Statistical Analysis of Ecotoxicity Studies E-Book

John W. Green

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 1284

Veröffentlichungsjahr: 2018

Beschreibung

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.

Leseprobe

Table of Contents

Cover

Preface

Chapter 1: An Introduction to Toxicity Experiments

1.1 NATURE AND PURPOSE OF TOXICITY EXPERIMENTS

1.2 REGULATORY CONTEXT FOR TOXICITY EXPERIMENTS

1.3 EXPERIMENTAL DESIGN BASICS

1.4 HIERARCHY OF MODELS FOR SIMPLE TOXICITY EXPERIMENTS

1.5 BIOLOGICAL VS. STATISTICAL SIGNIFICANCE

1.6 HISTORICAL CONTROL INFORMATION

1.7 SOURCES OF VARIATION AND UNCERTAINTY

1.8 MODELS WITH MORE COMPLEX STRUCTURE

1.9 MULTIPLE TOOLS TO MEET A VARIETY OF NEEDS OR SIMPLE APPROACHES TO CAPTURE BROAD STROKES?

Chapter 2: Statistical Analysis Basics

2.1 INTRODUCTION

2.2 NOEC/LOEC

2.3 PROBABILITY DISTRIBUTIONS

2.4 ASSESSING DATA FOR MEETING MODEL REQUIREMENTS

2.5 BAYESIAN METHODOLOGY

2.6 VISUAL EXAMINATION OF DATA

2.7 REGRESSION MODELS

2.8 BIOLOGY‐BASED MODELS

2.9 DISCRETE RESPONSES

2.10 TIME‐TO‐EVENT DATA

2.11 EXPERIMENTS WITH MULTIPLE CONTROLS

EXERCISES

Chapter 3: Analysis of Continuous Data

3.1 INTRODUCTION

3.2 PAIRWISE TESTS

3.3 PRELIMINARY ASSESSMENT OF THE DATA TO SELECT THE PROPER METHOD OF ANALYSIS

3.4 PAIRWISE TESTS WHEN DATA DO NOT MEET NORMALITY OR VARIANCE HOMOGENEITY REQUIREMENTS

3.5 TREND TESTS

3.6 PROTOCOL FOR NOEC DETERMINATION OF CONTINUOUS RESPONSE

3.7 INCLUSION OF RANDOM EFFECTS

3.8 ALTERNATIVE ERROR STRUCTURES

3.9 POWER ANALYSES OF MODELS

EXERCISES

Chapter 4: Analysis of Continuous Data

4.1 INTRODUCTION

4.2 MODELS iN COMMON USE tO DESCRIBE ECOTOXICITY DOSE–RESPONSE DATA

4.3 MODEL FITTING AND ESTIMATION OF PARAMETERS

4.4 EXAMPLES

4.5 SUMMARY OF MODEL ASSESSMENT TOOLS FOR CONTINUOUS RESPONSES

EXERCISES

Chapter 5: Analysis of Continuous Data with Additional Factors

5.1 INTRODUCTION

5.2 ANALYSIS OF COVARIANCE

5.3 EXPERIMENTS WITH MULTIPLE FACTORS

EXERCISES

Chapter 6: Analysis of Quantal Data

6.1 INTRODUCTION

6.2 PAIRWISE TESTS

6.3 MODEL ASSESSMENT FOR QUANTAL DATA

6.4 PAIRWISE MODELS THAT ACCOMMODATE OVERDISPERSION

6.5 TREND TESTS FOR QUANTAL RESPONSE

6.6 POWER COMPARISONS OF TESTS FOR QUANTAL RESPONSES

6.7 ZERO‐INFLATED BINOMIAL RESPONSES

6.8 SURVIVAL‐ OR AGE‐ADJUSTED INCIDENCE RATES

EXERCISES

Chapter 7: Analysis of Quantal Data

7.1 INTRODUCTION

7.2 PROBIT MODEL

7.3 WEIBULL MODEL

7.4 LOGISTIC MODEL

7.5 ABBOTT’S FORMULA AND NORMALIZATION TO THE CONTROL

7.6 PROPORTIONS TREATED AS CONTINUOUS RESPONSES

7.7 COMPARISON OF MODELS

7.8 INCLUDING TIME‐VARYING RESPONSES IN MODELS

7.9 UP‐AND‐DOWN METHODS TO ESTIMATE LC50

7.10 METHODS FOR EC

X

ESTIMATION WHEN THERE IS LITTLE OR NO PARTIAL MORTALITY

EXERCISES

Chapter 8: Analysis of Count Data

8.1 REPRODUCTION AND OTHER NONQUANTAL COUNT DATA

8.2 TRANSFORMATIONS TO CONTINUOUS

8.3 GLMM AND NLME MODELS

8.4 ANALYSIS OF OTHER TYPES OF COUNT DATA

EXERCISES

Chapter 9: Analysis of Ordinal Data

9.1 INTRODUCTION

9.2 PATHOLOGY SEVERITY SCORES

9.3 DEVELOPMENTAL STAGE

EXERCISES

Chapter 10: Time‐to‐Event Data

10.1 INTRODUCTION

10.2 KAPLAN–MEIER PRODUCT‐LIMIT ESTIMATOR

10.3 COX REGRESSION PROPORTIONAL HAZARDS ESTIMATOR

10.4 SURVIVAL ANALYSIS OF GROUPED DATA

EXERCISES

Chapter 11: Regulatory Issues

11.1 INTRODUCTION

11.2 REGULATORY TESTS

11.3 DEVELOPMENT OF INTERNATIONAL STANDARDIZED TEST GUIDELINES

11.4 STRATEGIC APPROACH TO INTERNATIONAL CHEMICALS MANAGEMENT (SAICM)

11.5 THE UNITED NATIONS GLOBALLY HARMONIZED SYSTEM OF CLASSIFICATION AND LABELLING OF CHEMICALS (GHS)

11.6 STATISTICAL METHODS IN OECD ECOTOXICITY TEST GUIDELINES

11.7 REGULATORY TESTING: STRUCTURES AND APPROACHES

11.8 TESTING STRATEGIES

11.9 NONGUIDELINE STUDIES

Chapter 12: Species Sensitivity Distributions

12.1 INTRODUCTION

12.2 NUMBER, CHOICE, AND TYPE OF SPECIES ENDPOINTS TO INCLUDE

12.3 CHOICE AND EVALUATION OF DISTRIBUTION TO FIT

12.4 VARIABILITY AND UNCERTAINTY

12.5 INCORPORATING CENSORED DATA IN AN SSD

EXERCISES

Chapter 13: Studies with Greater Complexity

13.1 INTRODUCTION

13.2 MESOCOSM AND MICROCOSM EXPERIMENTS

13.3 MICROPLATE EXPERIMENTS

13.4 ERRORS‐IN‐VARIABLES REGRESSION

13.5 ANALYSIS OF MIXTURES OF CHEMICALS

13.6 BENCHMARK DOSE MODELS

13.7 LIMIT TESTS

13.8 MINIMUM SAFE DOSE AND MAXIMUM UNSAFE DOSE

13.9 TOXICOKINETICS AND TOXICODYNAMICS

EXERCISES

Appendix 1: Dataset

Appendix 2: Mathematical Framework

A2.1 BASIC PROBABILITY CONCEPTS

A2.2 DISTRIBUTION FUNCTIONS

A2.3 METHOD OF MAXIMUM LIKELIHOOD

A2.4 BAYESIAN METHODOLOGY

A2.5 ANALYSIS OF TOXICITY EXPERIMENTS

A2.6 NEWTON’S OPTIMIZATION METHOD

A2.7 THE DELTA METHOD

A2.8 VARIANCE COMPONENTS

Appendix 3: Tables

References

Author Index

Subject Index

End User License Agreement

List of Tables

Chapter 01

Table 1.1 Daphnid First Day of Reproduction Data for Example 1.1

Table 1.2 Mite Survival Data

Table 1.3 Mouse Litter Size and Sex Ratio

Table 1.4 Example Developmental Stage Data from AMA Study

Table 1.5 Severity Scores for Liver Basophilia in Female F2 Medaka at 8 Weeks

Chapter 02

Table 2.1 Rainbow Trout Weight

Table 2.2 Comparison of Adjusted and Unadjusted

p

‐Values

Table 2.3 Mean Sizes of Rainbow Trout for Figure 2.5

Table 2.4 Daphnia Reproduction Data

Table 2.5 Daphnia First Day of Reproduction

Table 2.6 False Positive Rate Associated with Number of Tested Responses

Chapter 03

Table 3.1 Comparison of Bonferroni and Bonferroni–Holm Adjusted

p

‐Values

Table 3.2 Total Protein (TP) Levels in Blood from Rats After 90 Days on Various Diets

Table 3.3 Rainbow Trout Size Data from Early Life‐Stage Study

Table 3.4 Dunnett’ Test Results for Rainbow Trout Length

Table 3.5 Power of Tests to Detect Non‐normality in Cauchy‐Distributed Samples of Sizes 4–30

Table 3.6 Power of Tests to Detect Non‐normality in Exponentially Distributed Samples of Sizes 4–30

Table 3.7 Power of Tests to Detect Non‐normality in Uniformly Distributed Samples of Sizes 4–30

Table 3.8 False Positive Rate of Tests for Normally Distributed Samples of Sizes 4–30

Table 3.9 Outlier Example Data

Table 3.10 Collembola Summary Data

Table 3.11 Algae Density 48 h After Treatment

Table 3.12 Mann–Whitney Calculations

Table 3.13 Rainbow Trout Summary Statistics for Williams’ Test

Table 3.14 Williams’ Test Calculations for Rainbow Trout Length

Table 3.15 Meanlog and STD Are the Mean and Natural Logarithms of the Fluorescence Values and PAVA Are the Amalgamated Meanlog Values

Table 3.16 Rainbow Trout Length Data Analyzed by Jonckheere–Terpstra Test

Table 3.17 Algal Data Analyzed by Jonckheere–Terpstra Test

Table 3.18 Comparison of Dunnett’ Test Results for RBT Length Under Type 3, Maximum Likelihood, and REML Estimation Methods with Analysis of Replicate Means

Table 3.19 Summary Statistics for Daphnia Reproduction Data

Table 3.20 Summary Statistics for Algae Density at 48 h

Table 3.21 Power for

t

‐Test to Detect a Decrease of Magnitude

d

with

n

0

 = 

n

1

 = 10,

s

p

 = 1

Table 3.22 Earthworm Reproduction

Table 3.23 RBT ELS Results

Table 3.24 Myriophyllum Lengths

Table 3.25 Duckweed Growth

Table 3.26 Daphnia Magna Reproduction

Table 3.27 Rainbow Trout First Day of Hatch

Table 3.28 Daphnia Chronic Length

Table 3.29 Daphnia Length Data

Chapter 04

Table 4.1 Extrapolation of Rainbow Trout Length

Table 4.2 Observed and Predicted Percent Change from Control

Table 4.3 Observed and Predicted Percent Change from Control from Expanded Data

Table 4.4 Comparison of Estimates in Each Test Concentration

Table 4.5 Selenastrum Cell Counts

Table 4.6 HS4PE Model Fitting Summary

Table 4.7 OE3 and BVP Model Fitting Summary

Table 4.8 Replicate Mean Rainbow Trout Dry Weights at the End of an ELS Study Are Presented

Table 4.9 Model Summary for Hormetic Models Fit to Rainbow Trout Weight

Table 4.10 Soybean Shoot Height

Table 4.11 Summary of the Fit of the Model HORM1 to the Soybean Data.

Table 4.12 Summary of Models Fit to Rainbow Trout Weights

Table 4.13 Summary of Models Fit to Collembola Data

Table 4.14 Cucumber Data from Vegetative Vigor Study

Table 4.15 Model OE3 Overestimates the Effect Near the Observed 10% Effects Rate and in the Two Highest Application Rates

Table 4.16 Frond Counts from Lemna Gibba Study

Table 4.17 Value of

q

for Selected Values of

p

Table 4.18 Collembola Reproduction

Table 4.19 Earthworm Body Weight

Chapter 05

Table 5.1 Mouse Reproduction Study

Table 5.2 Summary of Treatment Mean Responses of Potential Covariates

Table 5.3 Tests for Equality of Slope Relative to Potential Mouse Covariates

Table 5.4 ANCOVA Results for Mouse Data

Table 5.5 ANOVA table for ANCOVA

Table 5.6 Unadjusted and Adjusted Fetal Weight Treatment Means

Table 5.7 Calculations for Fetal Weight ANCOVA Table

Table 5.8 ANCOVA for Fetal Weight Adjusted for Sex Ratio

Table 5.9 Nonparametric ANCOVA of Mouse Fetal Weight

Table 5.10 Shirley’s Antidote Data

Table 5.11 MEORGT Data for Fish Exposed to 4‐Tert‐octylphenol – Generation F1

Table 5.12 MEORGT Data for Fish Exposed to 4‐Tert‐octylphenol – Generation F2

Table 5.13 Summary of F‐tests of 4‐Tert‐octylphenol ANOVA Models

Table 5.14 Summary of Secondary Model Interactions (Slices) for 4‐Tert‐octylphenol ANOVA Models

Table 5.15 Summary of Contrast Tests for 4‐Tert‐octylphenol ANOVA Models

Table 5.16 Degradation Dataset 1

Table 5.17 Weighted and Unweighted Models Fit to Data from Table 5.16

Table 5.18 ANOVA Table for Male Motion Data

Table 5.19 Contrasts for Motion Data, Part 1

Table 5.20 Contrasts for Motion Data, Part 2

Table 5.21 Outliers Found by Tukey Rule in Motion Data

Table 5.22 Soil Degradation Dataset 2

Chapter 06

Table 6.1 Quantal Data from Toxicity Study

Table 6.2 Medaka Exposed to a Potentially Endocrine‐Disrupting Chemical

Table 6.3 Example 2 × 2 Incidence Table

Table 6.4 Two‐Sided Fisher’s Exact Tests Applied to Medaka Sex Ratio Data

Table 6.5 Proportion Female from FSDT Assay

Table 6.6 Shelled and Unshelled Mud Snail Embryos

Table 6.7 Summary Calculations from Tarone’s Test

Table 6.8 Incidence of Intersex Zebrafish Assay 1

Table 6.9 Zebrafish Sex Ratio Data from FSDT Assay 2

Table 6.10 Results from Beta‐Binomial Model Fit to Zebrafish Assay 2 Sex Ratio Data

Table 6.11 Results of Cochran–Armitage Test Applied to Medaka Sex Ratio Data

Table 6.12 Summary of Onion Data and Analyses

Table 6.13 Summary of Trend Tests for Zebrafish Phenotypic Sex

Table 6.14 Intermediate Calculations for Rao–Scott Test of Zebrafish Data

Table 6.15 Power Comparison: No Overdispersion, Mild Trend

Table 6.16 Incidence of Shortened Cervical Ribs in Rat Fetuses

Table 6.17 Results from ZIB Model for Shortened Cervical Ribs in Rat Fetuses

Table 6.18 Summary of 2‐Year Rat Toxicity Test for Liver Tumors

Table 6.19 Intermediate Calculations for the Poly‐3 Test Applied to ACM

Table 6.20 Contingency Table for Death Time

t

k

Table 6.21 Renal Tumor Incidence in 2‐year Rat Study

Table 6.22 Midge Emergence

Chapter 07

Table 7.1 Mites Exposed to Herbicide

Table 7.2 Parameter Estimates for Mite Probit Model for Mortality

Table 7.3 Comparison of Observed and Probit Predicted Incidence Rates for Mite Mortality

Table 7.4 Comparison of EC

x

Estimates from (7.3) Applied to Both Mortality and Survival

Table 7.5 Comparison of EC

x

Estimates from Model (7.3) for Mite Mortality and (7.5) for Survival

Table 7.6 Parameter Estimates for Mite Probit Model for Mortality with Replicates

Table 7.7 Comparison of Observed and Probit Predicted Incidence Rates for Mite Mortality

Table 7.8 EC

x

Estimates from Probit Model with Replicates Taken into Account

Table 7.9 Emergence Data from a Nontarget Terrestrial Plant Study (OECD TG 208) of Peas

Table 7.10 Parameter Estimates from NTTP Study of Peas, with Overdispersion

Table 7.11 Comparison of Observed and Probit Predicted Emergence Rates When Overdispersion Is Modeled

Table 7.12 EC

x

Estimates from Probit Model When Overdispersion Is Modeled

Table 7.13 Weibull Model Summary for Mite Mortality

Table 7.14 Comparison of Observed and Weibull Predicted Incidence Rates for Mite Mortality

Table 7.15 Logistic Model Summary for Mite Mortality

Table 7.16 Comparison of Observed and Logistic Predicted Incidence Rates for Mite Mortality

Table 7.17 Comparison of EC

x

Estimates from Normalized and Nonnormalized Quantal Data

Table 7.18 Comparison of EC

x

Estimates from Probit and Normalized Probit Analysis

Table 7.19 Fish Sexual Development Test Data

Table 7.20 Comparison of Models Fit to Tamoxifen‐Citrate Data

Table 7.21 Comparison of EC

x

Estimates from Models for Tamoxifen‐Citrate Data

Table 7.22 Further Comparison of Estimates Based on Normalized and Untransformed Data

Table 7.23 Bruce–Versteeg Model for Mite Data: Comparison of Observed and Predicted Survival

Table 7.24 Bruce–Versteeg Model EC

x

Estimates

Table 7.25 Summary of Simulation Results for Slope 1, Sample Size 10

Table 7.26 Summary of Simulation Results for Slope 5, Sample Size 10

Table 7.27 Summary of Simulation Results for Slope 10, Sample Size 10

Table 7.28 Summary of EC20 and EC30 Simulation Results for Slope 10, Sample Size 10

Table 7.29 Parameter Estimates for Models Fit to Daphnia Survival Data

Table 7.30 Estimated Proportions from Models Fit to Daphnia Survival Data

Table 7.31 LC

x

Estimates from Models Fit to Daphnia Survival to Day 21

Table 7.32 Example Moving Average Angle Calculations

Table 7.33 Example Data with No Partial Mortality

Table 7.34 Spearman–Karber Calculations for Mite Data with

α

 = 0

Table 7.35 Spearman–Karber Calculations for

Daphnia magna

Chronic Data with

α

 = 0

Table 7.36 Spearman–Karber Calculations for

Daphnia magna

Chronic Data with

α

 = 10

Table 7.37 Spearman–Karber Confidence Interval for Daphnia LC50 with 0% Trim

Table 7.38 Spearman–Karber Confidence Interval for Daphnia LC50 with 10% Trim

Table 7.39 Daphnia Chronic Mortality Data 2

Table 7.40 Daphnia Chronic Mortality Data 3 (μg l

−1

)

Table 7.41 Mysid Mortality After 96 Hours’ Exposure

Table 7.42 Stickleback Mortality After 96 Hours’ Exposure

Table 7.43 Earthworm Mortality After 96 Hours’ Exposure

Table 7.44 Fish Acute Mortality Data

Table 7.45 Fish Acute Mortality Raw Data

Table 7.46 Rainbow Trout Mortality Data

Table 7.47 Daphnid Mortality

Chapter 08

Table 8.1

Daphnia

Chronic Reproduction

Table 8.2 Summary of Unweighted Analysis of Means

Table 8.3 Summary of Transformed Analysis of Means

Table 8.4 Summary of Observed Effects in

Daphnia

Reproduction Data

Table 8.5 Another Daphnia Chronic TLY21 Dataset

Table 8.6 NOEC Results for Example Data from Table 8.5

Table 8.7 Normal Errors Regression Results for Example Data from Table 8.5

Table 8.8 Poisson Errors Bruce–Versteeg Model Fit to Example Data from Table 8.5

Table 8.9 Comparison of Models for Simulated

Daphnia

Chronic Reproduction Data

Table 8.10 Rainbow Trout First Day of Swimup

Table 8.11 Summary of Normal Errors BVP Fit to Swimup

Table 8.12 Summary of Poisson Errors BVP Model Fit to Swimup

Table 8.13 Snail Reproduction Data

Table 8.14 Summary of Observations and Model Predictions for Snail Reproduction

Table 8.15 Comparison of Snail Model EC

x

Estimates

Table 8.16 First Day of Swimup in ELS Study

Table 8.17 Secondary Sex Characteristics for Medaka: Dataset 1

Table 8.18 Secondary Sex Characteristics for Medaka: Dataset 2

Table 8.19 Last Day of Hatch from Rainbow Trout ELS Study

Table 8.20 Last Day of Hatch from Rainbow Trout ELS Study: Dataset 2

Table 8.21 Last Day of Hatch from Rainbow Trout ELS Study: Dataset 3

Table 8.22 First Day of Swimup from Rainbow Trout ELS Study: Dataset 2

Chapter 09

Table 9.1 Contingency Table of Incidence of Findings

Table 9.2 Liver Basophilia Severity Scores of Second‐generation Female Medaka, Showing Replicate Information

Table 9.3 Summary of Liver Basophilia Severity Scores and Slice 2

Table 9.4 Summary of Liver Basophilia Severity Scores and Slice 3

Table 9.5 Quantiles for Frog4 Data

Table 9.6 Change in Quantiles for Frog4 Data

Table 9.7 MQJT Results for Frog4 Data

Table 9.8 Quantiles for Frog2 Data

Table 9.9 Change in Quantiles for Frog4 Data

Table 9.10 MQJT Results for Frog2 Data

Table 9.11 Power of JT and MQJT Tests for 3 Treatment Groups Plus Control w/ 4 Reps of 20

Table 9.12 Power of JT and MQJT Tests for 3 Treatment Groups Plus Control w/ 3 Reps of 15

Table 9.13 Heterogeneity Check of Between‐REP Variances – Doses = 5 for Response = Liv_Basophilia with Severity Score ≥2

Table 9.14 Rao–Scott Slice at Score = 2

Table 9.15 Heterogeneity Check of Between‐REP Variances – Doses = 5 for Response = Liv_Basophilia with Severity Score ≥2

Table 9.16 Rao–Scott Slice at Score = 2

Chapter 10

Table 10.1 Time to Metamorphosis

Table 10.2 Daphnia First Day of Reproduction

Table 10.3 Survival at Time

t

j

Table 10.4 Trend Tests for Daphnia Reproduction Data

Table 10.5 Summary of Proportion Hazards Model Fit to Rat Survival Data

Table 10.6 LAGDA Negative Control Data

Table 10.7 Sandwich Estimators for LAGDA Time to Metamorphosis

Table 10.8 GLMM Estimators for LAGDA Time to Metamorphosis

Table 10.9 Comparison of Sandwich and Frailty Models for Males in LAGDA Study

Table 10.10 Medaka First Day of Hatch

Chapter 11

Table 11.1 Examples of Toxcast Free Services

Table 11.2 OECD Conceptual Framework for Testing and Assessment of Endocrine Disrupters

Table 11.3 Hazard Class and Categories, Pictogram, Signal Word, Hazard Statement Code, and Description of Selected Hazard Classes for GHS Environmental Hazards

Table 11.4 Summarized Main Mechanistic and Apical Endpoints in All Nonmammalian Biotic OECD Test Guidelines (TG) and the Recommended Statistical Method(s) to Use to Evaluate the Data (Tests for Normality and Homogeneity of Variance as well as Data Transformation Methods Are Not Described in This Table)

Table 11.5 Grouping of the OCSPP Guidelines

Table 11.6 OCSPP Group 850 Group A Guidelines: Aquatic and Sediment‐dwelling Fauna and Aquatic Microcosms

Table 11.7 Statistical Recommendations and Requirements in the OCSPP Group 850 Group A Guidelines

Table 11.8 REACH Requirements for Ecotoxicological Information on Vertebrate and Invertebrate Animals (Abiotic Tests and Tests on Microorganisms and Plants Not Shown)

Chapter 12

Table 12.1 Power of Tests to Detect Nonnormality in Samples from a Cauchy Distribution

Table 12.2 Power of Tests to Detect Nonnormality in Samples from an Exponential Distribution

Table 12.3 HC5 Estimates from Lognormal SSD Fit to Data from Various Distributions

Table 12.4 HC5 Estimates from Exponential SSD Fit to Data from Various Distributions

Table 12.5 Aquatic Plant Data

Table 12.6 HC5 Estimates for Aquatic Plant Data

Table 12.7 HC5 Estimates from Lognormal SSD Fit to Data from Various Distributions

Table 12.8 Aldenberg–Jaworska Factors for HC5 Estimates from Lognormal SSD

Table 12.9 Comparison of HC5 Point Estimates with Censored Data

Table 12.10 Comparison of HC5(P5) Estimates with 30% Censoring

Table 12.11 Summary of Estimates for Normal SSDs with 8 Species Using fifth Percentile

Table 12.12 Comparison of Aldenberg–Jaworska HC5 Estimates with Eight Species and 30% Censoring

Table 12.13 Species EC50 Values for Figure 12.2

Table 12.14 Algae Data for SSD

Table 12.15 Aquatic Species EC50 Values

Chapter 13

Table 13.1 Classes of Minimum Detectable Differences (MDD) in EFSA Aquatic Guidance Document

Table 13.2 Example Mesocosm Measures on

Sagittaria sagittifolia

Table 13.3 MDD% for

Sagittaria sagittifolia

Measures

Table 13.4 Williams’ Test with Four Groups Amalgamated

Table 13.5 XETA Data with TRIAC

Table 13.6 Treatment Means of TRIAC Data

Table 13.7 Summary of OE3 Fit to TRIAC Data

Table 13.8 Summary of BVP Fit to TRIAC Data

Table 13.9 Summary of 3PL Fit to TRIAC Data

Table 13.10 The Hong and Lee Human Squamous Cell Carcinoma Data

Table 13.11 Parameter Estimates From Our Fit of the Kong and Lee Model

Table 13.12 Predicted Results From Our Fit of the Kong and Lee Model

Table 13.13 Algae Cell Count

Table 13.14 Limit Test Results

Table 13.15 Probability of Significant Limit Mortality

Table 13.16 Probability of Control and Limit Mortalities

Table 13.17

Daphnia magna

Length Data Summary for MAXSD

λ

Test (SD2PC Version)

Table 13.18 Parameter Estimates for Unequal Rates Model for RBC ChE

Table 13.19 Soil Degradation Data

Table 13.20 Results of SFO Models Fit to Soil Degradation Data

Table 13.21 Uptake Period of Bioconcentration Study

Table 13.22 Parameter Estimates for the Jointly Fitted BCF Aquatic Uptake and Depuration Model

Table 13.23 Parameter Estimates for the Jointly Fitted BCF Aquatic Uptake and Depuration Model with the Optimal Box–Cox Transformation

Appendix 02

Table A2.1 ANOVA Table for Simple Means Model

Appendix 03

Table A3.1 Studentized Maximum Distribution

Table A3.2 Studentized Maximum Modulus Distribution

Table A3.3 Linear and Quadratic Contrast Coefficients

Table A3.4 Williams’ Test

for

α

 = 0.05

List of Illustrations

Chapter 01

Figure 1.1 First day of daphnid reproduction. Diamonds, replicate means; solid line, joins treatment means.

Figure 1.2 Example tissue slide for histopathology grading. Expert judgment is used to score tissue slides such as these.

Figure 1.3 Example severity scale. Varying widths for different scores indicate possible differences in the range of severities given the same score.

Chapter 02

Figure 2.1 Step function. The endpoints are exaggerated for effect, with solid dots indicating that the point is on the plot and the open circles indicate that the point is not on the plot.

Figure 2.2 Histogram of Sprague‐Dawley adult male body weights probabilities (vertical axis values) that have been multiplied by 100. Overlaid on the histogram is a theoretical curve that attempts to capture the general shape of the histogram. The curve displayed here is a normal density function, as described in Eq. (2.6). We will defer to for the moment how one obtains the values of the parameters

θ

and

σ

in that equation. Appendix 2 contains a description of methods for estimating the parameters for a model from the data collected.

Figure 2.3 Normal density function with probability intervals scale on horizontal axis is in multiples of standard deviation above or below the zero mean.

Figure 2.4 Muscle myrofibrils.

Figure 2.5 Scatterplot with Trend Line Dots = observations. Stars = mean of observations for the indicated treatment level. Solid line merely joins the means.

Figure 2.6 Example of influential observation. Single observation at dose = 30 is an influential observation. The fitted regression line shown is highly influenced by this observation. Without this observation, there is little apparent relationship between dose and response.

Figure 2.7 Scatter plots of TLY21 and sqrt(TLY21). The transform had little impact on the trend or spread in the response.

Figure 2.8 Daphnid first day of reproduction. The response is flat until the highest test concentration. There is no information from which to determine an appropriate curve to describe the data. Four possible dose–response shapes connecting the two highest test concentrations are shown to illustrate the range of possibilities.

Figure 2.9 Solvent effects in aquatic studies: Acute toxicity endpoints far exceed the regulatory solvent limit of 0.1 mg l

−1

(dotted line). Figure and related results are discussed further in Green and Wheeler (2013), which in turn is based on data in Hutchinson et al. (2006).

Figure 2.10 Solvent effects in aquatic studies: Chronic studies. Chronic toxicity endpoints exceed the regulatory solvent limit of 0.1 mg l

−1

(dotted line). Figure and related results are discussed further in Green and Wheeler (2013), which in turn is based on data in Hutchinson et al. (2006).

Figure 2.11 False‐positive rates for five schemes for using two controls test for treatment effects: Related material is given in Green (2014a). Protocol, combine if controls not significantly different, use solvent only otherwise. Separate, compare treatments to each control: Claim effect if either is significant. Solvent % effect, 100 * (Solvent control mean − Water control mean)/Water control mean, where the true difference in mean response is indicated. ErrorRate = False − Positive rate, the likelihood of claiming a treatment effect when there is none.

Figure 2.12 Little difference is observed in false‐positive rates among solvent only, always combine, and Protocol approaches, but there remain much higher false‐positive rates for the approaches of always using the water control only or always doing separate comparisons to each control.

Figure 2.13 Power to detect a real effect. The water only and always combine approaches have very poor power when the solvent “effect” is opposite to treatment effect. The power for the protocol approach ranges from 6% below to 9% above the power for the solvent‐only approach over this entire range.

Figure 2.14 Surface water mercury vs. cadmium. Line = simple regression of the indicated variables. Left panel contains all observations. Right panel excludes Ln(cadmium) values greater than −7.

Figure 2.15 Surface water mercury vs. chromium. Line = simple regression of the indicated variables. Left panel contains all observations. Right panel excludes Ln(chromium) values greater than −5.

Figure 2.16 Surface water mercury vs. copper. Line = simple regression of the indicated variables. Left panel contains all observations. Right panel excludes Ln(copper) values greater than −5.

Figure 2.17 Surface water mercury vs. lead. Line = simple regression of the indicated variables. Left panel contains all observations. Right panel excludes Ln(lead) values greater than −6.

Chapter 03

Figure 3.1 Rainbow trout length. Replicate mean lengths of rainbow trout are plotted as dots. Treatment means are plotted as stars and joined by line segments. The slight rise at dose 4 compared to dose 3, and the larger rise at dose 5 are evident, but overall, there is a downward trend.

Figure 3.2 Pure Error Residuals Dots are observations. Horizontal segments are plotted at the arithmetic mean,

, of observations for indicated treatment level. Vertical segment indicates the residual.

Figure 3.3 Histogram of rainbow trout length. Solid line is overlaid normal density function. A slight skew toward lower values is evident, but overall, plot is consistent with a normal distribution.

Figure 3.4 QQ‐plots. The left plot shows pure error residuals from the trout data and appears consistent with the expected normal distribution. There is a slight deviation at each extreme, suggesting more extreme values than expected, but the deviation is so slight as not to indicate a serious problem. A straight reference line from a normal distribution is shown to make the assessment easier. A slight rise of observations above the reference line toward the lower end is an indication of the slight skewness mentioned for Figure 3.3. The right plot is presented as an example of what a QQ‐plot might look like when the data are not consistent with the expected (normal) distribution. The data for the right plot are not residuals from an ANOVA. We will consider formal tests of goodness of fit to a specified distribution in Section 3.3.5.

Figure 3.5 Scatterplot of Residuals Dots is individual fish lengths. The horizontal reference line at 0 is provided as a visual aid. One expects roughly the same number of points above the zero‐line as below, both randomly distributed across treatments, and the width of the vertical data spreads across treatment groups should be roughly the same.

Figure 3.6 Scatterplot of residuals from outlier data Dots is observations. Solid line is a mean residual, which is always zero. High residual in treatment 6 is an apparent outlier.

Figure 3.7 Collembola reproduction. Reproduction in individual test chambers shown as dots. Treatment means are shown as stars and connected by straight line segments. Variance in doses 2 and 3 is noticeably less than in the control and especially in dose 4. Treatment groups (doses) are plotted by order rather than concentration. Downward concentration–response trend is very clear.

Figure 3.8 Rainbow trout length data with PAVA means. Dashed line is for PAVA means. Solid line for arithmetic means.

Figure 3.9

Xenopus laevis

fluorescence replicate means. Run means of log‐transformed

Xenopus

fluorescence data are plotted as solid boxes, solid line segments join treatment means, and dashed line segments join amalgamated means. Concentrations are plotted by order rather than value. While there seems to be a general downward trend in treatment means through 30 mg l

−1

, there is a sharp rise at 100 mg l

−1

that the amalgamated means discount.

Figure 3.10 Possible flowchart for use of Williams’ test. The 1% trim is arbitrary. While in general, we do not support automatic outlier elimination, for data that are prone to strange aberrations, possible from empty wells read by automated machines, a trim of the 1–5% most extreme values at the low and high ends of the distribution may be useful.

Figure 3.11 Possible statistics flow chart for continuous responses.

Figure 3.12 Three dose–response shapes illustrate a range of dose–response relationships used for power simulations. The maximum simulated effect at the highest concentration is varied from 1 to 99%.

Figure 3.13 Power comparison of several tests for effects on rainbow trout in ELS studies.

Figure 3.14 Example power plot solid line is the power (expressed as a percent rather than a probability) to detect a percent change from control of magnitude given on the horizontal axis. From the plot it can be seen that the power to detect a 15% change from the control is 80%. The dotted lines are 95% confidence bounds on the power estimated from a computer simulation study.

Chapter 04

Figure 4.1 Exponential curve fit to rainbow trout length data. Solid square, replicate means; Solid line, predicted concentration–response curve; Dashed lines, 95% confidence bounds on predicted mean response.

Figure 4.2 Exponential curve fit to expanded rainbow trout length data. Control mean is underestimated.

Figure 4.3 Hockey‐stick models. Three example hockey‐stick models that might describe the same data.

Figure 4.4 Find on the vertical scale of the untransformed model and confidence band, the point corresponding to an

x

% change from the estimated control mean. Draw a horizontal line through that point. Where this line intersects the curve determines the estimated EC

x

. Where this line intersects the confidence band determines the fiducial bounds on EC

x

. If the line does not intersect the upper (respectively, lower) band, then no upper (respectively, lower) fiducial bound can be obtained. In this illustration using the density data of Table 3.11, the fiducial bounds are (0.19, 0.31), while the maximum likelihood bounds are (0.17, 0.35). The solid vertical line segment locates the fiducial estimate of EC50, which is always the same as the MLE.

Figure 4.5 Pure error and regression residuals. The fitted model is shown as a solid line. Individual observations are dots. The mean response at each value of

x

is shown as a star. Here

y

51

is an observed response at

x

 = 5,

is the response predicted by the model at

x

 = 5, and

is the mean of the observed responses at

x

 = 5.

Figure 4.6 Comparison of QQ‐plots. Pure error residuals in the left panel are very consistent with a normal distribution. The top two residuals deviate slightly from the reference line, indicating slightly heavy tail. The middle panel shows higher residuals at the extremes and lower residuals in the mid‐range. The right panel shows more marked deviation from the reference line in the low range, indicating a very heavy tail, followed by a group of lower residuals in the lower range.

Figure 4.7 Comparison of residual histograms. Some skewness is evident in the right panel. The middle panel shows that a wider spread of residuals than in the other two panels, indicating greater variability about the two‐parameter exponential fitted curve compared with the hormetic model or the pure error residuals.

Figure 4.8 Comparison of residual scatter plots. The residuals from the hormetic model (right panel) resemble more closely the pure error residuals (left panel) and are more centered on the control mean than those from the two‐parameter exponential model (middle panel). The latter model captures the middle treatment groups better than the alternative regression model. Both models tend to overestimate group 5.

Figure 4.9 Comparison of model fits. The underestimation of the middle concentrations is evident in the left panel, as it is the better fit to those groups in the right panel. The difference in estimates of the control mean is also clear. In left panel, replicate means are indicated as solid squares. In right panel, replicate means are asterisks, and treatment means are solid dots. In both panels, the regression curve is a solid line, and dotted lines indicate 95% confidence bounds on the mean predicted value.

Figure 4.10 AICc probability function. Horizontal axis is unitless.

Figure 4.11 Hockey‐stick model HS4PE fit to selenastrum data. The horizontal axis is in log‐scale, with an adjustment to plot the control observations.

Figure 4.12 Model BVP fit to selenastrum data. There is good fit of the model to the data across the entire range of test concentrations.

Figure 4.13 Model OE3 fit to selenastrum data. The model fits the data well except at the highest test concentration, where the model underestimates the observations and the confidence interval for the prediction at that concentration is unrealistically short.

Figure 4.14 QQ‐Plot of pure error residuals from ANOVA of rainbow trout weight data.

Figure 4.15 HORM2 (Cedergreen) model fit to rainbow trout weight data.

Figure 4.16 HORM1 (Brain–Cousens) model fit to rainbow trout weight data. Star, treatment mean; Filled square, replicate mean; Solid line, model; and Dotted lines, confidence curves.

Figure 4.17 HORM1 fit to soybean shoot height data. Star, treatment mean; Filled square, replicate mean; Solid line, model; and Dashed lines, confidence curves.

Figure 4.18 OE2 Model fit to rainbow trout length data in Table 3.3. Open squares, replicate means; Solid line, fitted curve; Dashed lines, 95% confidence bounds. Wide bounds on predicted values are apparent.

Figure 4.19 Model OE4 fit to collembola reproduction data. Filled squares, replicate means; Solid line, fitted curve; Dashed lines, 95% confidence curves.

Figure 4.20 Observations in the highest two application rates are underestimated and the width of the confidence interval for the predicted mean at 180 g a.s. ha

−1

appears unrealistically small.

Figure 4.21 Model OE5 fit to cucumber data. Model OE5 does not capture the slight decline at the 180 g a.s. ha

−1

application rate, but overall, the model fits the data well.

Chapter 05

Figure 5.1 Plots of residuals from normal errors ANOVA of 4‐tert‐octylphenol data. Histogram and QQ‐plots of normal errors ANOVA studentized residuals provide visual evidence of normality.

Figure 5.2 Plots of residuals from Poisson errors ANOVA of 4‐tert‐octylphenol data. Histogram and QQ‐plots of Poisson errors ANOVA studentized residuals provide visual evidence of deviation from normality, indicating model inadequacy.

Figure 5.3 Plots of residuals from negative binomial errors ANOVA of 4‐tert‐octylphenol data. The QQ‐plot still shows some large residuals, but only four studentized residuals exceeded 3. The histogram is now restricted to the expected range of −3 to 3, except as noted, but the percentage of values around zero was inflated relative to a normal distribution, and there was modest skewness apparent. There were 38 zero eggs recorded out of 423 observations across the two generations. Perhaps a zero‐inflated negative binomial model would improve matters, but that will not be pursued here.

Figure 5.4 Parent and metabolite vs. time. Amount (μg l

−1

) of parent (star) and metabolite (dot) vs. days post exposure.

Figure 5.5 Absolute variability of parent and metabolite vs. time. Deviation from mean (μg l

−1

) of parent (star) and metabolite (dot) vs. days post exposure.

Figure 5.6 Relative variability of parent and metabolite vs. time. Adjusted deviation from mean (μg l

−1

) of parent (star) and metabolite (dot) vs. days post exposure obtained at each time point by dividing the deviation from the mean by the mean.

Figure 5.7 Histograms of normalized pure error residuals. Left panel shows normalized pure error residuals for the parent. Right panel is for metabolite. Dotted curve is overlaid normal density function with same mean and standard deviation as data.

Figure 5.8 Histograms of regression residuals. Regression residuals from models for parent (left panel) and metabolite (right panel).

Figure 5.9 Optimizing variance estimates for model parameters. The top and bottom curves in the left panel are the partial derivatives of the metabolite degradation curve with respect to

C

and

k

m

, respectively, and the curve in the right panel is the partial derivatives of the parent degradation curve with respect to

k

p

.

Figure 5.10 Models for parent and metabolite. Left panel is for parent, right for metabolite. Star = observed mean. Thick line = model. Thin lines = 95% confidence bounds.

Figure 5.11 Check of normal errors assumption for motion data. Right panel = histogram of model residuals with overlaid normal density function. Left panel = residuals with horizontal axis given by time = 100 * day + 50 * dose + 5 * bin.

Chapter 06

Figure 6.1 Simulated concentration–response shapes. Example shapes for simulated dose–response curves with 20% background incidence and a maximum of 36% incidence.

Figure 6.2 Power comparison for no overdispersion, mild trend. C, Cochran–Armitage; R, Rao–Scott Cochran–Armitage; G, GLMM with Dunnett; W, Williams; J, Jonckheere–Terpstra; D, Dunnett (standard); B, beta‐binomial; N, Dunn test; 20% background incidence; four reps per treatment; and five test concentrations plus control.

Figure 6.3 Power comparison for no overdispersion, but delayed response. C, Cochran–Armitage; R, Rao–Scott Cochran–Armitage; G, GLMM with Dunnett; W, Williams; J, Jonckheere–Terpstra; D, Dunnett (standard); B, beta‐binomial; N, Dunn test; 20% background incidence; four reps per treatment; and five test concentrations plus control.

Figure 6.4 Power comparison for 50% overdispersion, mild trend. C, Cochran–Armitage; R, Rao–Scott Cochran–Armitage; G, GLMM with Dunnett; W, Williams; J, Jonckheere–Terpstra; D, Dunnett (standard); B, beta‐binomial; N, Dunn test; 20% background incidence; 50% overdispersion; four reps per treatment; and five test concentrations plus control.

Chapter 07

Figure 7.1 Model (7.3) used for both mortality and survival. Left panel models mortality and right panel models survival for the same mite data, both using model (7.3). This makes clear that (7.3) is not suitable for modeling survival.

Figure 7.2 Comparison of probit model (7.3) for mite mortality and (7.5) for survival. Left and right panels for mite data mortality and survival using models (7.3) and (7.5), respectively. Model (7.5) captures background survival properly.

Figure 7.3 Weibull model for mite mortality. Solid squares are actual replicate proportions dead. Dashed lines are 95% lower and upper confidence bounds for model predictions. Solid line is model prediction.

Figure 7.4 Logistic model for mite mortality. Solid squares are actual replicate proportions dead. Dashed lines are 95% lower and upper confidence bounds for model predictions. Solid line is model prediction.

Figure 7.5 Comparison of EC

x

estimates from normalized probit models fit to continuous response to estimates from mathematically sound models. Bottom right is simulated dose–response curve from a BVP model with

γ

 = 0.5 (see Eq. 4.1*). Histograms of estimated EC10 values: upper left = BVP, upper right = OE3, lower left = normalized probit. Dose–response curve not unusual, but normalized probit estimates greatly overestimate EC10, whereas estimates from the other models are centered near the true value and are much less variable.

Figure 7.6 GNLM probit model of tamoxifen‐citrate data with replicates considered. Solid squares are observed replicate proportions. Dashed lines are 95% confidence bounds. Solid line is predicted concentration mean. A generalized nonlinear model was fit with binomial error structure and replicates modeled.

Figure 7.7 Three‐parameter exponential model fit to female tamoxifen‐citrate proportions. Solid squares are observed replicate female proportions. Dashed lines are 95% confidence bounds. Solid line is predicted concentration mean. A three‐parameter exponential model was fit with normal error structure and replicates modeled.

Figure 7.8 Bruce–Versteeg model fit to mite data. PRPSURV is the proportion surviving. Conc = concentration in g a.s. ha

−1

.

Chapter 08

Figure 8.1 Bruce–Versteeg normal errors model fit to Table 2.4

Daphnia magna

chronic TLY21 data. Adult

Daphnia

were housed one to a beaker. Solid curve is the fitted model. Dashed curves are the 95% confidence bonds for the predicted mean response. Solid squares are the observed values.

Figure 8.2 Normal errors BVP model fit to swimup data. Solid line is crude depiction of model predictions. Dashed lines are crude depictions of 95% confidence bounds for model predictions. Squares are observations. Horizontal scale is log scale. Observations do not show censoring.

Figure 8.3 Poisson errors BVP model fit to swimup data. Solid line is crude depiction of model predictions. Dashed lines are crude depictions of 95% confidence bounds for model predictions. Squares are observations. Horizontal scale is log scale. Observations do not show censoring.

Figure 8.4 LAGDA time to metamorphosis. MET, percent of frogs that have reached metamorphosis (stage 62).

Figure 8.5 Comparison of models for snail reproduction. There is little or no visual reason to infer that does better at estimating the response below the lowest tested concentration.

Chapter 09

Figure 9.1 Semiquantitative severity grading of lamellar epithelial hyperplasia in the gills of fish. Grading is based on the approximate degree to which the spaces between adjacent gill lamellae (arrows) are filled in by proliferating cells. For example, grade 1 (minimal) = 10–25% filled, grade 2 (mild) = 26–50% filled, grade 3 (moderate) = 51–75% filled, and grade 4 (severe) = 76–100% filled. Cell proliferation less than 10% filled is recorded as “not remarkable.” Hematoxylin and eosin stain. All bars = 50 μm. We are indebted to Jeff Wolf of Experimental Pathology Laboratories, Inc. who created this slide and caption expressly for this book.

Figure 9.2 Schematic for variation within and between severity scores. Width of interval indicates possible disparity in the range of injury to tissue that merits the indicated score.

Figure 9.3 Shifted quantiles for MQJT. Control = lower left density curve. Treatment is upper right density curve. Vertical scales shown for the two density functions.

Figure 9.4 MQJT test for Frog4 dataset. Line segments join the median quantile Q

x

for each treatment group,

x

 = 20–80. A consistent drop from group 4 to 5 is evident. A drop is also evident from group 2 to 3, but it is followed by a rise or flat response from group 3 to 4.

Figure 9.5 MQJT test for Frog2 dataset. A strong decrease from group 4 to 5 is evident in all quantiles. The trend from group 3 to 4 is less compelling.

Chapter 10

Figure 10.1 Two types of survival curves. Curves on the left cross and show no obvious treatment relationship, while the curves on the right do not cross one another, but treatment 1 curve is below that for the other treatments.

Figure 10.2 Survival curves showing concentration–response trends. The levels of the curves exhibit a trend, with lower curves corresponding to higher treatments.

Figure 10.3 Survival function for metamorphosis. Time_on_Test = days till metamorphosis minus 50.

Figure 10.4 Daphnia first day of reproduction. The data consist of six integer values with many duplicate values. No standard model for continuous response or survival or time to event can be fit. The response is flat until the highest test concentration. There is no information from which to determine a “standard” regression curve to describe the data. Four possible dose–response shapes connecting the two highest test concentrations are shown to illustrate the range of possibilities. No basis for positing a regression model between highest two concentrations. Any EC

x

estimate from models introduced in previous chapters would be arbitrary.

Figure 10.5 Another view of Daphnia first day of reproduction. There were six daphnid in separate beakers each treatment group. When only two or three points are displayed in some treatment group, then some daphnid had the same first day of reproduction.

Figure 10.6 Survival curves for Daphnia first day of reproduction. Step function is typical presentation for time‐to‐event data. Each treatment has a unique pattern to display the survival function. Differences among survival functions are difficult to assess from this display.

Figure 10.7 Studentized residuals from daphnia repday. Histogram and QQ‐plot for studentized residuals from Poisson model of first day of reproduction. Some deviation from expected symmetry observed, suggesting the Poisson model may not fit well.

Figure 10.8 Survival curves for 2‐year rat study. Only days >350 are shown for visual clarity. No deaths occurred on earlier days. Survival functions do cross, though there is little difference in the survival functions for groups 1, 2, and 4, so the proportional hazards model may still be appropriate. Group 3, 500 ppm, appears to have decreased survival between days 525 and 640, but after that, the differences with other groups go away.

Figure 10.9 LAGDA negative control data. Survival here means not yet reached metamorphosis. It should be noted that the survival curves are not monotonic, since the delay in group 3 is less pronounced than that in groups 2 and 4.

Figure 10.10 Survival curves by sex LAGDA study. Upper and lower panels are time to metamorphosis for males and females, respectively.

Chapter 11

Figure 11.1 A generalized stepwise approach to assess the safety of a chemical.

Chapter 12

Figure 12.1 QQ‐plot consistent with lognormality. Observations (dots) lie close to the line, indicating agreement with a normal distribution.

Figure 12.2 QQ‐plot not consistent with lognormality. Observations (dots) deviate substantially from the line, indicating inconsistency with a normal distribution. Data is presented in Exercise 12.1.

Figure 12.3 SSD with extreme low species values. Log‐logistic SSD fit to nine species EC50 values.

Lemna

values 2+ orders of magnitude lower than all others. Log scale on horizontal axis.

Figure 12.4 Spaghetti plot. The many lognormal distribution functions generated by the 2‐D Monte Carlo process are illustrated by thin curves. The median curve is the heavy black curve. Where the horizontal line at

y

 = 0.05 intersects the median curve defines the median HC5 estimate. Where that same line intersects the collection of distribution curves defines the distribution of HC5 estimates. It will be apparent that the width of the middle 90 or 95% of this distribution can be very wide, especially when one realizes the horizontal axis is on a log scale. Consequently, the HC5LB can be a very small value.

Figure 12.5 Censoring considered vs. ignored. HC5C = HC5 and HC5LBC = HC5LB when censoring is taken into account. HC5NC = HC5 and HC5LBNC = HC5LB when censoring is ignored.

Figure 12.6 Comparison of three methods of estimating HC5 from a normal distribution with 30% censoring. Vertical line shows true HC5. Bottom figure with mathematically correct treatment of censored values shows a strong tendency to underestimate HC5, and the spread is slightly wider than with the other methods. Also, a tiny percentage (0.87%) of extreme underestimates occurs. One observation out of 10 000 grossly overestimated HC5. Middle figure shows results when censored values are discarded and sampling continues until eight uncensored values are obtained. There is a tendency to overestimate HC5. Top figure shows results when censored values are treated as uncensored. There is a tendency to overestimate HC5.

Figure 12.7 Sublethal HC5 simulation results (using the Aldenberg–Jaworska adjusted HC5 values). Normal distribution

w

/8 species, 30% censoring. Top panel shows distribution of HC5 estimates when censoring is ignored. Middle panel shows distribution of HC5 estimates when censored values are dropped and sampling continues until eight uncensored values are available. Bottom panel shows distribution of HC5 estimates when censored values are treated as censored using Eq. (12.4). Vertical line in each plot shows true HC5 value. The HC5 estimates from bottom panel are shifted toward lower values, and those in top panel are shifted toward higher values. A smaller shift toward higher values is also apparent in the middle panel.

Chapter 13

Figure 13.1 MDD%

vs

. minimum value for macrophytes and macro‐algae. The increase in Log

10

(MDD%) over the range 0 < 

a

 < 2000 is less than 22.5%.

Figure 13.2 Principal response curve analysis of chlorpyrifos mesocosm data. Species codes on the right indicate species positively and negatively correlated with the first principle response curve.

Figure 13.3 96‐Well titerplate. Treatments are arranged in columns. Solids are controls. Other patterns indicate the three treatment groups.

Figure 13.4 XETA 96‐well design, plate 1. Dark gray wells are blanks, except well A1, which is empty due to a mechanical configuration. Otherwise, rows A and B = FETAX, C and D = T3, E and F = T3 + T4, G and H = test chemical low concentration.

Figure 13.5 Regression model fit to data from Table 13.6. One of three models fit to data in Table 13.6. Wide confidence bounds for EC25 apparent.

Figure 13.6 Isobologram for mixture of two chemicals with EC

x

(2) illustrated as 30 and EC

x

(1) illustrated as 70. The value of

x

is irrelevant.

Figure 13.7 Plot of observed and predicted RBC ChE in high treatment group. Squares = observations. Solid line is fitted curve from model (13.50). Dashed lines are 95% confidence bounds for each predicted mean response.

Figure 13.8 QQ‐plot of residuals from model fit to RBC ChE. Observations appear close to linear, supporting a normal distribution. Label comes from programs fit_tkxmpl1.sas, fit_tkxmpl1_b1.sas, and QQplot RBC ChE.sas in Appendix 1.

Figure 13.9 SFO models fit to soil degradation data. Left panel is for model (13.47) fit to the parent compound. Right panel is for model (13.48) fit to a metabolite.

Figure 13.10 Depuration model for fish bioconcentration at high exposure concentration. Observations, adjusted for censoring, as squares, prediction as solid curve, 95% confidence bounds as dashed curves.

Figure 13.11 Uptake model for fish bioconcentration at high exposure concentration. Observations, adjusted for censoring, as squares, prediction as solid curve, 95% confidence bounds as dashed curves.

Figure 13.12 Joint nonlinear model fit of the uptake and depuration phases for the untransformed data.

Figure 13.13 Joint nonlinear model fit of the uptake and depuration phases for the optimal Box–Cox transformation:

λ

 = 0.3.

Appendix 02

Figure A2.1 Step function. The end points are exaggerated for effect, with solid dots indicating the point is on the plot and the open circles indicate the point is not on the plot.

Figure A2.2 Histogram of Sprague‐Dawley adult male body weights. Probabilities (vertical axis values) have been multiplied by 100. Overlaid on the histogram is a theoretical curve that attempts to capture the general shape of the histogram.

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Statistical Analysis of Ecotoxicity Studies

John W. Green, Ph.D. (Mathematics), Ph.D. (Statistics)

Principal Consultant: BiostatsticsDuPont Data Science and Informatics

Timothy A. Springer, Ph.D. (Wildlife and Fisheries Science)

Director of Special Projects and IT OperationsEAG/Wildlife International

Henrik Holbech, Ph.D. (Ecotoxicology)

Associate ProfessorInstitute of Biology, University of Southern Denmark

This edition first published 2018© 2018 John Wiley & Sons, Inc.

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Library of Congress Cataloging‐in‐Publication Data

Names: Green, John William, 1943– author. | Springer, Timothy A., 1948 March 3– author. | Holbech, Henrik, 1969– author.Title: Statistical analysis of ecotoxicity studies / by John W. Green, Ph.D., Timothy A. Springer, Ph.D., Henrik Holbech, Ph.D.Description: First edition. | Hoboken, NJ : John Wiley & Sons, 2018. | Identifiers: LCCN 2018008775 (print) | LCCN 2018014558 (ebook) | ISBN 9781119488828 (pdf) | ISBN 9781119488811 (epub) | ISBN 9781119088349 (cloth)Subjects: LCSH: Environmental toxicology–Statistical methods. | Toxicity testing–Statistical methods.Classification: LCC QH541.15.T68 (ebook) | LCC QH541.15.T68 G74 2018 (print) | DDC 615.9/07–dc23LC record available at https://lccn.loc.gov/2018008775

Cover design by WileyCover image: © Ross Collier/Alamy Stock Photo

Preface

John Green and Tim Springer developed a one‐day training course, Design and Analysis of Ecotox Experiments, for the Society for Environmental Toxicology and Chemistry (SETAC) and delivered it for the first time at the SETAC Europe 13th Annual Meeting in Hamburg, Germany, in 2003. Since then, in many years we have taught this course at the annual SETAC conferences in Europe and North America, updating it each time to stay abreast of the evolving regulatory requirements. In 2011, Henrik Holbech joined us and has made valuable contributions ever since. In 2014, Michael Leventhal of Wiley approached us with the idea of turning the training course into a textbook. The result is the current book, and we appreciate the opportunity to reach a wider audience.