Version log e-book "Modelling survival under chemical stress"
Version 1.0 (Date 18 January 2018)
This was the first version of the e-book.
Version 2.0 (Date 8 December 2018)
The most important changes in this version of the book relates to the statistical treatment:
- The method mentioned for making predictions from the frequentist joint confidence region (old Section 2.3.4, Section 4.5.2) was incorrect, or at least incomplete. Simulation studies showed us that the resulting CIs on model predictions had a coverage of more than 95%. Thanks to a pivotal paper by Kreutz et al (2012), we now realise that the approach should be different, altough a sample from parameter space can still be used. We corrected and extended the text where needed, but this finding also affects some of the ring test results (the incorrect method was used by BYOM and Mathematica, which will have exaggerated the CIs on LCx and LPx).
- The description in Chapter 2 is updated to describe the correct procedure (Section 2.3.5), and also the mathematics Chapter 3 (a completely new Section 3.5.6). A new Appendix D was added to provide an explanation in more detail, including explanatory graphics, since the use of a sample is less intuitive in a frequentist framework.
- For the dieldrin case study of Chapter 4, this correct frequentist approach is now used instead of the Bayesian approach in the first version of the book. The reason is that, with improper priors (i.e., uniform from 0-infinity), the posteriors will be improper (i.e., cannot be integrated). A thorough discussion on how to use informative priors to ensure proper posteriors is outside of the scope of this book, and hence the move to frequentist inference here. This also led to some small changes for the model evaluation in Chapter 7, as the sensitivity plots (Fig. 7.2 and 7.4) are now based on the frequentist sample instead of the Bayesian posterior.
- The issue of improper priors led us to think more about parameter identifiability, which is now reflected much more explicitly, and discussed more extensively, in the description (Section 2.3.6) and in the new Appendix C. This appendix incorporates the fast-slow kinetics from the appendix A.7 of the first book version. However, it is seriously extended and demonstrated with examples.
- The propiconazole case study (Chapter 5) kept the Bayesian analysis, but this is extended with frequentist profiling to demonstrate that all parameters can indeed be identified from the data. Furthermore, plots of the raw sample are included to aid the evaluation of the MCMC output (e.g., to judge the autocorrelation in the sample).
Moved sections:
- The ring test is moved to the appendices. This chapter is a bit different from the rest, and actually could do with a new round of ring testing as most software platforms have evolved since these calculations were made.
- The sections on background mortality (old Section 2.4.1) and starting values (old Section 2.4.2) are moved up in this chapter (to new Section 2.3.4) where they fit much better.
- The section in the appendix on extrapolations was removed. The parts that overlapped with Chapter 6 were deleted, and the remaining parts now form a new Section 6.11 (apart from the temperature extrapolations, which are now covered in Appendix B.5).
Small changes:
- Numerous small changes to correct spelling/grammar errors and to clarify parts of the text. Furthermore, new references are added, such as to the recent GUTS validation study by Focks et al.
- On the second page, the preferred reference to the book now includes the publisher (Toxicodynamics Ltd., York, UK).
- We added a thanks to Anna-Maija Nyman for pointing out relevant REACH documents for Chapter 6.
- In Table 7.1, k_k corrected to b_w.
- For the GUTS-RED-IT and GUTS-IT special cases (Eq. 3.20 and 3.22), the background mortality was not included, which is now corrected.
- The manner in which the likelihood is defined in various textbooks and papers differs a bit, as does the notation. We think the notation we selected for the book is clear, used consistently, and thus should not lead to problems. However, we added a few clarifying notes in Section 3.5.1 (and a footnote with link in Section 2.3.1).
- The EFSA has released an opinion on TKTD models, with special focus on GUTS. This opinion is now referenced in various places.
- Appendix B.3.2. is extended with more analytical solutions for damage: a solution that can be used when exposure changes linearly over time.
- Small change to Eq. 3.39 and 3.40. The subscript i is used in this section for the interval between two observations. However, S and y use i for the actual time point. This was not entirely clear in the first version, so here it is made explicit (S_i and y_i are meant to be at the start of the interval i).
Version 2.1 (Date 21 November 2022)
- Numerous small textual clarifications, small additions, and many new references to reflect the most recent developments of GUTS (e.g., the development of the openGUTS software).
- Added a section in Chapter 3 to present an additional likelihood function to be used when a survival test sports destructive sampling (as is quite common for soil- and sediment-dwelling invertebrates). This results in a simple set of independent bionomial distributions.
- The footnote below Eq. 3.28 needed a bit more explanation (thanks to Johannes Ranke for pointing this out to me). Going seamlessly from probabilities to probability densities in a likelihood function is only allowed when the observations are made with good precision (and for example not censored or given as classes). This is now added to the footnote.
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Known errors/limitation that will be corrected, and updates that will be included, in the next version:
- A publication on an extended GUTS model, to deal with immobility/recovery in acute toxicity tests, is under development. Elements from this model will be explained in the next version of this book.
- We need to add a case study with openGUTS to the model, as the current case studies are a bit 'old fashioned'. The new case study should reflect the openGUTS facilities, but also the workflow adopted in the EFSA SO on TKTD models.
- ...