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.

• Preface ix Acknowledgments xiAbout the Companion Website xiii1. An Introduction to Toxicity Experiments 11.1 Nature and Purpose of Toxicity Experiments 11.2 Regulatory Context for Toxicity Experiments 71.3 Experimental Design Basics 81.4 Hierarchy of Models for Simple Toxicity Experiments 121.5 Biological vs. Statistical Significance 131.6 Historical Control Information 151.7 Sources of Variation and Uncertainty 151.8 Models with More Complex Structure 161.9 Multiple Tools to Meet a Variety of Needs or Simple Approaches to Capture Broad Strokes? 162. Statistical Analysis Basics 192.1 Introduction 192.2 NOEC/LOEC 192.3 Probability Distributions 242.4 Assessing Data for Meeting Model Requirements 292.5 Bayesian Methodology 302.6 Visual Examination of Data 302.10 Time‐to‐Event Data 372.11 Experiments with Multiple Controls 383. Analysis of Continuous Data: NOECs 473.1 Introduction 473.2 Pairwise Tests 473.3 Preliminary Assessment of the Data to Select the Proper Method of Analysis 533.4 Pairwise Tests When Data do not Meet Normality or Variance Homogeneity Requirements 623.5 Trend Tests 673.6 Protocol for NOEC Determination of Continuous Response 753.7 Inclusion of Random Effects 753.8 Alternative Error Structures 763.9 Power Analyses of Models 77 Exercises 814. Analysis of Continuous Data: Regression 894.1 Introduction 894.2 Models in Common Use to Describe Ecotoxicity Dose–Response Data 924.3 Model Fitting and Estimation of Parameters 954.4 Examples 1044.5 Summary of Model Assessment Tools for Continuous Responses 112Exercises 1145. Analysis of Continuous Data with Additional Factors 1235.1 Introduction 1235.2 Analysis of Covariance 1235.3 Experiments with Multiple Factors 135Exercises 416. Analysis of Quantal Data: NOECs 1576.1 Introduction 1576.2 Pairwise Tests 1576.3 Model Assessment for Quantal Data 1606.4 Pairwise Models that Accommodate Overdispersion 1626.5 Trend Tests for Quantal Response 1656.6 Power Comparisons of Tests for Quantal Responses 1686.7 Zero‐Inflated Binomial Responses 1726.8 Survival‐ or Age‐Adjusted Incidence Rates 175Exercises 1797. Analysis of Quantal Data: Regression Models 1817.1 Introduction 1817.2 Probit Model 1817.3 Weibull Model 1887.4 Logistic Model 1887.5 Abbott’s Formula and Normalization to the Control 1907.6 Proportions Treated as Continuous Responses 1977.7 Comparison of Models 1987.8 Including Time‐Varying  Responses in Models 1997.9 Up‐and‐Down Methods to Estimate LC50 2047.10 Methods for ECx Estimation When there is Little or no Partial Mortality 206Exercises 2158. Analysis of Count Data: NOEC and Regression 2198.1 Reproduction and Other Nonquantal Count Data 2198.2 Transformations to Continuous 2198.3 GLMM and NLME Models 2238.4 Analysis of Other Types of Count Data 228Exercises 2379. Analysis of Ordinal Data 2439.1 Introduction 2439.2 Pathology Severity Scores 2439.3 Developmental Stage 249Exercises 25510. Time‐to‐Event Data 25910.1 Introduction 25910.2 Kaplan–Meier  Product‐Limit Estimator 26110.3 Cox Regression Proportional Hazards Estimator 26610.4 Survival Analysis of Grouped Data 268Exercises 27111. Regulatory Issues 27511.1 Introduction 27511.2 Regulatory Tests 27511.3 Development of International Standardized Test Guidelines 27611.4 Strategic Approach to International Chemicals Management (SAICM) 27911.5 The United Nations Globally Harmonized System of Classification and Labelling of Chemicals (GHS) 27911.6 Statistical Methods in OECD Ecotoxicity Test Guidelines 27911.7 Regulatory Testing: Structures and Approaches 27911.8 Testing Strategies 28711.9 Nonguideline Studies 29112. Species Sensitivity Distributions 29312.1 Introduction 29312.2 Number, Choice, and Type of Species Endpoints to Include 29412.3 Choice and Evaluation of Distribution to Fit 29412.4 Variability and Uncertainty 30012.5 Incorporating Censored Data in an SSD 302Exercises 30713. Studies with Greater Complexity 30913.1 Introduction 30913.2 Mesocosm and Microcosm Experiments 31013.3 Microplate Experiments 31613.4 Errors‐in‐Variables Regression 32113.5 Analysis of Mixtures of Chemicals 32313.6 Benchmark Dose Models 32613.7 Limit Tests 32713.8 Minimum Safe Dose and Maximum Unsafe Dose 32913.9 Toxicokinetics and Toxicodynamics 331Exercises 343Appendix 1  Dataset 345Appendix 2 Mathematical Framework 347A2.3 Method of Maximum Likelihood 350A2.4 Bayesian Methodology 352A2.5   Analysis of Toxicity Experiments 354A2.6 Newton’s Optimization Method 358 Table A3.3 Linear and Quadratic ContrastA2.7 The Delta Method 359   Coefficients 366A2.8 Variance Components 360  Table A3.4 Williams’ Test tᾱ ,k for α = 0.05 367Appendix 3 TablesTable A3.1 Studentized Maximum Distribution 364Table  A3.2 Studentized Maximum Modulus Distribution 365Table A3.3 Linear and Quadratic Contrast Coefficients 366Table A3.4 Williams’ Test t̅α,k for α = 0.05 367References 371Author Index 385Subject Index 389

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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.

• Preface ix Acknowledgments xiAbout the Companion Website xiii1. An Introduction to Toxicity Experiments 11.1 Nature and Purpose of Toxicity Experiments 11.2 Regulatory Context for Toxicity Experiments 71.3 Experimental Design Basics 81.4 Hierarchy of Models for Simple Toxicity Experiments 121.5 Biological vs. Statistical Significance 131.6 Historical Control Information 151.7 Sources of Variation and Uncertainty 151.8 Models with More Complex Structure 161.9 Multiple Tools to Meet a Variety of Needs or Simple Approaches to Capture Broad Strokes? 162. Statistical Analysis Basics 192.1 Introduction 192.2 NOEC/LOEC 192.3 Probability Distributions 242.4 Assessing Data for Meeting Model Requirements 292.5 Bayesian Methodology 302.6 Visual Examination of Data 302.10 Time‐to‐Event Data 372.11 Experiments with Multiple Controls 383. Analysis of Continuous Data: NOECs 473.1 Introduction 473.2 Pairwise Tests 473.3 Preliminary Assessment of the Data to Select the Proper Method of Analysis 533.4 Pairwise Tests When Data do not Meet Normality or Variance Homogeneity Requirements 623.5 Trend Tests 673.6 Protocol for NOEC Determination of Continuous Response 753.7 Inclusion of Random Effects 753.8 Alternative Error Structures 763.9 Power Analyses of Models 77 Exercises 814. Analysis of Continuous Data: Regression 894.1 Introduction 894.2 Models in Common Use to Describe Ecotoxicity Dose–Response Data 924.3 Model Fitting and Estimation of Parameters 954.4 Examples 1044.5 Summary of Model Assessment Tools for Continuous Responses 112Exercises 1145. Analysis of Continuous Data with Additional Factors 1235.1 Introduction 1235.2 Analysis of Covariance 1235.3 Experiments with Multiple Factors 135Exercises 416. Analysis of Quantal Data: NOECs 1576.1 Introduction 1576.2 Pairwise Tests 1576.3 Model Assessment for Quantal Data 1606.4 Pairwise Models that Accommodate Overdispersion 1626.5 Trend Tests for Quantal Response 1656.6 Power Comparisons of Tests for Quantal Responses 1686.7 Zero‐Inflated Binomial Responses 1726.8 Survival‐ or Age‐Adjusted Incidence Rates 175Exercises 1797. Analysis of Quantal Data: Regression Models 1817.1 Introduction 1817.2 Probit Model 1817.3 Weibull Model 1887.4 Logistic Model 1887.5 Abbott’s Formula and Normalization to the Control 1907.6 Proportions Treated as Continuous Responses 1977.7 Comparison of Models 1987.8 Including Time‐Varying  Responses in Models 1997.9 Up‐and‐Down Methods to Estimate LC50 2047.10 Methods for ECx Estimation When there is Little or no Partial Mortality 206Exercises 2158. Analysis of Count Data: NOEC and Regression 2198.1 Reproduction and Other Nonquantal Count Data 2198.2 Transformations to Continuous 2198.3 GLMM and NLME Models 2238.4 Analysis of Other Types of Count Data 228Exercises 2379. Analysis of Ordinal Data 2439.1 Introduction 2439.2 Pathology Severity Scores 2439.3 Developmental Stage 249Exercises 25510. Time‐to‐Event Data 25910.1 Introduction 25910.2 Kaplan–Meier  Product‐Limit Estimator 26110.3 Cox Regression Proportional Hazards Estimator 26610.4 Survival Analysis of Grouped Data 268Exercises 27111. Regulatory Issues 27511.1 Introduction 27511.2 Regulatory Tests 27511.3 Development of International Standardized Test Guidelines 27611.4 Strategic Approach to International Chemicals Management (SAICM) 27911.5 The United Nations Globally Harmonized System of Classification and Labelling of Chemicals (GHS) 27911.6 Statistical Methods in OECD Ecotoxicity Test Guidelines 27911.7 Regulatory Testing: Structures and Approaches 27911.8 Testing Strategies 28711.9 Nonguideline Studies 29112. Species Sensitivity Distributions 29312.1 Introduction 29312.2 Number, Choice, and Type of Species Endpoints to Include 29412.3 Choice and Evaluation of Distribution to Fit 29412.4 Variability and Uncertainty 30012.5 Incorporating Censored Data in an SSD 302Exercises 30713. Studies with Greater Complexity 30913.1 Introduction 30913.2 Mesocosm and Microcosm Experiments 31013.3 Microplate Experiments 31613.4 Errors‐in‐Variables Regression 32113.5 Analysis of Mixtures of Chemicals 32313.6 Benchmark Dose Models 32613.7 Limit Tests 32713.8 Minimum Safe Dose and Maximum Unsafe Dose 32913.9 Toxicokinetics and Toxicodynamics 331Exercises 343Appendix 1  Dataset 345Appendix 2 Mathematical Framework 347A2.3 Method of Maximum Likelihood 350A2.4 Bayesian Methodology 352A2.5   Analysis of Toxicity Experiments 354A2.6 Newton’s Optimization Method 358 Table A3.3 Linear and Quadratic ContrastA2.7 The Delta Method 359   Coefficients 366A2.8 Variance Components 360  Table A3.4 Williams’ Test tᾱ ,k for α = 0.05 367Appendix 3 TablesTable A3.1 Studentized Maximum Distribution 364Table  A3.2 Studentized Maximum Modulus Distribution 365Table A3.3 Linear and Quadratic Contrast Coefficients 366Table A3.4 Williams’ Test t̅α,k for α = 0.05 367References 371Author Index 385Subject Index 389

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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.

• Preface ix Acknowledgments xiAbout the Companion Website xiii1. An Introduction to Toxicity Experiments 11.1 Nature and Purpose of Toxicity Experiments 11.2 Regulatory Context for Toxicity Experiments 71.3 Experimental Design Basics 81.4 Hierarchy of Models for Simple Toxicity Experiments 121.5 Biological vs. Statistical Significance 131.6 Historical Control Information 151.7 Sources of Variation and Uncertainty 151.8 Models with More Complex Structure 161.9 Multiple Tools to Meet a Variety of Needs or Simple Approaches to Capture Broad Strokes? 162. Statistical Analysis Basics 192.1 Introduction 192.2 NOEC/LOEC 192.3 Probability Distributions 242.4 Assessing Data for Meeting Model Requirements 292.5 Bayesian Methodology 302.6 Visual Examination of Data 302.10 Time‐to‐Event Data 372.11 Experiments with Multiple Controls 383. Analysis of Continuous Data: NOECs 473.1 Introduction 473.2 Pairwise Tests 473.3 Preliminary Assessment of the Data to Select the Proper Method of Analysis 533.4 Pairwise Tests When Data do not Meet Normality or Variance Homogeneity Requirements 623.5 Trend Tests 673.6 Protocol for NOEC Determination of Continuous Response 753.7 Inclusion of Random Effects 753.8 Alternative Error Structures 763.9 Power Analyses of Models 77 Exercises 814. Analysis of Continuous Data: Regression 894.1 Introduction 894.2 Models in Common Use to Describe Ecotoxicity Dose–Response Data 924.3 Model Fitting and Estimation of Parameters 954.4 Examples 1044.5 Summary of Model Assessment Tools for Continuous Responses 112Exercises 1145. Analysis of Continuous Data with Additional Factors 1235.1 Introduction 1235.2 Analysis of Covariance 1235.3 Experiments with Multiple Factors 135Exercises 416. Analysis of Quantal Data: NOECs 1576.1 Introduction 1576.2 Pairwise Tests 1576.3 Model Assessment for Quantal Data 1606.4 Pairwise Models that Accommodate Overdispersion 1626.5 Trend Tests for Quantal Response 1656.6 Power Comparisons of Tests for Quantal Responses 1686.7 Zero‐Inflated Binomial Responses 1726.8 Survival‐ or Age‐Adjusted Incidence Rates 175Exercises 1797. Analysis of Quantal Data: Regression Models 1817.1 Introduction 1817.2 Probit Model 1817.3 Weibull Model 1887.4 Logistic Model 1887.5 Abbott’s Formula and Normalization to the Control 1907.6 Proportions Treated as Continuous Responses 1977.7 Comparison of Models 1987.8 Including Time‐Varying  Responses in Models 1997.9 Up‐and‐Down Methods to Estimate LC50 2047.10 Methods for ECx Estimation When there is Little or no Partial Mortality 206Exercises 2158. Analysis of Count Data: NOEC and Regression 2198.1 Reproduction and Other Nonquantal Count Data 2198.2 Transformations to Continuous 2198.3 GLMM and NLME Models 2238.4 Analysis of Other Types of Count Data 228Exercises 2379. Analysis of Ordinal Data 2439.1 Introduction 2439.2 Pathology Severity Scores 2439.3 Developmental Stage 249Exercises 25510. Time‐to‐Event Data 25910.1 Introduction 25910.2 Kaplan–Meier  Product‐Limit Estimator 26110.3 Cox Regression Proportional Hazards Estimator 26610.4 Survival Analysis of Grouped Data 268Exercises 27111. Regulatory Issues 27511.1 Introduction 27511.2 Regulatory Tests 27511.3 Development of International Standardized Test Guidelines 27611.4 Strategic Approach to International Chemicals Management (SAICM) 27911.5 The United Nations Globally Harmonized System of Classification and Labelling of Chemicals (GHS) 27911.6 Statistical Methods in OECD Ecotoxicity Test Guidelines 27911.7 Regulatory Testing: Structures and Approaches 27911.8 Testing Strategies 28711.9 Nonguideline Studies 29112. Species Sensitivity Distributions 29312.1 Introduction 29312.2 Number, Choice, and Type of Species Endpoints to Include 29412.3 Choice and Evaluation of Distribution to Fit 29412.4 Variability and Uncertainty 30012.5 Incorporating Censored Data in an SSD 302Exercises 30713. Studies with Greater Complexity 30913.1 Introduction 30913.2 Mesocosm and Microcosm Experiments 31013.3 Microplate Experiments 31613.4 Errors‐in‐Variables Regression 32113.5 Analysis of Mixtures of Chemicals 32313.6 Benchmark Dose Models 32613.7 Limit Tests 32713.8 Minimum Safe Dose and Maximum Unsafe Dose 32913.9 Toxicokinetics and Toxicodynamics 331Exercises 343Appendix 1  Dataset 345Appendix 2 Mathematical Framework 347A2.3 Method of Maximum Likelihood 350A2.4 Bayesian Methodology 352A2.5   Analysis of Toxicity Experiments 354A2.6 Newton’s Optimization Method 358 Table A3.3 Linear and Quadratic ContrastA2.7 The Delta Method 359   Coefficients 366A2.8 Variance Components 360  Table A3.4 Williams’ Test tᾱ ,k for α = 0.05 367Appendix 3 TablesTable A3.1 Studentized Maximum Distribution 364Table  A3.2 Studentized Maximum Modulus Distribution 365Table A3.3 Linear and Quadratic Contrast Coefficients 366Table A3.4 Williams’ Test t̅α,k for α = 0.05 367References 371Author Index 385Subject Index 389

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