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Abstract
W Western W estern Washingt ashington Univ on University ersity W Western CED estern CEDAR AR IETC Publications Categories 2-17-2020 De Dev velopment of a elopment of a hybrid Ba hybrid Bay yesian network esian network model for pr model for predicting edicting acute fish acute fish t to oxicity using xicity using multiple lines multiple lines of e of evidence vidence S. Jannicke Moe Norwegian Institute for Water Research (NIVA) Anders L. Madsen Aalborg University Kristin A. Connors Procter & Gamble Jane M. Rawlings Procter & Gamble Scott E. Belanger Procter & Gamble See next page for additional authors Follow this and additional works at: https://cedar.wwu.edu/ietc_publications Part of the Environmental Chemistry Commons, Environmental Health Commons, and the Toxicology Commons Recommended Citation Recommended Citation Moe, S. Jannicke; Madsen, Anders L.; Connors, Kristin A.; Rawlings, Jane M.; Belanger, Scott E.; Landis, Wayne G.; Wolf, Raoul; and Lillicrap, Adam D., "Development of a hybrid Bayesian network model for predicting acute fish toxicity using multiple lines of evidence" (2020). IETC Publications. 4. https://cedar.wwu.edu/ietc_publications/4 This Article is brought to you for free and open access by the Categories at Western CEDAR. It has been accepted for inclusion in IETC Publications by an authorized administrator of Western CEDAR. For more information, please contact [email protected]. A Authors uthors S. Jannicke Moe, Anders L. Madsen, Kristin A. Connors, Jane M. Rawlings, Scott E. Belanger, Wayne G. Landis, Raoul Wolf, and Adam D. Lillicrap This article is available at Western CEDAR: https://cedar.wwu.edu/ietc_publications/4 Environmental Modelling and Software 126 (2020) 104655 Contents lists available at ScienceDirect Environmental Modelling and Software journal homepage: http://www.elsevier.com/locate/envsoft Development of a hybrid Bayesian network model for predicting acute fish toxicity using multiple lines of evidence a, * b, c d d S. Jannicke Moe , Anders L. Madsen , Kristin A. Connors , Jane M. Rawlings , d e a a Scott E. Belanger , Wayne G. Landis , Raoul Wolf , Adam D. Lillicrap Norwegian Institute for Water Research (NIVA), Gaustadall� een 21, 0349, Oslo, Norway HUGIN EXPERT A/S, Gasværksvej 5, 9000, Aalborg, Denmark Dept. of Computer Science, Aalborg University, Selma Lagerlof Vej 300, 9220, Aalborg, Denmark Procter and Gamble, Cincinnati, OH, USA Western Washington University, Bellingham, WA, USA ARTICLE INFO ABSTRACT Keywords: A hybrid Bayesian network (BN) was developed for predicting the acute toxicity of chemicals to fish, using data Hybrid bayesian network model from fish embryo toxicity (FET) testing in combination with other information. This model can support the use of Acute fish toxicity FET data in a Weight-of-Evidence (WOE) approach for replacing the use of ju-venile fish. The BN predicted Fish embryo toxicity correct toxicity intervals for 69%–80% of the tested substances. The model was most sensitive to components Weight of evidence quantified by toxicity data, and least sensitive to compo-nents quantified by expert knowledge. The model is Animal alternatives publicly available through a web interface. Fur-ther development of this model should include additional lines of Risk assessment evidence, refinement of the discre-tisation, and training with a larger dataset for weighting of the lines of evi- dence. A refined version of this model can be a useful tool for predicting acute fish toxicity, and a contribution to more quantitative WOE approaches for ecotoxicology and environmental assessment more generally. 1. Introduction and assess their uncertainty to support decision-making for environ- mental protection. These processes would benefit from more quantita- Weight of evidence (WOE) is a term commonly used about the as- tive and rigorous approaches to WOE. sembly, weighting, and integration of multiple pieces of evidence for More systematic frameworks for WOE approaches in scientific as- environmental assessment and decision-making. However, the term has sessments have recently been proposed, for example by the European been used in multiple ways, including metaphorical, theoretical and Chemicals Agency (ECHA, 2016), by the European Food Safety Au- methodological, without consensus about its meaning (Weed, 2005). thority (EFSA Scientific Committee et al., 2017) and by the US Envi- Historically, environmental risk assessors have relied upon narrative ronmental Protection Agency (USEPA, 2016) to assist ecological and qualitative approaches such as expert knowledge, or limited quan- assessment. The basic steps in these frameworks are to (1) assemble titative methods such as direct scoring to integrate multiple lines of evidence, (2) to weight the evidence by assigning scores depending on e. evidence (Linkov et al., 2009). These historical methods lacked trans- g. relevance, strength and reliability, and (3) to integrate the evidence parency and reproducibility. A review of WOE methods applied for (weigh the body of evidence). Suter et al. describe how the US EPA ecological risk assessment (Linkov et al., 2009) showed that only 9 out of framework can be used to infer qualitative properties (2017a) as well as 44 published studies had used a quantitative approach (scoring, index- quantitative estimates (2017b). Use of such frameworks can increase the ing or other type of quantification). Therefore, WOE approaches have consistency and rigor of WOE practices and provide greater trans- been criticised for being too vague, intransparent and subjective (Linkov parency than ad hoc and narrative-based approaches. et al., 2016). Nevertheless, methods are needed for integrating evidence The weight-of-evidence was first proposed as a Bayesian statistical Abbreviations: AFT, acute fish toxicity; BN, Bayesian network; CV, coefficient of variation; EC , effect concentration for 50% of the test individuals; ECHA, European Chemicals Agency; FET, fish embryo toxicity; LC , lethal concentration for 50% of the test individuals; QSAR, quantitative structure-activity relationship; REACH, registration, evaluation, authorisation and restriction of chemicals; WOE, weight of evidence. * Corresponding author. E-mail address: [email protected] (S.J. Moe). https://doi.org/10.1016/j.envsoft.2020.104655 Received 29 August 2019; Received in revised form 27 January 2020; Accepted 12 February 2020 Available online 17 February 2020 1364-8152/© 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). S.J. Moe et al. Environmental Modelling and Software 126 (2020) 104655 approach (Good, 1960). In Bayesian statistics, a model is based on researchers, regulators or other potential users to this first BN version updating prior beliefs in (probabilities of) a hypothesis after evaluating will be used for improving future versions of the model, with the aim of of evidence in order to achieve a posterior belief. In this context, the making it a useful tool in a WOE approach for predicting acute fish WOE is defined as the logarithm of the Bayes factor, which is calculated toxicity. as the ratio of the posterior odds to the prior odds (Good, 1985). In this paper, we return to the Bayesian origin of the WOE term and develop a 2. Materials and methods Bayesian network to combine lines of information in a probabilistic model to support risk assessment of chemicals. 2.1. Data Environmental risk assessment is a process for quantifying the probability of an adverse effect from a chemical exposure. Traditionally, An expanded version of the Threshold Database (Rawlings et al., acute toxicity data from three trophic levels (i.e., fish, invertebrates, 2019) was obtained from Procter & Gamble and used to construct the algae) are required for risk assessments. However, ethical considerations BN. This database contains acute freshwater toxicity values for fish and recent EU regulation have required that the number of animals used (AFT), fish embryos (FET), algae, and invertebrates for 237 chemical for toxicity testing is kept at a minimum, and that the use of vertebrate substances. The toxicity values are measured as EC (Effect Concen- species (such as fish) should be avoided as far as possible (OECD, 1996). tration for 50% of the test individuals) for non-lethal effects, and as LC Therefore, various alternative methods have been developed and pro- (Lethal Concentration of 50% of the test individuals) for lethal effects. posed to replace the use of live fish in toxicity testing (Lillicrap et al., The dataset used for development of this model, which will be referred 2016), including predictive toxicity modelling (Luechtefeld et al., 2018). to as “our dataset”, contained the following toxicity data: Legislative authorities in some geographic regions have encouraged the use of fish embryos, which are in this context considered as a non- � Algae: 264 values of EC based on OECD test no. 201 acute algal protected life stage, over more developed life stages such as juvenile growth inhibition tests (OECD, 2006). fish. The test of fish embryo toxicity (FET; OECD method 236) (OECD, � Daphnia: 1164 values EC based on OECD test no. 202 Daphnia sp. 2013) has therefore been proposed and evaluated as an alternative to acute immobilisation tests (OECD, 2004), using crustaceans of the using juvenile fish for testing acute fish toxicity (AFT; OECD method genus Daphnia (daphnids). 203) (OECD, 1992) (Busquet et al., 2014). Previous studies show a good � Juvenile fish: 1459 LC values based on OECD test no. 203 acute fish correlation of FET with the standard acute fish toxicity (AFT) test toxicity test (OECD, 1992). (Belanger et al., 2013; Rawlings et al., 2019). Nevertheless, it has been � Fish embryo: 541 LC values based on OECD test no. 236 Fish em- found that the fish embryo toxicity test alone is currently not sufficient bryo test (OECD, 2013). to replace the acute fish toxicity data as required by the European REACH regulation (Regulation, Evaluation, Authorisation and Restric- In addition to the data obtained from laboratory assays, modelled tion of Chemicals) (Sobanska et al., 2018). However, the authors have acute fish LC values were calculated using quantitative structure- suggested that “the test may be used within weight-of-evidence ap- activity relationships (QSARs) for each chemical, including the US proaches together with other independent, relevant, and reliable sources EPA Ecological Structure Activity Relationship (ECOSAR 1.11) models of information". and the Danish QSAR database (extracting values for Leadscope and To this end, we have developed a Bayesian network (BN) model for SciQSAR SARs). Data were then averaged for each chemical, resulting in integrating fish embryo toxicity data with other information to predict 152 QSAR values representing modelled toxicity to juvenile fish. More the acute toxicity to (juvenile) fish for any given chemical substance. A details on QSAR model selection, equation acceptability criteria and Bayesian network is a probabilistic graphical model over a set of random results can be found in (Lillicrap et al., 2020). variables. Bayesian networks are commonly used in environmental modelling (Aguilera et al., 2011; Barton et al., 2012; Landuyt et al., 2.2. BN model objective and structure 2013). For example, there are numerous BN models developed for assessment and management of water quality (Barton et al., 2014; A BN model consists of a directed, acyclic graph with nodes repre- Borsuk et al., 2004, 2012; Moe et al., 2016, 2019). BN modelling has senting the random variables and arrows (arcs) representing conditional been applied more rarely within ecotoxicology and ecological risk probability distributions (Kjærulff and Madsen, 2008). Each node has a assessment, but recent publications have demonstrated the applicability probability distribution conditional on its parents in the graph. The of BN modelling in these fields (Graham et al., 2019; Landis et al., 2017, probability distributions quantify the strengths for the dependence re- 2019; Lehikoinen et al., 2015). Compared to traditional qualitative WOE lations defined by the structure of the graph. The nodes are typically approaches, the network structure and probabilistic framework of BN defined by limited number of discrete states (categories or intervals) provide advantages by capturing the impacts of multiple sources of which are quantified by a prior probability distribution. New evidence is quantifiable uncertainty on predictions of ecological risk (Carriger et al., combined with the prior probabilities to calculate posterior probability 2016). Another example of applying a BN model for a quantitative WOE distributions, using Bayes’ rule from 1763 (see e.g. Linkov et al., 2016). and testing strategy is provided by Jaworska et al. (2015). The objective of the BN model presented here is to predict the acute Here, we develop a BN model for integrating four lines of evidence in toxicity of a chemical substance to juvenile fish, corresponding to the a quantitative framework: (1) information on physical and chemical interval of LC values from the AFT assay (OECD, 1992), by integrating properties of the substance, (2) toxicity data for chemically related toxicity data from testing of fish embryos (OECD, 2013) with other substances, (3) toxicity data for other species (crustaceans and algae) relevant physical, chemical and toxicological information for the given and (4) fish embryo toxicity data. By implementing this WOE model in a substance. The BN model is structured along the four lines of evidence Bayesian network, we aim to meet the demands for making WOE ap- (Fig. 1), representing different types of information for a given chemical proaches more transparent, structured and quantitative (Linkov et al., substance for which a user wants to predict the acute fish toxicity. The 2016). parameterisation of all lines is described in Supplementary material The purpose of this paper is to describe the development, parame- (Tables S.1-S.21), while more details on the assumptions are provided by terisation and evaluation of the BN model. The paper will also present an Lillicrap et al. (2020). online web interface to the model. More detailed information on this model’s performance for specific chemical substances and endpoints, � Line 1: Physical and chemical properties of the substance. The and the implications for current legislation and guidelines for toxicity selected nodes quantify the size (molecular weight, g/mol), hydro- testing, are addressed by Lillicrap et al. (2020). Feedback from phobicity (octanol water partitioning coefficient, logK ) and ow 2 S.J. Moe et al. Environmental Modelling and Software 126 (2020) 104655 Fig. 1. The main structure of the BN model: the four lines of evidence for predicting the interval of acute toxicity of a substance to fish. Nodes with double outline represent continuous value nodes (e.g. “Toxicity to algae (value 1)"), while nodes with single outline are interval or categorical nodes. All of the left-most nodes are input nodes for a given substance. For simplicity, only three continuous input nodes are shown for each of algae, Daphnia and embryo. “Value n" denotes the maximum number of input variable nodes in the web interface (currently 10). modelled toxicity to juvenile fish based on the structure (QSAR) of Daphnia and algae, and a toxicity at the same level (although with the substance. Substances with a low molecular size and low hy- more uncertainty) is assumed for fish. The conventional cut-off drophobicity (i.e. high solubility) are assumed to have a high ability values of 0.5 and 2.0 and more details underlying these assump- to cross a biological membrane. For a substance that is modelled via tions are described by ECETOC (2005). QSAR to be toxic (low LC value) and have a high ability of mem- � Line 4: Toxicity to fish embryo. The measured toxicity of a substance brane crossing, the predicted toxicity to juvenile fish from this line of to fish embryos is used directly as the fourth line of evidence. evidence will have highest probability of the higher toxicity intervals. The development and application of this BN is comparable to a � Line 2: Chemical category of the substance. This line of evidence is weight-of-evidence approach (e.g., Suter et al., 2017a), with the based on existing data on toxicity of substances to juvenile fish, assignment of conditional probabilities to different variables within in a aggregated by chemical category. The 237 chemicals used to line of evidence in the BN corresponding to setting weights to pieces of parametrize this model were assigned to 42 different chemical cat- evidence in a WOE. For example, assignment of low weight to a piece of egories (Table S.11), based on model output ECOSAR and further evidence can be obtained by setting wide probability distributions refined by expert knowledge (S. Belanger). (representing high uncertainty or variability) in the relation from this � Line 3: Toxicity to other taxa, representing lower trophic levels: node to its child node. Within a line of evidence (e.g. Line 3 “Toxicity to crustaceans (Daphnia magna or D. pulex) or unicellular algae. This other taxa”, Fig. 1), the calculation of posterior probabilities for the last line of evidence also considers whether the substance has a species- child node of this line (“Toxicity to fish predicted from other taxa”) specific (or more generally, taxon-specific) mode of action by accumulates the weights given to all parent nodes in this line. examining the ratio of Daphnia and algal toxicity. If the ratio of When using the BN to predict the toxicity to juvenile fish from all toxicity to Daphnia vs. algae is below 0.5, Daphnia has a considerably lines of evidence for a chemical of concern, the weighing of the total lower tolerance (lower EC50 value) to the substance that the algae. evidence for each hypothesis in a WOE (Suter et al., 2017a) can corre- In this case, the substance’s mode of action is assumed to be specific spond to calculating the posterior probability of each toxicity level to invertebrates (e.g. an insecticide). Likewise, if the ratio is above 2, (“very low”, “low” etc.) in the BN. For example, given two lines of evi- then the mode of action is assumed to be more specific to algae (e.g. a dence with posterior probability distributions both centred around “high herbicide). In either case, the substance can be assumed to have low toxicity”, the line with the more narrow probability distribution will toxicity to fish. Conversely, if the toxicity ratio is between 0.5 and 2, typically contribute more to the posterior probability of “high toxicity” then the toxicity to fish is assumed to be approximately equal to in the final child node (“Toxicity to fish predicted from other taxa”). In a 3 S.J. Moe et al. Environmental Modelling and Software 126 (2020) 104655 WOE approach, this would correspond to this line of evidence having a continuous input values (e.g. measured toxicity values) and their vari- higher weight for the hypothesis “high toxicity to juvenile fish ” than the ability. Consequently, this model is a hybrid BN with both discrete and line with a wider probability distribution. continuous nodes (Fig. 1). In this model, the continuous nodes are The BN was implemented in the software HUGIN Researcher version assumed to follow the conditional linear Gaussian distribution (Eq. (2)): 8.7, developed by HUGIN EXPERT A/S (http://www.hugin.com). The � � PðYjI¼ i; Z¼ zÞ¼ N αðiÞþ βðiÞz ; γðiÞ ; (2) model is available through a web interface (described in Section 3), j which is published on the demonstration web site http://demo.hugin. com/example/FET. The aim of this web interface is to facilitate feed- where Y is a continuous node, I is a set of discrete nodes, Z is a set of back for further improvement of the model, as recommended by Marcot continuous nodes, and I[Z is the set of parents of Y. (2017). As an intermediate step between the continuous nodes and the discrete categorical nodes, we used discrete interval nodes (Table 1). For 2.3. Model parametrization example, the categorical node “Toxicity to Daphnia (level)" has five labelled states such as “low” and “medium”; the corresponding interval 2.3.1. Node types and discretisation node “Toxicity to Daphnia (interval)" has intervals such as [5–100] and BN models are usually constructed with discrete nodes with a low [0.5–5] mg/L. In addition, the interval nodes have two more extreme number of states, such as categories or intervals (Kjærulff and Madsen, states with very low prior probability, to avoid the dominance of 2008). In these cases, the BN is an efficient and compact representation extreme values (explained below). We let interval nodes represent the of a joint probability distribution (Eq. (1)): true, but unknown toxicity of a substance. This true toxicity property was considered to be the cause of the observed toxicity values, therefore PðVÞ¼ PðXjpaðXÞÞ (1) the toxicity observations were modelled by continuous nodes as children x2V (realisations) of the interval nodes. The parameterisation of all nodes, i. e. priors, conditional probabilities and conditional density functions, is where V is the set of discrete nodes X to X and pa(X) are the parents of 1 n described in Supplementary material (Tables S.1 to S.21), following the X. recommendations for good practice in BN modelling (Chen and Pollino, An area of recent interest and progress is the development of 2012). continuous BN models (Qian and Miltner, 2015), where quantitative For the physical and chemical properties (Line 1), we chose only two variables are not discretised into intervals but instead are represented by intervals (Table 2) with cut-off values commonly used in ecotoxicology: equations or statistical distributions, or hybrid BNs (e.g., Aguilera et al., molecular weight with the threshold 600 g/mol (Brooke et al., 1986) 2010), which contain both discrete and continuous nodes (Marcot and and hydrophobicity with the threshold log K 5.5 (OECD, 2012). Penman, 2019). For our model, categorical nodes with few states would OW Because the use of strict cut-off criteria to define bioaccumulation po- be the most convenient for parameterisation of conditional probability tential has been criticized (Arnot et al., 2010), the child node “Mem- tables in cases where expert knowledge was required. On the other hand, brane crossing” was defined by three intervals (low, medium and high) continuous nodes would be preferable to optimise the use of the Table 1 Overview and description of nodes in the BN model. The node types are also reflected in the node names: continuous nodes have names with the suffix " (value)"; discrete interval nodes have the suffix " (interval)"; and categorical nodes have the suffix " (level)". The sources of information for probability distributions are described in Section 2. “Proportions” refers to count of observations in our dataset. For more details, see Supplementary material. Node group Node name Node type No. of Source of probability In-/output in web Additional states distribution interface information Physical and chemical properties of Molecular weight (value) Continuous NA Proportions Input the substance Molecular weight (interval) Interval 2 Proportions Root node Hydrophobicity (value) Continuous NA Proportions Input Hydrophobicity (interval) Interval 2 Proportions Root node Toxicity based on QSAR (value) Continuous NA Statistical rule Input Toxicity based on QSAR (interval) Interval 7 Proportions Root node Toxicity based on QSAR (level) Categorical 5 Deterministic Membrane crossing Categorical 3 Expert judgement Toxicity to fish predicted from Categorical 5 Expert judgement Output See Fig. 3a chemical properties Chemical category of the substance Chemical category Categorical 10 Uniform distribution Input Root node Toxicity to fish predicted from Categorical 6 Proportions Output See Fig. 3b chemical category Toxicity of the substance to other taxa Toxicity to algae (value n) Continuous NA Statistical rule Input See Fig. 3c (algae and Daphnia) Toxicity to algae (interval) Interval 7 Proportions Root node Toxicity to algae (level) Categorical 5 Deterministic Output Toxicity to Daphnia (value n) Continuous NA Statistical rule Input Toxicity to Daphnia (interval) Interval 7 Proportions Root node Toxicity to Daphnia (level) Categorical 5 Deterministic Output Ratio toxicity Daphnia/algae Continuous Proportions Calculated from Root node input Species-specific mode of action Interval 3 Proportions Toxicity to fish pre-dicted from Categorical 5 Expert judgement Output other taxa Toxicity of the substance to fish Toxicity to embryo (value n) Continuous NA Statistical rule Input embryo Toxicity to embryo (interval) Interval 7 Proportions Root node Toxicity to embryo (level) Categorical 5 Deterministic Output Predicted toxicity to juvenile fish Toxicity to fish predicted from all Categorical 5 Combination rule (equal Output See Fig. 3d evidence weights) The web interface calculates the variable “Ratio toxicity Daphnia/algae” from the provided inpute values to “Toxicity to algae (value n)" and “Toxicity to Daphnia (value n)". 4 S.J. Moe et al. Environmental Modelling and Software 126 (2020) 104655 Table 2 their toxicity data as original values (EC or LC ) instead of discretised 50 50 Prior probabilities for interval nodes with two states: molecular weight and states. The function of the continuous nodes is to create a likelihood on hydrophobicity. The probability of each state was set equal to the proportion of the interval nodes using multiple findings entered as exact values. count of values in our dataset. Although the continuous value nodes serve as input nodes for this BN, they are defined as child nodes of toxicity interval nodes (Fig. 1). The Molecular weight (interval) Hydrophobicity (interval) reasoning is that the observed toxicity values for a given substance, e.g. Label Interval Count Probability Interval Count Probability “Toxicity to algae (value 1)", are realisations of an inherent true toxicity (unit: g/mol) (unit: k ) OW value for this substance. This true value is unknown but can be modelled Low 0–600 231 0.9914 -inf - 5.5 213 0.9682 by the probability distribution of the toxicity interval node, “Toxicity to High 600 - inf 2 0.0086 5.5 - inf 7 0.0318 (sum) 233 1 220 1 algae (interval)". The BN has multiple continuous input nodes for each of the algae, Daphnia, and fish embryo endpoints (Fig. 1). The purpose was to let the BN model (1) retain as much details as possible from the input values, to allow for intermediate levels of membrane crossing potential. The (2) account for variability in the provided data (i.e. variation among mode-of-action node (Line 3) also had three intervals based on the input values), and (3) account for inherent uncertainty in the toxicity pre-defined cut-off values of ratio <0.5 or >2 (ECETOC, 2005). values (e.g. a toxicity value closer to an interval boundary would have The predicted toxicity nodes (e.g. “Toxicity to algae (level)") were higher probability of being assigned to the next interval). initially modelled by categorical nodes with 5 states, ranging from very In the current version of the web interface, there are ten continuous low toxicity (>100 mg/L) to very high toxicity (<0.01 mg/L). Note that input nodes for each of these endpoints, assuming that this is a increasing toxicity level corresponds to decreasing concentration of the reasonable maximum number of toxicity values available for a chemical substance (Table 3). The discretisation of continuous toxicity values for substance. In this dataset, the number of observations per substance the discrete nodes (Table 3) was based on the classification and labelling exceeds ten for only 3%, 19% and 7% of the substances for algae, of toxicity levels in the Globally Harmonized System (OECD, 2001), Daphnia and fish embryos, respectively. If needed, the number of which has four toxicity levels with interval boundaries 1, 10, and 100 continuous input nodes can easily be increased without affecting the mg/L. To increase the resolution of the highest toxicity levels, we model prediction. The unused input nodes will be so-called barren selected 5 intervals with the boundaries 0.01, 0.5, 5 and 100 mg/L. variables (Kjærulff and Madsen, 2008), which will be updated by evi- The integration of the four lines of evidence was based on these 5- dence in their sibling nodes but will not themselves influence other state categorical nodes. The toxicity interval nodes (e.g. “Toxicity to nodes. algae (interval)") were added to provide a link to the continuous nodes for input values (e.g. “Toxicity to algae (value 1)"). Since interval nodes 2.3.2. Prior probabilities must have intervals in increasing order, the order of the toxicity in- Prior probability distributions were defined for all root nodes, i.e. all tervals was reversed compared to the order of toxicity states. It was not nodes with no parent nodes in the graph (Table 1). For all root nodes of strictly necessary to keep both the categorical and the interval version of interval type, the prior probability distribution was set equal to the the same toxicity node (e.g. toxicity to algae), but we found that it frequency distribution of our dataset. This approach was used for prior facilitated the interpretation and helped avoid confusion regarding the probabilities of the following interval-type nodes: Molecular weight order of toxicity intervals vs. toxicity levels. An additional benefit of the (Table S.2), Hydrophobicity (Table S.4), Toxicity based on QSAR interval nodes was to enable the extraction of a single expected value (Table S.7), Toxicity to algae (Table S.13), Toxicity to Daphnia (“mean value”) from a toxicity node, which could for example facilitate (Table S.14), Ratio toxicity Daphnia/algae (Table S.15) and Toxicity to the comparison of posterior probability distributions of toxicity nodes embryo (Table S.18). For example, for the node “Molecular weight for different substances. For this purpose, the toxicity interval nodes (interval)", 231 substances had low molecular weight (<600 g/mol) were given two additional extreme states (Table 3) with very low while only 2 substances had high molecular weight (>600 g/mol); the probability. The extreme states served as buffers for obtaining reason- resulting prior probability distribution across these two states was able calculations of mean values to summarise the probability distri- 99.14% and 0.86% (Table 2). bution of a node. In this paper, however, we will focus on the probability For the toxicity interval nodes for QSAR, algae, Daphnia and embryo, distribution of the 5-state categorical toxicity nodes rather than the the probabilities of states were also based on the counts of values. mean values of the corresponding interval nodes. However, because of low numbers of values in the most extreme The continuous input value nodes (Fig. 1) allowed users to provide Table 3 Prior probabilities for toxicity interval nodes (QSAR, algae, Daphnia and embryo), based on counts of values in our dataset. For fish, the toxicity values represent LC (the concentration resulting in a lethal effect to 50% of the tested population). For algae and Daphnia, the toxicity values represent EC (the concentration resulting in a given sublethal effect to 50% of the tested population). Note that the two most extreme intervals of the interval toxicity nodes (e.g. “100–1000 and “1000 - inf”) are merged into one categorical state (“very low”). The probabilities of the two intervals “100–1000 and “1000 - Inf” were set to respectively 99.9% and 0.01% of the 00 00 proportion of counts in toxicity level “very low”. The probabilities of the intervals “0.001–0.01 and “0–0.001 were calculated correspondingly from the of count of values in toxicity level “very high". States of interval States of categorical Toxicity based on QSAR Toxicity to algae (interval) Toxicity to Daphnia Toxicity to embryo toxicity nodes (mg/L) toxicity nodes (levels) (interval) (interval) (interval) Count Probability Count Probability Count Probability Count Probability 0–0.001 very high 1 6.58E-06 6 2.27E-05 155 1.33E-04 4 7.39E-06 0.001–0.01 0.00658 0.0227 0.133 0.00739 0.01–0.5 high 20 0.132 84 0.318 412 0.354 82 0.152 0.5–5 medium 29 0.191 67 0.254 221 0.190 141 0.261 5–100 low 63 0.415 84 0.318 256 0.220 176 0.325 100–1000 very low 39 0.256 23 0.0870 120 0.103 138 0.255 1000 - inf 2.56 E 04 8.71E-05 1.03E-04 2.55E-04 (sum) 152 1 264 1 1164 1 541 1 5 S.J. Moe et al. Environmental Modelling and Software 126 (2020) 104655 intervals, the counts were merged for the two intervals “100–1000 and observations of “low”, 4 observations of “medium” and 2 observations of “1000 - inf”, and the probabilities of these intervals were set to “high”, from altogether 13 chemical substances. The number of obser- respectively 99.9% and 0.01% of the proportion of values in toxicity vations per chemical category was sometimes quite low (e.g. Imidazole, level “very low” (Table 3). The probability of the intervals “0.001–0.01 Fig. 2b). To optimise the use of the available data, multiple toxicity and “0–0.001 , likewise, were set to respectively 99.9% and 0.01% of observations for the same substance were counted independently. For the proportion of values in toxicity level “very high". chemical categories with a low total number of observations One root node was of categorical type: “Chemical category” (Table S.11), the proportions would not properly represent a probability (Table 1). Since this was also an input node to be instantiated by the distribution (Marcot, 2017), therefore the model predictions will be less user, the prior distribution was not of importance, and was set to uni- reliable for these chemical categories. In addition, a chemical category form distribution (Table S.11). “unknown/other” can be selected. When this state is chosen, this line of evidence is excluded from the final predicted toxicity node. 2.3.3. Conditional probability tables and density functions For the continuous nodes, the conditional probability distributions The conditional probability tables (CPTs) of the BN were parame- were quantified by a conditional density function (CDF), defined by a trized by four main approaches, illustrated by the four examples in Gaussian distribution with mean and variance specified for each interval Fig. 2: (1) expert knowledge (Fig. 2a), (2) frequency distributions of the parent node (i.e. the corresponding interval node, see Table 1). derived from our dataset (Fig. 2b), (3) statistical considerations For the physico-chemical nodes of Line 1, mean values were calculated (Fig. 2c), and a rule for combining the lines of evidence (Fig. 2d). to reflect the chemicals in our dataset. Variances were calculated ac- Expert knowledge (A. Lillicrap) was used for CPT of the nodes cording to a pre-defined coefficient of variation (CV; standard deviation “Membrane crossing” (Table S.6), “Toxicity to fish predicted from divided by the mean). We chose not to let the variance be calculated chemical properties” (Table S.10) and “Toxicity to fish predicted from directly from our dataset, as the variance would have been sensitive to other taxa” (Table S.17). The ability of a molecule to crossing a bio- the number of observations in each interval. Instead, we assumed low logical membrane decreases both with its size and its hydrophobicity. CV of physico-chemical properties of substances such as molecular For “Membrane crossing”, therefore, the combination of low hydro- weight (10% CV) and hydrophobicity (5% CV). For example, for the phobicity and low molecular weight was assumed to result in respec- node “Molecular weight (value)", the CV was set to 5% of the mean tively 0%, 25% and 75% probability of low, medium and high ability of value. In the CDF for this node (Table S.3), the two intervals (<600 g/ membrane crossing, while the opposite combination of hydrophobicity mol and >600 g/mol) had mean values of 179 and 200,380, respec- and molecular weight was assigned the opposite probability distribu- tively, calculated from the respective counts of 231 and 2 observations tion. The two combinations of high/low and low/high hydrophobicity (see Table 2). and molecular weight were assigned a probability distribution of 25%, For all continuous nodes representing toxicity values, based on 50% and 25% for the three states of membrane crossing. More details on QSAR, algae, Daphnia or embryo, the density functions were defined in the underlying assumptions are given by Lillicrap et al. (2020). We have the same way. The mean for each interval of the parent node was assumed this very simple relationship as a starting point, which can later calculated as the midpoint of the interval, except for the extreme in- be refined with more indicators of molecular properties. terval “1000- inf”; here the mean was set to 1550, which was equal to the An example is shown for “Toxicity to fish predicted from chemical lower boundary plus the midpoint of the previous interval. For each properties” (Fig. 2a). When a substance’s ability to cross a biological interval, the variance was set so that a 90% of a Gaussian distribution membrane is high, the predicted toxicity to fish based on chemical was within the interval while 5% of the distribution was in either of the properties is equal to the acute fish toxicity modelled by QSAR. When neighbour intervals (see Appendix A, Figure A.1). The resulting vari- the membrane crossing ability is low, we assigned only 80% chance that ances (Fig. 2c, Table S.8) correspond to ca. 30% CV of the upper interval the predicted acute toxicity corresponds to the modelled QSAR result. boundary, for all intervals except the highest (inf). For toxicity data from The reasoning behind the CPT of “Toxicity to fish predicted from standard assays performed in various laboratories, CV up to 30% is a other taxa” is explained for all 50 combinations of the parent states by reasonable assumption (Rawlings et al., 2019). Lillicrap et al. (2020). In brief, if the ratio of the average toxicity values The CPT of the final child node, “Toxicity to fish predicted from all to Daphnia vs. algae is between 0.5 and 2, it can be assumed that the evidence”, was defined by a combination rule to ensure that all four lines chemical has a similar mode of action for the two taxa, and that the of evidence were given equal weight. Following the recommendation of chemical will affect fish in a similar way. Therefore, the CPT converts Marcot (2017) to obtain more tractable CPT dimensionality, we first set the EC values from algae and Daphnia to LC values for fish with high the probabilities for combination of two lines (Fig. 2d). The combination 50 50 precision (a narrow distribution), which corresponds to assigning a high of lines 1 þ 2 and of lines 3 þ 4 each resulted in two intermediate child weight to these pieces of evidence in a WOE approach. Moreover, more nodes, which were subsequently combined with the same rule (Fig. 2d) weight (i.e. narrower probability distributions) has been assigned to the to produce a new “grandchild” node. The two intermediate nodes were evidence from Daphnia than from algae, assuming that the closer then absorbed, which resulted in a CPT combining the four “grandpar- phylogenetic relationship of fish with invertebrates than with plants ents” nodes with the one “grandchild” node, as described in the Sup- makes their responses to a chemical more similar. Conversely, a ratio of plementary material (Table S.21). <0.5 (or >2) indicates that the chemical has a species-specific mode of action, which affects Daphnia more strongly than algae (or vice versa). In 2.4. Model assessment these cases, we have less confidence in extrapolating the toxicity data from Daphnia or algae to fish, and have therefore set wider probability 2.4.1. Sensitivity analysis distributions in this part of the CPT. This wider distribution corresponds The sensitivity of the target node (“Toxicity to fish predicted from all to lower weighting in a WOE approach. evidence”) to the different lines of evidence was analysed by two CPTs for the node “Toxicity to fish predicted from chemical cate- methods: Parameter sensitivity analysis and value-of-information gory”, as well as for all continuous nodes (identified in Table 1), were analysis. created using frequency distributions derived from our dataset. The CPT The parameter sensitivity analysis measures the functional re- for “Toxicity to fish predicted from chemical category” is illustrated in lationships between a parameter (i.e., a probability value in the CPT of a Fig. 2b. For each chemical category, the values represent the proportion node) and the posterior probability of a given state of the target node of juvenile fish LC values in each of the given toxicity levels. For (Chan and Darwiche, 2002). In general, the posterior probability P (h|ε) example, the 50 observations in the chemical category “Aniline” is a ratio of two linear functions (Eq. (3)) in any parameter t of the BN comprised 4 observations of the toxicity level “very low”, 40 where t is an entry in a CPT of the model. 6 S.J. Moe et al. Environmental Modelling and Software 126 (2020) 104655 Fig. 2. Examples of conditional probability tables (CPTs) and density functions (CDFs) for selected nodes, illustrating the different approaches used for parame- terisation of the conditional dependencies. The colour code represents the scale from green (zero) to red (1 or 100%). (a) CPTs for the node “Membrane crossing”: the probability of a substance crossing a biological membrane based on its physical properties (molecular weight and hydrophobicity). Probabilities are based on expert judgement. (b) Extract of the CPT for the node “Toxicity to fish predicted from chemical category”. The probabilities are derived from frequency distributions in our dataset. The supplementary data contains the full CPT for all 42 chemical categories (Table S1.11). (c) CDF for the node “Toxicity to algae (value 1)": mean and variance of observations for each toxicity interval (Table 1). The values are set based on a statistical rule (see Appendix A). (d) CPT for the node “Toxicity to fish predicted from all evidence”: combination rule representing equal weighting of the four lines of evidence. This table shows combination of two of the four lines, while the combination of all four lines (Table S1.21) is described in the Supplementary material. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 7 S.J. Moe et al. Environmental Modelling and Software 126 (2020) 104655 Pðh; εÞðtÞ αtþ β one value for each node defined as Input node (Table 1): Molecular PðhjεÞðtÞ¼ ¼ (3) weight, Hydrophobicity, QSAR, Toxicity to algae, Toxicity to PðεÞðtÞ γtþ δ Daphnia and Toxicity to embryo, as well as Toxicity to juvenile. For where ε denotes the evidence and h denotes a specific state of the target this subset, the validation would be less influenced by the prior node, here referred to as the hypothesis. probabilities (Tables 2 and 3), since evidence would be available to The sensitivity analysis was run relative to all states (toxicity levels) update the probabilities of all input nodes. of the target node, under the default scenario of no evidence, i.e. no data � Subset 4: cases with a minimum of 3 observations for both embryo were used to run the model. Due to the structure of the evidence in this and juvenile toxicity data (number of substances: 20). The reasoning scenario, i.e. no downstream evidence relative to the target variable, the was that these two nodes are the most crucial for the purpose of the functional relationship shown in Eq. (3) is linear (Coup� e and van der model. A higher number of observations would make the model Gaag, 2002). predictions more precise and reduce bias due to variability in these Value-of-information (VoI) analysis can quantify the potential types of data. benefit of additional information in the face of uncertainty (Keisler et al., 2014), and can aid the decision on allocation of resources between For the purpose of comparing predicted and observed probability obtaining new information and improving management actions distributions, it is common to define the state with the highest proba- (Mantyniemi € et al., 2009). The method quantifies the VoI as reduction of bility as the “correct” state (Marcot, 2012). We followed this practice entropy (a measure of uncertainty) for a given node in isolation, aver- and defined the toxicity interval with the highest probability as the aging the values of other nodes. The VoI analysis was run under different “correct” predicted or observed state. This way, we could calculate the scenarios of evidence, i.e. different information applied to the model: number of correct predictions for each toxicity interval and for each data the default scenario of no evidence, as well as data for three example subset. This practice does not, however, account for the whole proba- substances, using all available data either for the first three lines of bility distribution. More advanced methods for model validation evidence (excluding embryo data) or for all four lines of evidence. The consider the probability distributions of predicted and observed vari- purpose was to assess the potential benefit of including embryo data as a ables will be investigated in further work with this model. line of evidence. 3. Web interface to the BN model 2.4.2. Model evaluation The BN model performance and uncertainty was evaluated by A web-based user interface to the BN model for demonstration pur- several of the metrics recommended (Marcot, 2012). Model perfor- poses has been published on HUGIN’s web portal for BN examples, http mance was assessed by running with input data from our dataset and ://demo.hugin.com/example/FET. Our model is the first example of a comparing the outcome, i.e. the predicted acute toxicity of selected BN within the field of ecotoxicology and ecological risk assessment on chemical substances to juvenile fish, to the observed toxicity of the same this platform. The web interface to this preliminary BN version will give substances to this endpoint. The model validation should ideally be researchers and other potential users the opportunity to provide feed- performed with an independent dataset that had not already been used back for improving the model. In the longer term, our intention is to for parametrization of the model. However, additional fish embryo further develop this model into a more comprehensive online tool which toxicity data are not widely available, and our dataset represents the can be useful for regulatory authorities and chemical industries wanting largest collection of OECD 236 FET data in the public domain to our to submit fish embryo toxicity data in place of acute fish toxicity data. knowledge. Instead, we applied four different criteria for selecting Here we briefly describe the two interactive pages of the web subsets of our dataset for validation in order to consider the robustness interface: “Enter values” (Supplementary information, Figure S.1) and of the model from different perspectives. “Results” (Figure S.2). In the tab “Enter values”, a user can insert the requested information for any chemical substance for which they want � Subset 1: all chemical substances containing at least one observation to predict the acute toxicity to juvenile fish. The user should provide the of juvenile fish toxicity (AFT) data (number of substances: 159), requested information as follows, for the four lines of evidence: which was the minimum requirement for comparison with the model prediction. For substances missing one or more input values (e.g. � Line 1: Hydrophobicity (log K ), Molecular weight (g/mol), OW toxicity to algae), the prediction would be based on the prior prob- Toxicity based on QSAR (mg/L). The user must enter one continuous abilities of this node. The exception was Line 2 (toxicity of the value for each node. chemical category), which allowed for the state “unknown". � Line 2: Chemical category. The user must select the category from a � Subset 2: only the chemical categories that were represented with drop-down list, which includes the state “Unknown/other”. More minimum 10 different chemical substances in our dataset (number of chemical categories can be added upon request from users. substances: 106). Using Phenol as an example, the conditional � Line 3: Toxicity of the substance to other taxa - algae (OECD 201) and probabilities of a chemical category in the node “Toxicity to fish Daphnia (OECD 202). The user should first select the number of predicted from chemical category” (Fig. 2b), was calculated as the values (up to ten) for each taxon, then enter the EC values (mg/L). frequency distribution of observed toxicity to juvenile fish for all � Line 4: Toxicity of the substance to fish embryos (OECD 236). The substances in the category Phenol. When the predicted toxicity of a user should first select the number of values (up to ten), then enter substance belonging to the category Phenol was assessed (e.g. Tri- the LC values (mg/L). closan), the observed toxicity values of Triclosan used for compari- son have also been used in the CPT. For chemical categories The tab “Enter values” contains the buttons “Compute”, which will containing few substances in our dataset, there will be a high overlap carry out the calculation based on these input values, and “Load Case”, between the data used for parametrization and for validation. For which will load a built-in example: the substance carbamazepine. chemical categories with 10 or more substances, however, the data The tab “Results” displays the posterior probability distributions used for validation for one of these substances will constitute only a across the five toxicity levels for all four lines of evidence (“Toxicity to small proportion of the frequency distribution of the CPT. Therefore, fish predicted from chemical properties”, “Toxicity to fish predicted a validation based on such subsets will be more independent of the from chemical category”, “Toxicity to fish predicted from other taxa”, parametrization data. and Toxicity to embryo (level)"), as well as for the final child node � Subset 3: all substances with complete cases for input nodes (number (“Toxicity to fish predicted from all evidence”) (See Supplementary in- of substances: 77). This means that our dataset contained minimum formation). Two buttons generate tables as pop-up windows. The button 8 S.J. Moe et al. Environmental Modelling and Software 126 (2020) 104655 Table 4 Example of tables of (a) input values and (b) output values generated by the web interface, for the substance carbamazepine (see Fig. 3a). (a) The input table includes values that are derived directly from the input values (without calculation of probabilities): mean toxicity values for algae, Daphnia and embryo, and the most sensitive endpoint of those three. (b) The output table contains the predicted toxicity for the four lines of evidence, as well the combined predicted toxicity for juvenile fish (as probability distributions across the five toxicity levels). (a) Substance Node Value Unit carbamazepine Molecular weight (value) 236.28 g/mol carbamazepine Hydrophobicity (value) 2.45 log k ow carbamazepine Toxicity based on QSAR (value) 41.33 mg/L carbamazepine Chemical category Substituted urea carbamazepine Toxicity to algae: value 1 167.33 mg/L carbamazepine Toxicity to algae: value 2 49.4 mg/L carbamazepine Toxicity to Daphnia: value 1 97.815 mg/L carbamazepine Toxicity to Daphnia: value 2 111 mg/L carbamazepine Toxicity to embryo: value 1 148 mg/L carbamazepine Toxicity to embryo: value 2 158 mg/L carbamazepine Toxicity to embryo: value 3 150 mg/L carbamazepine Toxicity to embryo: value 4 156 mg/L carbamazepine Toxicity to embryo: value 5 157 mg/L carbamazepine Toxicity to embryo: value 6 153 mg/L carbamazepine Toxicity to embryo: value 7 136 mg/L carbamazepine Toxicity to embryo: value 8 150 mg/L carbamazepine Toxicity to embryo: value 9 153 mg/L carbamazepine Toxicity to embryo: value 10 172 mg/L carbamazepine Toxicity to algae: mean 108.4 mg/L carbamazepine Toxicity to Daphnia: mean 104.4 mg/L carbamazepine Daphnia/algae 0.96 carbamazepine Toxicity to embryo: mean 153.5 mg/L carbamazepine Most sensitive endpoint Daphnia (b) Substance Node Toxicity level Probability carbamazepine Toxicity to fish predicted from chemical properties very low 0.02 carbamazepine Toxicity to fish predicted from chemical properties low 0.96 carbamazepine Toxicity to fish predicted from chemical properties medium 0.01 carbamazepine Toxicity to fish predicted from chemical properties high 0 carbamazepine Toxicity to fish predicted from chemical properties very high 0 carbamazepine Toxicity to fish predicted from chemical category very low 0 carbamazepine Toxicity to fish predicted from chemical category low 0.45 carbamazepine Toxicity to fish predicted from chemical category medium 0.05 carbamazepine Toxicity to fish predicted from chemical category high 0.5 carbamazepine Toxicity to fish predicted from chemical category very high 0 carbamazepine Toxicity to fish predicted from chemical category unknown 0 carbamazepine Toxicity to fish predicted from other taxa very low 0.39 carbamazepine Toxicity to fish predicted from other taxa low 0.5 carbamazepine Toxicity to fish predicted from other taxa medium 0.11 carbamazepine Toxicity to fish predicted from other taxa high 0 carbamazepine Toxicity to fish predicted from other taxa very high 0 carbamazepine Toxicity to embryo (level) very low 1 carbamazepine Toxicity to embryo (level) low 0 carbamazepine Toxicity to embryo (level) medium 0 carbamazepine Toxicity to embryo (level) high 0 carbamazepine Toxicity to embryo (level) very high 0 carbamazepine Toxicity to fish predicted from all evidence very low 0.29 carbamazepine Toxicity to fish predicted from all evidence low 0.52 carbamazepine Toxicity to fish predicted from all evidence medium 0.14 carbamazepine Toxicity to fish predicted from all evidence high 0.05 carbamazepine Toxicity to fish predicted from all evidence very high 0 “View input values” provides a table of the entered values, as well as the 4. Results and discussion calculated ratio of toxicity to Daphnia vs. algae (Table 4a). This table also identifies the most sensitive endpoint (algae, Daphnia or fish em- 4.1. Examples of BN model predictions bryo), which is relevant for the application of these results for regulatory risk assessment (Lillicrap et al., 2020). The button “View output values” Examples of model predictions for three selected substances are provides a table with the posterior probability distributions for the five presented in Fig. 3. All examples are from subset 4 (see section 2.4.2), selected nodes mentioned above (Table 4b). The “Results” tab also which has minimum three toxicity data for both embryo and juvenile provides conclusive statements based on the calculated values, such as fish. The three examples represent three different levels of observed “The toxicity level of carbamazepine to juvenile fish is most likely low toxicity to juvenile fish: low, medium and high, respectively. (52.28% probability)". The first example (Fig. 3a) is Carbamazepine, an antiepileptic drug in the chemical category Substituted urea. This substance is also used as a built-in example in the online demonstration model (Figures S1-S2). The observed toxicity to juvenile fish, to which the predicted toxicity will be 9 S.J. Moe et al. Environmental Modelling and Software 126 (2020) 104655 compared, is 100% in the low toxicity interval (four observations; not evidence again resulted in a more accurate prediction, although with shown). The node “Toxicity to embryo (level)" was almost 100% “very lower precision than the original AFT data. low”, while the toxicity based on QSAR, algae and Daphnia was “low” to The third example (Fig. 3c), Triclosan, is an antimicrobial agent in “very low”. The information from the chemical category, however, the chemical category Phenol. This substance had six LC values for indicated a 50% probability of high toxicity to juvenile fish. This line of juvenile fish in the high toxicity interval. The data based on embryo, evidence contributed to higher predicted toxicity to juvenile fish (26% Daphnia and QSAR showed the same toxicity level, while toxicity to probability of medium or higher toxicity) than the other three lines. algae was very high. Toxicity based on the chemical category, on the After combination of the four lines, the most likely state was low toxicity other hand, was almost 50% likely to be medium or lower. When the to juvenile fish (52% probability), which was consistent with the four lines of evidence were combined, the most probable toxicity level measured toxicity interval, although with higher uncertainty. In this was high (60%), which was again consistent with the observations. case, information on toxicity to embryo (very low) alone would have underestimated the risk to juvenile fish (low), while the embryo data in 4.2. Sensitivity analysis combination with the other three lines of evidence resulted in a more accurate prediction on toxicity to juvenile fish. The parameter sensitivity analysis (Table 5) showed that under the The second example (Fig. 3b) was Tetradecyl sulfate, a drug in the default evidence scenario of no evidence, the state “very high” of the chemical category Anionic surfactant. Our dataset contained three LC target node (“Toxicity to fish predicted from all evidence”) as expected values from AFT assays (toxicity to juvenile fish), all of which fell into was the most sensitive to changes in single parameters in the probability the medium toxicity interval. The node “Toxicity to embryo (level)" tables of the parent nodes. The target node was most sensitive to pa- predicted a 100% probability the high toxicity interval, while the pre- rameters of the nodes “Toxicity to embryo (interval)" and “Toxicity dictions from the other lines of evidence were centred around low-to- based on QSAR (interval)". The maximum sensitivity value averaged medium toxicity interval. The resulting predicted toxicity to juvenile across all states of the target node was 0.16 for both parent nodes. This fish had highest probability (41%) of the medium state, which was means that an increase of þ0.1 in the parameters of “Toxicity to embryo consistent with the measured toxicity. In this case, information on (interval)" will result in an increase in þ0.016 in the posterior proba- toxicity to embryo alone would have overestimated the risk to juvenile bility of “Toxicity to fish predicted from all evidence” (see Eq. (3)). The fish, while the embryo data in combination with the other lines of highest sensitivity was found for the state “high toxicity” of the target Fig. 3. Examples of BN model predictions for three selected substances: (a) Carbamazepine, (b) Tetradecyl sulfate, (c) Triclosan. Monitor windows with posterior probability distributions are shown for selected nodes in each line of evidence (please see Fig. 1 for complete node lables and arrows). The full set of input values and selected output values for example (a) are given in Table 4. 10 S.J. Moe et al. Environmental Modelling and Software 126 (2020) 104655 Fig. 3. (continued). node, with slopes 0.21 (QSAR) and 0.19 (embryo). These nodes are root data, such as “Toxicity based on QSAR” and “Toxicity to embryo”. nodes (Table 1), with probability tables containing prior probabilities Conversely, the analysis indicated weaker influence of lines of evidence (Tables S.6 and S.18). The analysis shows that the prior probabilities of that rely strongly on expert knowledge, such as “Membrane crossing” these nodes may have a strong influence on the prediction, which im- and “Toxicity predicted from other taxa”. Although these lines of evi- plies that the approach used for setting priors (Appendix A) may need to dence are also based on data, e.g. measured toxicity to algae and be refined. Daphnia, expert knowledge is applied in weighting and combining these The third most influential parameters were for “Chemical category”, pieces of evidence. Hence, there is a potential for making the model to which the sensitivity of the target node was 0.08 on average and 0.12 more sensitive by refining the CPTs that are currently based on expert for the state “high toxicity”. The prior probability table of this root node knowledge (e.g. Fig. 2a). The sensitivity analysis also shows that the has a uniform distribution, assuming that for a new chemical substance, posterior distribution of the target node is robust to changes in any all chemical categories are equally likely. But considering the high in- single parameter of the BN as all sensitivity values are less than one. fluence of this probability table on the target node, future research may The value-of-information (VOI) analysis (Table 6) showed that under explore a more informative prior probability distribution, e.g. which the default scenario of no evidence, all four lines of evidence contribute better reflects the frequency of the different chemical categories in our almost equally and relatively little to entropy reduction: no more than dataset or other larger datasets. 7% (0.09/1.36) of the entropy of the target node. Line of evidence 3 The fourth and fifth most influential parameters were for “Toxicity to (other taxa) contribute slightly more than the other lines. This can Daphnia (interval)" and. reflect the fact that the conditional probabilities of “Toxicity predicted “Toxicity to algae (interval)". The influence of these nodes on the from other taxa” (Table S.17) can be either highly correlated with the target node were weakened by the additional node “species-specific target node or be non-informative (flat distribution), depending on the mode of action”, which is meant to introduce uncertainty related to the input values (node “Ratio toxicity Daphnia/algae”) (Lillicrap et al., extrapolation of results from plants and invertebrates to fish. The target 2020). node is slightly more sensitive to changes in parameters for Daphnia than For scenarios where information is provided only for the lines of for algae. This is consistent with the closer phylogenetic relationship of evidence 1–3 (i.e. excluding information on toxicity to embryos), addi- fish with invertebrates than with plants, which we tried to account for in tional information on embryo toxicity can reduce the uncertainty of the the CPT (Table S.17) (Lillicrap et al., 2020). target node by 5–7% (Table 6). The relative importance of information In general, this sensitivity analysis reflects the strongest influence of on embryo toxicity varies among the three example substances, which parameters in the parts of the model that are most directly based on suggests that the importance of this type of information cannot be 11 S.J. Moe et al. Environmental Modelling and Software 126 (2020) 104655 Fig. 3. (continued). Table 5 Parameter sensitivity analysis for the default scenario of no evidence. The target node is “Toxicity to fish predicted from all evidence”. The sensitivity values represent the slope of the linear relationship between a change in one parameter of the CPT for a given node and the resulting change in the probability of each state of the target node. The maximum and minimum values are extracted across all states of the parent nodes. For example, consider the parent node “Toxicity to embryo (interval)". If the probability of each state separately is changed by þ0.1, then the resulting change in the posterior probability of predicted toxicity being “very low” ranges from 0.017 to 0.0072. In the column “all states”, max and min values are averaged across the five states of the parent node. The rows are ordered by decreasing sensitivity in the columns “all states”, where sensitivity values are averaged across the five states of the target node. Target node all states very low low medium high very high Parent node max min max min max min max min max min max min Toxicity to embryo (interval) 0.162 0.085 0.170 0.072 0.150 0.156 0.162 0.114 0.194 0.075 0.134 0.008 Toxicity based on QSAR (interval) 0.160 0.083 0.159 0.069 0.140 0.172 0.163 0.099 0.207 0.070 0.130 0.005 Chemical category 0.082 0.058 0.081 0.047 0.119 0.099 0.070 0.070 0.118 0.070 0.021 0.006 Toxicity to Daphnia (interval) 0.039 0.037 0.044 0.028 0.063 0.048 0.025 0.040 0.043 0.057 0.018 0.012 Toxicity to algae (interval) 0.023 0.019 0.025 0.016 0.026 0.029 0.020 0.022 0.027 0.023 0.017 0.005 Tox. pred. from chemical category 0.018 0.016 0.020 0.020 0.022 0.021 0.021 0.021 0.017 0.016 0.010 0.001 Tox. pred. from chemical properties 0.012 0.009 0.017 0.010 0.014 0.019 0.017 0.007 0.009 0.006 0.004 0.002 Tox. pred. from other taxa 0.010 0.007 0.013 0.005 0.012 0.009 0.010 0.008 0.009 0.010 0.006 0.003 Tox. pred. from all evidence 0.009 0.006 0.008 0.006 0.010 0.008 0.010 0.008 0.010 0.006 0.006 0.001 Ratio toxicity Daphnia/algae 0.003 0.003 0.001 0.001 0.005 0.006 0.002 0.002 0.005 0.005 0.001 0.001 Membrane crossing 0.001 0.001 0.001 0.001 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 Hydrophobicity (interval) 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 Molecular weight (interval) 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 generalised across substances. Under the scenario of full information parameter sensitivity analysis (Table 5). (Lines 1–4), further information on embryo toxicity will not contribute to reduction in entropy. This result suggests that the information on 4.3. Model performance embryo toxicity used in each example has already exerted a strong in- fluence on the prediction, which is consistent with the outcome of the The performance of the BN for the four different subsets of our 12 S.J. Moe et al. Environmental Modelling and Software 126 (2020) 104655 Table 6 Value-of-information analysis run for five evidence scenarios: no evidence (default) and three example substances with or without data on toxicity to embryo (Line of evidence 4). The row “Entropy of target node” contains the entropy (uncertainty) of the node “Toxicity to fish predicted from all evidence” under the given evidence scenario. The four subsequent rows contain the maximal entropy reduction that can obtained by additional information in each of the four parent nodes, considered separately while averaging the values of the other nodes. No evi-dence Carbamazepine Tetradecyl sulfate Triclosan Lines Lines Lines Lines Lines Lines 1–3 1–4 1–3 1–4 1–3 1–4 Entropy of target node 1.36 1.13 0.93 1.29 1.30 1.31 1.08 1) Chemical properties 0.05 0.01 0.01 0.06 0.07 0.02 0.03 2) Chemical category 0.05 0.07 0.10 0.03 0.02 0.04 0.07 3) Other taxa 0.09 0.05 0.09 0.09 0.10 0.09 0.14 4) Embryo 0.06 0.08 0 0.06 0 0.06 0 dataset is reported in Table 7 and summarised in Fig. 4. For each sub- substances (minimum 3 observations of both juvenile and embryo), had stance, the predicted juvenile toxicity state with the highest probability the highest correct prediction rate (80%). Although this increase in was compared with the most frequently observed juvenile toxicity state. prediction rate may simply be a random change due to the lower sample The first three subsets, which have a number of substances ranging from size (n ¼ 20), this improvement could also indicate that the higher 77 to 159, showed very similar results: The percentage of correctly number of observations leads to more accurate predictions and therefore predicted toxicity level was 69–71%, while the percentage of over- better model performance. The better performance of this final subset estimated toxicity was 14–18% and the percentage of underestimated therefore lends support to our decision of designing the BN with multiple toxicity was 12–16%. The model typically overestimated toxicity when continuous input nodes, which allows for the use of more observations. the observed toxicity was very low or low. Conversely, the few observed In practice, the risk assessment for a chemical substance is deter- cases of high toxicity were sometimes underestimated as medium. The mined by the most sensitive endpoint - algae, Daphnia or fish. For selected subsets of dataset were dominated by substances with very low example, for the selected substances in Subset 4 (Table 7d), the four to medium toxicity, which can explain the slightly higher proportion of substances with underestimated toxicity to juvenile fish were all more cases with overestimated toxicity. If the model is applied to a new toxic to algae or Daphnia than to fish embryos. In such cases, the pre- substance with high toxicity, the model is more likely to underestimate dicted toxicity to juvenile fish is less relevant, since the risk assessment its toxicity as medium than to overestimate it as very high. will be driven by another endpoint. For this reason, in the web interface The fourth subset, which had the strictest criteria for selection of to the model, information on the most sensitive endpoint is extracted from the input data and provided in the input table (Table 4a) and in the conclusive statements (Figure S.2). These implications are further dis- Table 7 cussed by Lillicrap et al. (2020). Summary of BN model predictions for different subsets of our dataset. (a) Subset 1: All chemical substances with juvenile toxicity data available (minimum one 4.4. Further development of the BN model value); no. of substances (n) ¼ 159. (b) Subset 2: All substances from chemical categories with data from minimum 10 different substances; n ¼ 106. (c) Subset Although this preliminary version of the BN model shows a high rate 3: All complete cases, i.e. substances with minimum one value for each input of correct predictions (up to 80%; Fig. 4), the model performance can be node (see Table 1); n ¼ 77. (d) Subset 4: Selected cases, i.e. substances with further improved. Moreover, the model showed relatively low value of minimum three values for both embryo and juvenile toxicity data; n ¼ 20. information for reducing uncertainty of model predictions, as indicated Predicted in Table 6, which suggests that the model needs refinement for making Observed very low low medium high very high sum better use of provided input data (cf. Table 4a). To increase the model sensitivity to the lines with weakest influence and to improve the ac- (a) very low 26 16 0 0 0 42 curacy of model predictions, the following issues should be addressed. low 2 42 10 0 0 54 For most nodes in Lines 1–3 (Fig. 1), which do not depend on fish medium 2 8 25 3 0 38 embryo toxicity data, the prior probability tables and conditional high 0 2 4 15 0 21 probability tables could be parametrized based on independent datasets. very high 0 0 1 2 1 4 This way, our dataset could be reserved for model validation. A candi- (b) date dataset for model parametrization is the aquatic toxicology data- very low 23 12 0 0 0 35 base EnviroTox (Connors et al., 2019). However, the EnviroTox Low 1 35 5 0 0 41 database has not yet received the same level of curation as our dataset medium 1 6 13 1 0 21 and may introduce additional noise into our model. For components of high 0 2 2 4 0 8 very high 0 0 1 0 0 1 the model where data are not available, the CPTs based on expert knowledge by the authors can be strengthened by a more formal (c) approach for external expert elicitation (e.g. (Castelletti and very low 10 6 0 0 0 16 Soncini-Sessa, 2007; Marcot, 2017)). Low 1 28 4 0 0 33 The toxicity intervals are relatively wide, some spanning more than medium 1 7 10 1 0 19 high 0 0 2 6 0 8 an order of magnitude (Table 3). Toxicity nodes with higher resolution very high 0 0 0 1 0 1 (more toxicity intervals) may be perceived as more informative. How- (d) ever, a model with more than 5 toxicity levels would require different approaches to parametrization of the CPTs, whether these are based on very low 3 0 0 0 0 3 expert knowledge (e.g. Fig. 2a) or on frequency distributions (e.g. Low 0 7 0 0 0 7 medium 0 3 4 0 0 7 Fig. 2b). For future versions of this BN we will explore more automated high 0 0 1 2 0 3 approaches to parametrization of CTPs, to obtain smoother probability very high 0 0 0 0 0 0 distributions and to avoid the extreme 0% and 100% probabilities. 13 S.J. Moe et al. Environmental Modelling and Software 126 (2020) 104655 Fig. 4. Summary of the BN model’s performance: the ability to predict the correct interval of toxicity to juvenile fish for the four subsets of chemical substances (see Table 7). “Correctly predicted” means that the predicted toxicity interval (i.e. the interval with the highest posterior probability) for a given substance is identical to the observed toxicity interval (i.e. the interval with the highest frequency of observations for juvenile fish) for that substance. “Underestimated” means that predicted toxicity interval is lower than the observed interval. The height of each bar corresponds to the number of substances (n) in the subset. For more details, see Table 7. The width of the toxicity intervals is decreasing exponentially: e.g. 5. Conclusions the state “low” has width 95 mg/L, “medium” has width 4.5 mg/L, and “high” has width 0.49 mg/L. While this non-linear scale reflects the We have developed a Bayesian network model for predicting the intervals and threshold values typically used in regulatory ecotoxicol- acute toxicity of chemical substances to juvenile fish, based on infor- ogy, it introduces a bias in the probability calculations (explained in mation on fish embryo toxicity in combination with physical and Appendix A, Figure A.2). Lower toxicity levels (corresponding to higher chemical properties, chemical category and toxicity of the substance to concentrations) with wider toxicity intervals will inherently have lower other taxa. This model can support a Weight-of-Evidence approach for probability than higher toxicity levels. The BN model may therefore replacing the OECD 203 acute fish toxicity assay (based on juvenile fish) show a tendency of overestimating toxicity (Fig. 4). From regulatory with animal alternative approaches, such as the OECD 236 fish embryo point of view, such a bias may not be a problem since the biased pre- toxicity assay. As a measure of model performance, the BN predicted the dictions will be more protective for the environment. However, while correct toxicity interval for 69%–80% of substances in our dataset, given risk assessment calculations often have built-in safety factors to obtain different quality criteria. For the subset of 20 substances with the highest more protective assessments, we aim for accuracy of the model pre- quality criteria, the prediction rate was 80% correct. The model pre- dictions for this BN model. A possible solution for reducing the bias is to dictions were most sensitive to the model components that were quan- model the toxicity values on logarithmic scale, so that the toxicity in- tified by toxicity data, such as fish embryo and QSAR. Conversely, the tervals will get more equal widths. model was least sensitive to the components that were quantified by The four lines of evidence has so far been integrated by equal expert knowledge, e.g. involving the chemical’s mode of action inferred weighting as a starting point. The CPT for combining the four lines from testing of other taxa. The model is publicly available through a web (Table S.21) could instead be trained by data to optimise the weighting interface for testing and feedback. Future development this model of the four lines. However, training the model by advanced methods should include more lines of evidence, refinement of the discretisation of such as machine-learning algorithms (Marcot and Penman, 2019) will toxicity intervals, training of the model with a larger toxicity dataset to require a higher number of substances with complete set of input data, weight the lines of evidence differently. A more mature version of this including fish embryo toxicity data, than what is currently available. model can be a useful WOE tool for predicting fish acute toxicity from In principle, this hybrid BN could be further developed into a fish embryo toxicity data. The model will also be a contribution to the continuous-variable BN. An example of a continuous-variable BN trend of developing more quantitative weight-of-evidence approaches, modelling framework, developed for setting nitrogen criteria in streams which are needed both in the context of animal alternatives in ecotox- and rivers, is presented by (Qian and Miltner, 2015). Their model icology and in environmental assessment more generally. retained the BN’s graphical representation of hypothesized causal con- nections among variables, while employing statistical modelling ap- Declaration of competing interest proaches for establishing functional relationships among these variables. A continuous BN model can avoid the problems related to The authors declare that they have no known competing financial discretisation of continuous toxicity value into intervals (Nojavan A interests or personal relationships that could have appeared to influence et al., 2017), and provide more precise predictions. However, con- the work reported in this paper. structing a continuous-variable BN poses other challenges. In our case, converting the BN into a continuous model would require more Acknowledgements advanced approaches to model parameterisation, especially for CPTs that are currently based on expert knowledge. Funding: This work was supported by NIVA’s research programme DigiSIS: New digital methods for monitoring and research. We thank the Norwegian Environment Agency and members of the Animal Alterna- tives in Environmental Science Interest Group of SETAC (Society of 14 S.J. Moe et al. Environmental Modelling and Software 126 (2020) 104655 Environmental Toxicology and Chemistry) for feedback on earlier ver- A.L.M. and R.W.; Funding acquisition, S.J.M. and A.D.L.; Project sions of the model and web interface, and three anonymous reviewers administration, S.J.M.; Web interface, A.L.M; Visualization, S.J.M.; for their helpful comments. Author contributions: Conceptualization, A. Writing – original draft, S.J.M. and A.L.M.; Writing – review & editing; S. D.L., S.E.B. and S.J.M; Data curation, K.A.C, J.M.R and S.E.B.; Data J.M, R.W., A.L.M., A.D.L, K.A.C., J.M.R., W.G.L. analysis, S.J.M.; A.L.M. and R.W., Methodology, S.J.M., A.D.L., W.G.L., Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.envsoft.2020.104655. Appendix A. Conditional probability distributions for continuous toxicity value nodes The continuous toxicity values nodes for QSAR, algae, Daphnia and embryo are input nodes for the BN model, but also child nodes of the respective interval-type nodes. Therefore, their conditional probability distributions must be specified by mean and variance for the seven toxicity intervals, as described in Section 2.4.3 Conditional Probability Tables. Figure A1 illustrates the probability distributions for each of the states ranging from very high toxicity (a) to very low toxicity (e), defined as Gaussian probability density functions. For each interval, the variance of the probability density function was set so that 90% of the distribution was within the interval while 5% of the distribution was in either of the neighbour intervals. For example, for the interval “medium toxicity” (Figure A1c), 90% of the area below the curve is contained within the interval 0.5–5 mg/L, 5% of the area is in the range <0.5 mg/L (“high toxicity” or higher), and 5% of the area is in the range >5 mg/L (“low toxicity” or lower). This can be interpreted as follows. Let us assume that the true but unknown toxicity of a substance to algae is in the interval “medium toxicity”. Then there is a 5% probability that a toxicity test of this substance will wrongly result in “low toxicity” to algae, and 5% probability that the test will wrongly result in “high toxicity". For all intervals displayed in Figure A1., the resulting variances (Fig. 2c, Table S1.13) correspond to ca. 30% CV of the upper interval boundary (i. e., the lowest toxicity of the interval). Figure A.1. Probability density function used for setting conditional probabilities of the continuous interval nodes, for the five toxicity intervals ranging from very high (a) to very low (e). Coloured curves are the probability density function generated by gaussian distribution with mean and variance as specified in Fig. 2c. Vertical lines indicate the toxicity interval boundaries, and the grey areas represent the probability of values occuring in this interval. When the BN model is run, the CPT of the continuous toxicity nodes (e.g., “Toxicity to algae (value 1)"are used together with evidence (inserted continuous toxicity values) to update the probabilities of the interval nodes (e.g., “Toxicity to algae (interval)" by backward calculation. Since the conditional probability distributions of the higher toxicity states have more narrow intervals than the lower toxicity states, the higher toxicity states will generally have higher probability density (Figure A1). As a consequence, if one enters a continuous toxicity value that is close to the lower boundary (i.e. close to the higher toxicity interval), then the posterior distribution of the interval toxicity node is more likely to be in the higher toxicity interval. For example (Figure A2a), consider an observed toxicity value of 6 mg/L, which belongs to the interval “low toxicity” (5–100 mg/L). However, for this interval, the conditional probability density of 6 mg/L is only 0.0038, while for the neighbour interval “medium toxicity”, the conditional probability density is five times as high (0.019). Therefore, this observation will result in a relatively high posterior probability of the “medium toxicity” interval. In contrast, consider an observed value is 4 mg/L, which belongs to the interval “medium toxicity”, but is close “low toxicity”. The probability density of this value of the correct interval “medium toxicity” is 0.19 (Figure A2b), which is 56 times as high as the 15 S.J. Moe et al. Environmental Modelling and Software 126 (2020) 104655 probability density of the neighbour interval “low toxicity” (0.0034). Hence, this observation result in virtually zero probability of “low probability”. In summary, the lower toxicity levels (corresponding to higher concentrations) with wider toxicity intervals will inherently have lower probability than the higher toxicity levels. Figure A.2. Probability density functions of conditional probabilities for two neighbour toxicity intervals: medium toxicity (0.5–5 mg/L) and low toxicity (5–100 mg/L). The shaded yellow area represents the probability that a toxicity test of a substance with (true) medium toxicity results in an observation of low toxicity. Conversely, the shaded green area represents the probability that a toxicity test of a substance with (true) low toxicity results in an observation of medium toxicity. Note the logarithmic scale of the y-axis. embryo toxicity test for acute aquatic toxicity testing. Regul. Toxicol. 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