 1  Dataset 345 Appendix 2 Mathematical Framework 347 A2.3 Method of Maximum Likelihood 350 A2.4 Bayesian Methodology 352 A2.5   Analysis of Toxicity Experiments 354 A2.6 Newton’s Optimization Method 358 Table A3.3 Linear and Quadratic Contrast A2.7 The Delta Method 359   Coefficients 366 A2.8 Variance Components 360  Table A3.4 Williams’ Test tᾱ ,k for α = 0.05 367 Appendix 3 Tables Table A3.1 Studentized Maximum Distribution 364 Table  A3.2 Studentized Maximum Modulus Distribution 365 Table A3.3 Linear and Quadratic Contrast Coefficients 366 Table A3.4 Williams’ Test t̅α,k for α = 0.05 367 References 371 Author Index 385 Subject Index 389

About the Author :
JOHN W. GREEN, PHD, PHD is currently a Principal Consultant Biostatistics in DuPont Data Science and Informatics Group. Dr. Green is the lead DuPont statistician developing internal expertise and training in probabilistic risk assessment methods following guidance developed by EUFRAM and has been very active in OECD expert groups developing test guidelines and guidance documents. TIMOTHY A. SPRINGER, PHD has served as the statistician for Wildlife International, a leading contract ecotoxicology testing laboratory, for over 25 years. HENRIK HOLBECH, PHD is an Associate Professor in Ecotoxicology at the University of Southern Denmark.