Methods for estimating no-effect toxicity concentrations in ecotoxicology.

A range of new statistical approaches is being developed and/or adopted in ecotoxicology that, when combined, can greatly improve the estimation of no-effect toxicity values from concentration-response (CR) experimental data. In particular, we compare the existing no-effect-concentration (NEC) threshold-based toxicity metric with an alternative no-significant-effect-concentration (NSEC) metric suitable for when CR data do not show evidence of a threshold effect. Using a model-averaging approach, these metrics can be combined to yield estimates of N(S)EC and of their uncertainty within a single analysis framework. The outcome is a framework for CR analysis that is robust to uncertainty in the model formulation, and for which resulting estimates can be confidently integrated into risk assessment frameworks, such as the species sensitivity distribution (SSD). Integr Environ Assess Manag 2024;20:279-293. © 2023 Commonwealth of Australia and The Authors. Integrated Environmental Assessment and Management published by Wiley Periodicals LLC on behalf of Society of Environmental Toxicology & Chemistry (SETAC).

Introducing the No-Significant-Effect Concentration.

The no-effect concentration (NEC) is the preferred threshold metric for single-species toxicity tests applied to derive safe concentration thresholds for contaminants in the environment for use in species sensitivity distributions. However, the NEC is only suitable when concentration-response (C-R) data exhibit a threshold response. We describe an alternative toxicity estimate, the no-significant-effect concentration (NSEC), which is better suited to C-R data for which the response is a monotonically decreasing function of concentration and no threshold effects are evident. We use a flexible, three-parameter sigmoidal function to describe the C-R relationship and detail both Bayesian and frequentist approaches to estimation and inference for the NSEC. While the NSEC is conceptually linked to the traditional no-observed-effect concentration (NOEC), it is a substantial improvement over the NOEC because it decouples the estimate from being directly dependent on the placement of treatment concentrations as well as admitting statements of precision of the resulting toxicity estimate. Environ Toxicol Chem 2023;42:2019-2028. © 2023 Commonwealth of Australia and The Authors. Environmental Toxicology and Chemistry published by Wiley Periodicals LLC on behalf of SETAC.

Comment on ET&C perspectives, November 2015-A holistic view.

In response to a recent collection of perspectives published in Environmental Toxicology and Chemistry, the authors argue that there is little value in revisiting and rehashing the well-documented issues around toxicity metrics, competing statistical paradigms, legitimacy of theoretical constructs for species sensitivity distributions, and a number of other unresolved (and perhaps unresolvable) attendant statistical issues that have occupied journal space for more than 30 yr. This is not to say that these matters are unimportant-they are; however, the discussion on these topics is mature, with very few new insights being offered. To move forward on some of these seemingly intractable issues, the authors suggest the ecotoxicological community would be better served by the formation of a subdiscipline of "statistical ecotoxicology," where professional statisticians and ecotoxicologists work in unison. As it currently stands, statistical developments in ecotoxicology are not necessarily undertaken or peer-reviewed by professional statisticians, a situation that has no doubt contributed to the lack of real progress on important recommendations such as the phasing out of no-observed-effect concentrations. Environ Toxicol Chem 2016;35:1337-1339. © 2016 SETAC.

Don't be fooled-A no-observed-effect concentration is no substitute for a poor concentration-response experiment.

Renowned mathematician and science historian Jacob Bronowski once defined science as "the acceptance of what works and the rejection of what does not" and noted "that needs more courage than we might think." Such would also seem to be the case with no-observed-effect concentrations (NOECs) and no-observed-effect levels in ecotoxicology. Compelling arguments were advanced more than a quarter of a century ago as to why the use of a model to describe the concentration-response relationship was preferable to an isolated metric, with the NOEC singled out as a particularly poor toxicity measure. In the ensuing years numerous articles critical of the NOEC have been written, with some calling for an outright ban on its use. More recently, arguments have been made for the retention of NOECs, with supporters suggesting that this metric is particularly useful in situations where the concentration-response relationship is weak or nonexistent. In addition, it has been claimed that there are situations in ecotoxicology where suitable models are simply not available. These arguments are not correct, and they also have impeded the decades-overdue incorporation of numerous recommendations based on research that NOECs should no longer be used. In the present study the authors counter some of the most recent claims in support of NOECs and provide new insights for 1 class of problem claimed not to be amenable to such modeling. They are confident that similar insights will be developed as further original research in this area is undertaken. Environ Toxicol Chem 2016;35:2141-2148. © 2016 SETAC.

More noise does not mean more precision: A review of Aldenberg and Rorije (2013).

This paper provides a critical review of recently published work that suggests that the precision of hazardous concentration estimates from Species Sensitivity Distributions (SSDs) is improved when the uncertainty in the input data is taken into account. Our review confirms that this counter-intuitive result is indeed incorrect.

Selection bias correction for species sensitivity distribution modeling and hazardous concentration estimation.

The species sensitivity distribution (SSD) has been an important development in ecotoxicology, and despite numerous concerns having been raised over many years, it remains the preferred (and often mandated) technique for establishing "safe" concentrations of contaminants in receiving water bodies by jurisdictions around the world. Although universally recognized as a crucial prerequisite for the statistical validity of the procedure, the assumption of random selection of species for SSD modeling is invariably violated. It is shown in the present study that, under very minimal assumptions, nonrandom species selection can result in hazardous concentration estimation errors of a factor of 20 or more. Importantly, if the toxicity data are biased toward the more sensitive species, then the conventional practice of using the lower confidence interval limit for the estimated hazardous concentration may be compensating in the wrong direction.

Time-dependent species sensitivity distributions.

Time is a central component of toxicity assessments. However, current ecotoxicological practice marginalizes time in concentration-response (C-R) modeling and species sensitivity distribution (SSD) analyses. For C-R models, time is invariably fixed, and toxicity measures are estimated from a function fitted to the data at that time. The estimated toxicity measures are used as inputs to the SSD modeling phase, which similarly avoids explicit recognition of the temporal component. The present study extends some commonly employed probability models for SSDs to derive theoretical results that characterize the time-dependent nature of hazardous concentration (HCx) values. The authors' results show that even from very simple assumptions, more complex patterns in the SSD time dependency can be revealed.

A Bayesian approach for determining the no effect concentration and hazardous concentration in ecotoxicology.

This paper describes a Bayesian modeling approach to the estimation of the no effect concentration (NEC) and the hazardous concentration (HC(x)) as an alternative to conventional methods based on NOECs - the no observed effect concentration. The advantage of the proposed method is that it combines a plausible model for dose-response data with prior information or belief about the model's parameters to generate posterior distributions for the parameters - one of those being the NEC. The posterior distribution can be used to derive point and interval estimates for the NEC as well as providing uncertainty bounds when used in the development of a species sensitivity distribution (SSD). This latter feature is particularly attractive and overcomes a recognized deficiency of the NOEC-based approach. Examples using previously published data sets are provided which illustrate how the NEC/HC(x) estimation problem is re-cast and solved in this Bayesian framework.

Tests for density dependence revisited.

We have examined a number of statistical issues associated with methods for evaluating different tests of density dependence. The lack of definitive standards and benchmarks for conducting simulation studies makes it difficult to assess the performance of various tests. The biological researcher has a bewildering choice of statistical tests for testing density dependence and the list is growing. The most recent additions have been based on computationally intensive methods such as permutation tests and boot-strapping. We believe the computational effort and time involved will preclude their widespread adoption until: (1) these methods have been fully explored under a wide range of conditions and shown to be demonstrably superior than other, simpler methods, and (2) general purpose software is made available for performing the calculations. We have advocated the use of Bulmer's (first) test as a de facto standard for comparative studies on the grounds of its simplicity, applicability, and satisfactory performance under a variety of conditions. We show that, in terms of power, Bulmer's test is robust to certain departures from normality although, as noted by other authors, it is affected by temporal trends in the data. We are not convinced that the reported differences in power between Bulmer's test and the randomisation test of Pollard et al. (1987) justifies the adoption of the latter. Nor do we believe a compelling case has been established for the parametric bootstrap likelihood ratio test of Dennis and Taper (1994). Bulmer's test is essentially a test of the serial correlation in the (log) abundance data and is affected by the presence of autocorrelated errors. In such cases the test cannot distinguish between the autoregressive effect in the errors and a true density dependent effect in the time series data. We suspect other tests may be similarly affected, although this is an area for further research. We have also noted that in the presence of autocorrelation, the type I error rates can be substantially different from the assumed level of significance, implying that in such cases the test is based on a faulty significance region. We have indicated both qualitatively and quantitatively how autoregressive error terms can affect the power of Bulmer's test, although we suggest that more work is required in this area. These apparent inadequacies of Bulmer's test should not be interpreted as a failure of the statistical procedure since the test was not intended to be used with autocorrelated error terms.