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.

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 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 t̅_α,k for α = 0.05 367

References 371

Author Index 385

Subject Index 389

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