ISO/TS 20281:2006
(Main)Water quality — Guidance on statistical interpretation of ecotoxicity data
Water quality — Guidance on statistical interpretation of ecotoxicity data
ISO/TS 20281:2006 offers guidance on statistical methods used for the analysis of data of standardized ecotoxicity tests. It focuses on statistical methods for obtaining statistical estimates of parameters. The methods described are intended to cover laboratory ecotoxicity tests (aquatic, sediment and/or terrestrial tests), and may also be relevant for other toxicity tests. Hypothesis testing, concentration-response modelling and biology-based modelling are discussed for the different data types (quantal, continuous and discrete data, corresponding to mortality, growth or reproduction). In addition, some guidance on experimental design is given. Although the main focus is on giving assistance to the experimentalist, a secondary aim is to help those who are responsible for evaluating toxicity tests. Finally, ISO/TS 20281:2006 may be helpful in developing new toxicity test guidelines by giving information on experimental design and statistical analysis issues.
Qualité de l'eau — Lignes directrices relatives à l'interprétation statistique de données écotoxicologiques
Kakovost vode - Navodilo za statistično interpretacijo ekotoksikoloških podatkov
Ta tehnična specifikacija podaja navodilo za statistične metode, ki se uporabljajo za analizo podatkov standardiziranih ekotoksikoloških preskusov. Osredotoča se na statistične metode za pridobivanje statističnih ocen parametrov v trenutni in prihodnji uporabi, npr. ECx (LCx), NOEC, NEC. Opisane metode zajemajo laboratorijske ekotoksikološke preskuse (preskusi vode, sedimentov in/ali zemlje) in so lahko primerne tudi za druge toksikološke preskuse. Glavni namen te tehnične specifikacije je zagotavljanje praktičnih navodil za analizo opažanj pri ekotoksikoloških preskusih. Obravnavano je preskušanje hipotez, modeliranje razmerja med koncentracijo in odzivom ter modeliranje na biološki osnovi za različne vrste podatkov (kvantalne, zvezne in posamične podatke, ki ustrezajo umrljivosti, rasti ali razmnoževanju). Poleg tega je podanih nekaj navodil za snovanje poskusov. Čeprav se v glavnem osredotoča na pomoč izvajalcu poskusa, pomaga tudi tistim, ki so odgovorni za vrednotenje toksikoloških preskusov. Končno je dokument lahko uporaben tudi pri razvijanju smernic za nove toksikološke preskuse, saj podaja informacije o snovanju poskusov in statistični analizi.
General Information
Standards Content (Sample)
SLOVENSKI STANDARD
01-september-2010
.DNRYRVWYRGH1DYRGLOR]DVWDWLVWLþQRLQWHUSUHWDFLMRHNRWRNVLNRORãNLKSRGDWNRY
Water quality - Guidance on statistical interpretation of ecotoxicity data
Qualité de l'eau - Lignes directrices relatives à l'interprétation statistique de données
écotoxicologiques
Ta slovenski standard je istoveten z: ISO/TS 20281:2006
ICS:
13.060.70 Preiskava bioloških lastnosti Examination of biological
vode properties of water
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
TECHNICAL ISO/TS
SPECIFICATION 20281
First edition
2006-04-01
Water quality — Guidance on statistical
interpretation of ecotoxicity data
Qualité de l'eau — Lignes directrices relatives à l'interprétation
statistique de données écotoxicologiques
Reference number
©
ISO 2006
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
© ISO 2006
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2006 – All rights reserved
Contents Page
Foreword.xii
Introduction .xiii
1 Scope .1
2 Normative references .1
3 Terms and definitions .1
4 General statistical principles.8
4.1 Different statistical approaches .8
4.1.1 General.8
4.1.2 Hypothesis-testing methods .8
4.1.3 Concentration-response modelling methods .10
4.1.4 Biology-based methods .11
4.2 Experimental design issues .11
4.2.1 General.11
4.2.2 NOEC or EC : Implications for design.12
x
4.2.3 Randomization .12
4.2.4 Replication.13
4.2.5 Multiple controls included in the experimental design.13
4.3 Process of data analysis.14
4.3.1 General.14
4.3.2 Data inspection and outliers.14
4.3.3 Data inspection and assumptions .15
4.3.3.1 Scatter .15
4.3.3.2 Heterogeneous variances and distribution .15
4.3.3.3 Heterogeneous variances and true variation in response.16
4.3.3.4 Consequences for the analysis .16
4.3.4 Transformation of data.16
4.3.5 Parametric and non-parametric methods .17
4.3.5.1 General .17
4.3.5.2 Parametric methods.17
4.3.5.3 Generalized linear models (GLMs) .18
4.3.5.4 Non-parametric methods.18
4.3.5.5 How to choose?.18
4.3.6 Pre-treatment of data.19
4.3.7 Model fitting.19
4.3.8 Model checking.20
4.3.8.1 Analysis of residuals .20
4.3.8.2 Validation of fitted dose-response model .21
4.3.9 Reporting the results.21
5 Hypothesis testing.21
5.1 Introduction.21
5.1.1 General.21
5.1.2 NOEC: What it is, and what it is not.25
5.1.3 Hypothesis used to determine NOEC.25
5.1.3.1 Understanding the question to be answered .25
5.1.3.2 One-sided hypothesis.26
5.1.3.3 Two-sided trend test .26
5.1.3.4 Trend or pair-wise test.26
5.1.4 Comparisons of single-step (pair-wise comparisons) or step-down trend tests to
determine the NOEC.28
5.1.4.1 General discussion . 28
5.1.4.2 Single-step procedures. 28
5.1.4.3 Step-down procedures. 29
5.1.4.4 Deciding between the two approaches . 30
5.1.5 Dose metric in trend tests . 31
5.1.6 Role of power in toxicity experiments . 31
5.1.7 Experimental design . 32
5.1.8 Treatment of covariates and other adjustments to analysis. 33
5.2 Quantal data (e.g. mortality, survival). 34
5.2.1 Hypothesis testing with quantal data to determine NOEC values . 34
5.2.2 Parametric versus non-parametric tests .35
5.2.2.1 Basis . 35
5.2.2.2 Single-step procedures. 36
5.2.2.3 Step-down procedures. 36
5.2.2.3.1 Choice of step-down procedure. 36
5.2.2.3.2 Test for monotone dose response . 36
5.2.2.3.3 Analysing the monotonic response for quantal data — Step-down procedure . 37
5.2.2.3.4 Possible modifications of the step-down procedure. 37
5.2.2.4 Alternative procedures . 37
5.2.2.4.1 Parametric and non-parametric procedures. 37
5.2.2.4.2 Pair-wise ANOVA-based methods . 38
5.2.2.4.3 Jonckheere-Terpstra trend test.38
5.2.2.4.4 Poisson tests . 38
5.2.2.5 Assumptions of methods for determining NOEC values . 38
5.2.3 Additional information. 39
5.2.4 Statistical items to be included in the study report. 40
5.3 Hypothesis testing with continuous data (e.g. mass, length, growth rate) to determine
NOEC . 40
5.3.1 General . 40
5.3.2 Parametric versus non-parametric tests .41
5.3.3 Single-step (pair-wise) procedures . 42
5.3.3.1 General . 42
5.3.3.2 Dunnett's test. 42
5.3.3.3 Tamhane-Dunnett test. 42
5.3.3.4 Dunn's test . 42
5.3.3.5 Mann-Whitney test. 43
5.3.4 Step-down trend procedures . 43
5.3.5 Determining the NOEC using a step-down procedure based on a trend test . 43
5.3.5.1 General . 43
5.3.5.2 Preliminaries . 43
5.3.5.3 Step-down procedure. 43
5.3.5.3.1 Preferred approach . 43
5.3.5.3.2 Williams' test. 44
5.3.5.3.3 Jonckheere-Terpstra test. 44
5.3.6 Assumptions for methods for determining NOEC values . 44
5.3.6.1 Small samples — Massive ties. 44
5.3.6.2 Normality . 45
5.3.6.3 Variance homogeneity . 45
5.3.7 Operational considerations for statistical analyses. 46
5.3.7.1 Treatment of experimental units. 46
5.3.7.2 Identification and meaning of outliers . 46
5.3.7.3 Multiple controls. 46
5.3.7.4 General . 47
5.4 Statistical items to be included in the study report. 47
6 Dose-response modelling . 48
6.1 Introduction . 48
6.2 Modelling quantal dose-response data (for a single exposure duration) . 49
6.2.1 General . 49
6.2.2 Choice of model . 50
iv © ISO 2006 – All rights reserved
6.2.2.1 General .50
6.2.2.2 Probit model .51
6.2.2.3 Logit model.53
6.2.2.4 Weibull model.54
6.2.2.5 Multi-stage models.55
6.2.2.6 Definitions of EC and EC .55
50 x
6.2.3 Model fitting and estimation of parameters .56
6.2.3.1 Software and assumptions .56
6.2.3.2 Response in controls.56
6.2.3.3 Analysis of data with various observed fractions at each dose group.57
6.2.3.4 Analysis of data with one observed fraction at each dose group .58
6.2.3.5 Extrapolation and EC .58
x
6.2.3.6 Confidence intervals.58
6.2.4 Assumptions .59
6.2.4.1 General .59
6.2.4.2 Statistical assumptions .59
6.2.4.3 Evaluation of assumptions .59
6.2.4.3.1 Evaluation of basic assumptions .59
6.2.4.3.2 Evaluation of the additional assumption.59
6.2.4.4 Consequences of violating the assumptions.60
6.2.4.4.1 Consequences of violating basic assumptions.60
6.2.4.4.2 Consequences of violating the additional assumption .60
6.3 Dose-response modelling of continuous data (for a single exposure duration) .60
6.3.1 Purpose.60
6.3.2 Terms and notation.60
6.3.3 Choice of model.61
6.3.3.1 First distinctions .61
6.3.3.2 Linear models.62
6.3.3.3 Threshold models .62
6.3.3.4 Additive versus multiplicative models.63
6.3.3.5 Models based on “quantal” models.63
6.3.3.6 Nested non-linear models .64
6.3.3.7 Hill model .67
6.3.3.8 Non-monotone models .67
6.3.4 Model fitting and estimation of parameters .68
6.3.4.1 Software and assumptions .68
6.3.4.2 Response in controls.68
6.3.4.3 Fitting the model assuming normal variation .68
6.3.4.4 Fitting the model assuming normal variation after log-transformation .68
6.3.4.5 Fitting the model assuming normal variation after other transformations.69
6.3.4.6 No individual data available.69
6.3.4.7 Fitting the model using GLM.69
6.3.4.8 Covariates .70
6.3.4.9 Heterogeneity and weighted analysis.71
6.3.4.10 Confidence intervals.73
6.3.4.11 Extrapolation .73
6.3.4.12 Analysis of data with replicated dose group.73
6.3.5 Assumptions .74
6.3.5.1 General .74
6.3.5.2 Statistical assumptions .74
6.3.5.3 Additional assumption .74
6.3.6 Evaluation of assumptions .75
6.3.7 Consequences of violating the assumptions .75
6.3.7.1 Basic assumptions .75
6.3.7.2 Additional assumption .76
6.4 To accept or not accept the fitted model? .77
6.4.1 Can the fitted model be accepted and used for its intended purpose?.77
6.4.2 Is the model in agreement with the data? .77
6.4.3 Do the data provide sufficient information for fixing the model? .77
6.5 Design issues . 81
6.5.1 General . 81
6.5.2 Location of dose groups . 81
6.5.3 Number of replicates . 81
6.5.4 Balanced versus unbalanced designs.82
6.6 Exposure duration and time. 82
6.6.1 General . 82
6.6.2 Quantal data. 82
6.6.3 Continuous data. 83
6.6.3.1 General . 83
6.6.3.2 Independent observations in time . 83
6.6.3.3 Dependent observations in time. 85
6.7 Search algorithms and non-linear regression . 85
6.8 Reporting statistics. 86
6.8.1 Quantal data. 86
6.8.2 Continuous data. 87
7 Biology-based methods . 87
7.1 Introduction . 87
7.1.1 Effects as functions of concentration and exposure time. 87
7.1.2 Parameter estimation. 89
7.1.3 Outlook. 89
7.2 Modules of effect-models. 90
7.2.1 General . 90
7.2.2 Toxico-kinetic model . 91
7.2.3 Physiological targets of toxicants. 91
7.2.4 Change in target parameter . 92
7.2.5 Change in endpoint. 93
7.3 Survival . 93
7.3.1 Relationship between hazard rate and survival probability . 93
7.3.2 Assumptions of survival probability at any concentration of test compound . 94
7.3.3 Summary. 94
7.4 Body growth . 97
7.4.1 Routes for affecting body growth. 97
7.4.2 Assumptions. 97
7.4.3 Von Bertalanffy growth curve. 98
7.5 Reproduction. 99
7.5.1 Routes that affect reproduction. 99
7.5.2 Assumptions. 100
7.5.3 Implication . 100
7.6 Population growth. 101
7.6.1 General . 101
7.6.2 Assumptions. 101
7.7 Parameters of effect models. 103
7.7.1 General . 103
7.7.2 Effect parameters. 103
7.7.2.1 Toxicity and dynamic parameters . 103
7.7.2.2 Killing rate, b . 104
k
7.7.3 Discussion . 105
7.7.4 Eco-physiological parameters. 107
7.8 Recommendations . 109
7.8.1 Goodness of fit. 109
7.8.2 Choice of modes of action . 110
7.8.3 Experimental design . 110
7.8.4 Building a database for raw data. 110
7.9 Software support. 110
7.9.1 General . 110
7.9.2 DEBtox . 111
7.9.3 DEBtool . 111
vi © ISO 2006 – All rights reserved
8 List of existing guidelines with references to the subclauses of this Technical
Specification.112
Annex A (informative) Analysis of an “acute immobilization of Daphnia magna” data set
(OECD GL 202 — ISO 6341) using the three presented approaches.115
A.1 Data set (see Table A.1) .115
A.2 Examples of data analysis using hypothesis testing (NOEC determination) .115
A.3 Example of data analysis by dose-response modelling.120
A.4 Example of data analysis using DEBtox (biological methods).125
Annex B (informative) Analysis of an “algae growth inhibition” data set using the three presented
approaches.127
B.1 General.127
B.2 Examples of data analysis using hypothesis testing (NOEC determination) .128
B.3 Example of data analysis by dose-response modelling.135
B.4 Examples of data analysis using DEBtox (biological methods).139
Annex C (informative) Analysis of an “Daphnia magna reproduction” data set (OECD GL 211 –
ISO 10706) using the three presented approaches.142
C.1 Examples of data analysis using hypothesis testing (NOEC determination) .143
C.2 Example of data analysis by dose-response modelling.148
C.3 Examples of data analysis using DEBtox (biological methods).155
Annex D (informative) Analysis of a “fish growth” data set (OECD GL 204/215 – ISO 10229) using
the three presented approaches .160
D.1 Data set .160
D.2 Examples of data analysis using hypothesis testing (NOEC determination) .162
D.3 Example of data analysis by dose-response modelling.172
D.4 Examples of data analysis using DEBtox (biological methods).177
Annex E (informative) Description and power of selected tests and methods.180
E.1 Description of selected methods for use with quantal data .180
E.2 Power of the Cochran-Armitage test .189
E.3 Description of selected tests for use with continuous data .198
E.4 Power of step-down Jonckheere-Terpstra test .218
Annex F (informative) Annex to Clause 7 “Biology-based methods”.231
F.1 General.231
F.2 Effects on survival.231
Bibliography .237
Figure 1 — Conceptual illustration of accuracy and precision. 2
Figure 2 — Illustration of a concentration-response relationship and of the estimates
of the EC and NOEC/LOEC . 5
x
Figure 3 — Analysis of quantal data: Methods for determining the NOEC . 23
Figure 4 — Analysis of continuous data: Methods for determining the NOEC. 24
Figure 5 — Analysis of continuous data: Methods for determining the NOEC (continued) . 24
Figure 6 — Flow-chart for dose-response modelling. 50
Figure 7 — Probit model fitted to observed mortality frequencies (triangles) as a function of log-dose .52
Figure 8 — Logit model fitted to mortality dose-response data (triangles) .53
Figure 9 — Weibull model fitted to mortality dose-response data (triangles) .54
Figure 10 — Logit model fitted to mortality dose-response data (triangles), with background mortality.57
Figure 11 — Two members from a nested family of models fitted to the same data set.66
Figure 12 — Cholinesterase inhibition as a function of dose at three exposure durations.71
Figure 13 — Relative liver masses against dose, plotted on log-scale .72
Figure 14 — Dose-response model fitted to the data of Figure 13, showing that the heterogeneous
variance was caused by males (triangles) and females (circles) responding differently to the chemical .73
Figure 15 — Model fitted to dose-response data with and without an outlier in the top dose .76
Figure 16 — Two different models (both with four parameters) fitted to the same data set resulting
in similar dose-response relationships.79
Figure 17 — Two data sets illustrating that passing a goodness-of-fit test is not sufficient
for accepting the model.80
Figure 18 — Observed biomasses (marks) as a function of time, for nine different concentrations
of Atrazine.84
Figure 19 — Growth rates as derived from biomasses observed in time (see Figure 18)
at nine different concentrations (including zero), with the Hill model fitted to them.84
Figure 20 — Estimated growth rates as a function of (log-)concentration Atrazine .85
Figure 21 — Fluxes of material and energy through an animal, as specified in the DEB model.92
Figure 22 — Time and concentration profiles of the hazard model, together with the data of Figure 27.95
Figure 23 — Time and concentration profiles for effects on growth of Pimephalus promelas via an increase
of specific maintenance costs by sodium pentachlorophenate (data by Ria Hooftman, TNO-Delft).98
Figure 24 — Time and concentration profiles for effects on growth of Lumbricus rubellus via
a decrease of assimilation by copper chloride (data from Klok and de Roos 1996) .99
Figure 25 — Effects of cadmium on the reproduction of Daphnia magna through an increase
of the costs per offspring — Data from the OECD ring-test .101
Figure 26 — Example of application of the DEBtox method.102
Figure 27 — The effect of a mixture of C,N,S-compounds on the growth of Skeletonema costatum
via an increase of the cos
...
TECHNICAL ISO/TS
SPECIFICATION 20281
First edition
2006-04-01
Water quality — Guidance on statistical
interpretation of ecotoxicity data
Qualité de l'eau — Lignes directrices relatives à l'interprétation
statistique de données écotoxicologiques
Reference number
©
ISO 2006
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
© ISO 2006
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2006 – All rights reserved
Contents Page
Foreword.xii
Introduction .xiii
1 Scope .1
2 Normative references .1
3 Terms and definitions .1
4 General statistical principles.8
4.1 Different statistical approaches .8
4.1.1 General.8
4.1.2 Hypothesis-testing methods .8
4.1.3 Concentration-response modelling methods .10
4.1.4 Biology-based methods .11
4.2 Experimental design issues .11
4.2.1 General.11
4.2.2 NOEC or EC : Implications for design.12
x
4.2.3 Randomization .12
4.2.4 Replication.13
4.2.5 Multiple controls included in the experimental design.13
4.3 Process of data analysis.14
4.3.1 General.14
4.3.2 Data inspection and outliers.14
4.3.3 Data inspection and assumptions .15
4.3.3.1 Scatter .15
4.3.3.2 Heterogeneous variances and distribution .15
4.3.3.3 Heterogeneous variances and true variation in response.16
4.3.3.4 Consequences for the analysis .16
4.3.4 Transformation of data.16
4.3.5 Parametric and non-parametric methods .17
4.3.5.1 General .17
4.3.5.2 Parametric methods.17
4.3.5.3 Generalized linear models (GLMs) .18
4.3.5.4 Non-parametric methods.18
4.3.5.5 How to choose?.18
4.3.6 Pre-treatment of data.19
4.3.7 Model fitting.19
4.3.8 Model checking.20
4.3.8.1 Analysis of residuals .20
4.3.8.2 Validation of fitted dose-response model .21
4.3.9 Reporting the results.21
5 Hypothesis testing.21
5.1 Introduction.21
5.1.1 General.21
5.1.2 NOEC: What it is, and what it is not.25
5.1.3 Hypothesis used to determine NOEC.25
5.1.3.1 Understanding the question to be answered .25
5.1.3.2 One-sided hypothesis.26
5.1.3.3 Two-sided trend test .26
5.1.3.4 Trend or pair-wise test.26
5.1.4 Comparisons of single-step (pair-wise comparisons) or step-down trend tests to
determine the NOEC.28
5.1.4.1 General discussion . 28
5.1.4.2 Single-step procedures. 28
5.1.4.3 Step-down procedures. 29
5.1.4.4 Deciding between the two approaches . 30
5.1.5 Dose metric in trend tests . 31
5.1.6 Role of power in toxicity experiments . 31
5.1.7 Experimental design . 32
5.1.8 Treatment of covariates and other adjustments to analysis. 33
5.2 Quantal data (e.g. mortality, survival). 34
5.2.1 Hypothesis testing with quantal data to determine NOEC values . 34
5.2.2 Parametric versus non-parametric tests .35
5.2.2.1 Basis . 35
5.2.2.2 Single-step procedures. 36
5.2.2.3 Step-down procedures. 36
5.2.2.3.1 Choice of step-down procedure. 36
5.2.2.3.2 Test for monotone dose response . 36
5.2.2.3.3 Analysing the monotonic response for quantal data — Step-down procedure . 37
5.2.2.3.4 Possible modifications of the step-down procedure. 37
5.2.2.4 Alternative procedures . 37
5.2.2.4.1 Parametric and non-parametric procedures. 37
5.2.2.4.2 Pair-wise ANOVA-based methods . 38
5.2.2.4.3 Jonckheere-Terpstra trend test.38
5.2.2.4.4 Poisson tests . 38
5.2.2.5 Assumptions of methods for determining NOEC values . 38
5.2.3 Additional information. 39
5.2.4 Statistical items to be included in the study report. 40
5.3 Hypothesis testing with continuous data (e.g. mass, length, growth rate) to determine
NOEC . 40
5.3.1 General . 40
5.3.2 Parametric versus non-parametric tests .41
5.3.3 Single-step (pair-wise) procedures . 42
5.3.3.1 General . 42
5.3.3.2 Dunnett's test. 42
5.3.3.3 Tamhane-Dunnett test. 42
5.3.3.4 Dunn's test . 42
5.3.3.5 Mann-Whitney test. 43
5.3.4 Step-down trend procedures . 43
5.3.5 Determining the NOEC using a step-down procedure based on a trend test . 43
5.3.5.1 General . 43
5.3.5.2 Preliminaries . 43
5.3.5.3 Step-down procedure. 43
5.3.5.3.1 Preferred approach . 43
5.3.5.3.2 Williams' test. 44
5.3.5.3.3 Jonckheere-Terpstra test. 44
5.3.6 Assumptions for methods for determining NOEC values . 44
5.3.6.1 Small samples — Massive ties. 44
5.3.6.2 Normality . 45
5.3.6.3 Variance homogeneity . 45
5.3.7 Operational considerations for statistical analyses. 46
5.3.7.1 Treatment of experimental units. 46
5.3.7.2 Identification and meaning of outliers . 46
5.3.7.3 Multiple controls. 46
5.3.7.4 General . 47
5.4 Statistical items to be included in the study report. 47
6 Dose-response modelling . 48
6.1 Introduction . 48
6.2 Modelling quantal dose-response data (for a single exposure duration) . 49
6.2.1 General . 49
6.2.2 Choice of model . 50
iv © ISO 2006 – All rights reserved
6.2.2.1 General .50
6.2.2.2 Probit model .51
6.2.2.3 Logit model.53
6.2.2.4 Weibull model.54
6.2.2.5 Multi-stage models.55
6.2.2.6 Definitions of EC and EC .55
50 x
6.2.3 Model fitting and estimation of parameters .56
6.2.3.1 Software and assumptions .56
6.2.3.2 Response in controls.56
6.2.3.3 Analysis of data with various observed fractions at each dose group.57
6.2.3.4 Analysis of data with one observed fraction at each dose group .58
6.2.3.5 Extrapolation and EC .58
x
6.2.3.6 Confidence intervals.58
6.2.4 Assumptions .59
6.2.4.1 General .59
6.2.4.2 Statistical assumptions .59
6.2.4.3 Evaluation of assumptions .59
6.2.4.3.1 Evaluation of basic assumptions .59
6.2.4.3.2 Evaluation of the additional assumption.59
6.2.4.4 Consequences of violating the assumptions.60
6.2.4.4.1 Consequences of violating basic assumptions.60
6.2.4.4.2 Consequences of violating the additional assumption .60
6.3 Dose-response modelling of continuous data (for a single exposure duration) .60
6.3.1 Purpose.60
6.3.2 Terms and notation.60
6.3.3 Choice of model.61
6.3.3.1 First distinctions .61
6.3.3.2 Linear models.62
6.3.3.3 Threshold models .62
6.3.3.4 Additive versus multiplicative models.63
6.3.3.5 Models based on “quantal” models.63
6.3.3.6 Nested non-linear models .64
6.3.3.7 Hill model .67
6.3.3.8 Non-monotone models .67
6.3.4 Model fitting and estimation of parameters .68
6.3.4.1 Software and assumptions .68
6.3.4.2 Response in controls.68
6.3.4.3 Fitting the model assuming normal variation .68
6.3.4.4 Fitting the model assuming normal variation after log-transformation .68
6.3.4.5 Fitting the model assuming normal variation after other transformations.69
6.3.4.6 No individual data available.69
6.3.4.7 Fitting the model using GLM.69
6.3.4.8 Covariates .70
6.3.4.9 Heterogeneity and weighted analysis.71
6.3.4.10 Confidence intervals.73
6.3.4.11 Extrapolation .73
6.3.4.12 Analysis of data with replicated dose group.73
6.3.5 Assumptions .74
6.3.5.1 General .74
6.3.5.2 Statistical assumptions .74
6.3.5.3 Additional assumption .74
6.3.6 Evaluation of assumptions .75
6.3.7 Consequences of violating the assumptions .75
6.3.7.1 Basic assumptions .75
6.3.7.2 Additional assumption .76
6.4 To accept or not accept the fitted model? .77
6.4.1 Can the fitted model be accepted and used for its intended purpose?.77
6.4.2 Is the model in agreement with the data? .77
6.4.3 Do the data provide sufficient information for fixing the model? .77
6.5 Design issues . 81
6.5.1 General . 81
6.5.2 Location of dose groups . 81
6.5.3 Number of replicates . 81
6.5.4 Balanced versus unbalanced designs.82
6.6 Exposure duration and time. 82
6.6.1 General . 82
6.6.2 Quantal data. 82
6.6.3 Continuous data. 83
6.6.3.1 General . 83
6.6.3.2 Independent observations in time . 83
6.6.3.3 Dependent observations in time. 85
6.7 Search algorithms and non-linear regression . 85
6.8 Reporting statistics. 86
6.8.1 Quantal data. 86
6.8.2 Continuous data. 87
7 Biology-based methods . 87
7.1 Introduction . 87
7.1.1 Effects as functions of concentration and exposure time. 87
7.1.2 Parameter estimation. 89
7.1.3 Outlook. 89
7.2 Modules of effect-models. 90
7.2.1 General . 90
7.2.2 Toxico-kinetic model . 91
7.2.3 Physiological targets of toxicants. 91
7.2.4 Change in target parameter . 92
7.2.5 Change in endpoint. 93
7.3 Survival . 93
7.3.1 Relationship between hazard rate and survival probability . 93
7.3.2 Assumptions of survival probability at any concentration of test compound . 94
7.3.3 Summary. 94
7.4 Body growth . 97
7.4.1 Routes for affecting body growth. 97
7.4.2 Assumptions. 97
7.4.3 Von Bertalanffy growth curve. 98
7.5 Reproduction. 99
7.5.1 Routes that affect reproduction. 99
7.5.2 Assumptions. 100
7.5.3 Implication . 100
7.6 Population growth. 101
7.6.1 General . 101
7.6.2 Assumptions. 101
7.7 Parameters of effect models. 103
7.7.1 General . 103
7.7.2 Effect parameters. 103
7.7.2.1 Toxicity and dynamic parameters . 103
7.7.2.2 Killing rate, b . 104
k
7.7.3 Discussion . 105
7.7.4 Eco-physiological parameters. 107
7.8 Recommendations . 109
7.8.1 Goodness of fit. 109
7.8.2 Choice of modes of action . 110
7.8.3 Experimental design . 110
7.8.4 Building a database for raw data. 110
7.9 Software support. 110
7.9.1 General . 110
7.9.2 DEBtox . 111
7.9.3 DEBtool . 111
vi © ISO 2006 – All rights reserved
8 List of existing guidelines with references to the subclauses of this Technical
Specification.112
Annex A (informative) Analysis of an “acute immobilization of Daphnia magna” data set
(OECD GL 202 — ISO 6341) using the three presented approaches.115
A.1 Data set (see Table A.1) .115
A.2 Examples of data analysis using hypothesis testing (NOEC determination) .115
A.3 Example of data analysis by dose-response modelling.120
A.4 Example of data analysis using DEBtox (biological methods).125
Annex B (informative) Analysis of an “algae growth inhibition” data set using the three presented
approaches.127
B.1 General.127
B.2 Examples of data analysis using hypothesis testing (NOEC determination) .128
B.3 Example of data analysis by dose-response modelling.135
B.4 Examples of data analysis using DEBtox (biological methods).139
Annex C (informative) Analysis of an “Daphnia magna reproduction” data set (OECD GL 211 –
ISO 10706) using the three presented approaches.142
C.1 Examples of data analysis using hypothesis testing (NOEC determination) .143
C.2 Example of data analysis by dose-response modelling.148
C.3 Examples of data analysis using DEBtox (biological methods).155
Annex D (informative) Analysis of a “fish growth” data set (OECD GL 204/215 – ISO 10229) using
the three presented approaches .160
D.1 Data set .160
D.2 Examples of data analysis using hypothesis testing (NOEC determination) .162
D.3 Example of data analysis by dose-response modelling.172
D.4 Examples of data analysis using DEBtox (biological methods).177
Annex E (informative) Description and power of selected tests and methods.180
E.1 Description of selected methods for use with quantal data .180
E.2 Power of the Cochran-Armitage test .189
E.3 Description of selected tests for use with continuous data .198
E.4 Power of step-down Jonckheere-Terpstra test .218
Annex F (informative) Annex to Clause 7 “Biology-based methods”.231
F.1 General.231
F.2 Effects on survival.231
Bibliography .237
Figure 1 — Conceptual illustration of accuracy and precision. 2
Figure 2 — Illustration of a concentration-response relationship and of the estimates
of the EC and NOEC/LOEC . 5
x
Figure 3 — Analysis of quantal data: Methods for determining the NOEC . 23
Figure 4 — Analysis of continuous data: Methods for determining the NOEC. 24
Figure 5 — Analysis of continuous data: Methods for determining the NOEC (continued) . 24
Figure 6 — Flow-chart for dose-response modelling. 50
Figure 7 — Probit model fitted to observed mortality frequencies (triangles) as a function of log-dose .52
Figure 8 — Logit model fitted to mortality dose-response data (triangles) .53
Figure 9 — Weibull model fitted to mortality dose-response data (triangles) .54
Figure 10 — Logit model fitted to mortality dose-response data (triangles), with background mortality.57
Figure 11 — Two members from a nested family of models fitted to the same data set.66
Figure 12 — Cholinesterase inhibition as a function of dose at three exposure durations.71
Figure 13 — Relative liver masses against dose, plotted on log-scale .72
Figure 14 — Dose-response model fitted to the data of Figure 13, showing that the heterogeneous
variance was caused by males (triangles) and females (circles) responding differently to the chemical .73
Figure 15 — Model fitted to dose-response data with and without an outlier in the top dose .76
Figure 16 — Two different models (both with four parameters) fitted to the same data set resulting
in similar dose-response relationships.79
Figure 17 — Two data sets illustrating that passing a goodness-of-fit test is not sufficient
for accepting the model.80
Figure 18 — Observed biomasses (marks) as a function of time, for nine different concentrations
of Atrazine.84
Figure 19 — Growth rates as derived from biomasses observed in time (see Figure 18)
at nine different concentrations (including zero), with the Hill model fitted to them.84
Figure 20 — Estimated growth rates as a function of (log-)concentration Atrazine .85
Figure 21 — Fluxes of material and energy through an animal, as specified in the DEB model.92
Figure 22 — Time and concentration profiles of the hazard model, together with the data of Figure 27.95
Figure 23 — Time and concentration profiles for effects on growth of Pimephalus promelas via an increase
of specific maintenance costs by sodium pentachlorophenate (data by Ria Hooftman, TNO-Delft).98
Figure 24 — Time and concentration profiles for effects on growth of Lumbricus rubellus via
a decrease of assimilation by copper chloride (data from Klok and de Roos 1996) .99
Figure 25 — Effects of cadmium on the reproduction of Daphnia magna through an increase
of the costs per offspring — Data from the OECD ring-test .101
Figure 26 — Example of application of the DEBtox method.102
Figure 27 — The effect of a mixture of C,N,S-compounds on the growth of Skeletonema costatum
via an increase of the costs for growth — Data from the OECD ring test .103
Figure 28 — A typical table of data that serves as input for the survival model, as can be used
in the software package DEBtox (Kooijman and Bedaux 1996).108
Figure 29 — This profile likelihood function of the NEC (right panel) for the data in Figure 28 results
from the software package DEBtox (Kooijman and Bedaux 1996) .108
Figure A.1 — Probit model fitted to mortality response at day 2 — CED = EC .122
Figure A.2 — The Weibull (left panel) and the two-stage LMS model fitted to the mortality data at day 2 .123
Figure A.3 — Probit model fitted to mortality data on day 1 (left panel), and fitted to both day 1
and day 2 simultaneously .
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