Comparing statistical analyses to estimate thresholds in ecotoxicology

Abstract

Different methods are used in ecotoxicology to estimate thresholds in survival data. This paper uses Monte Carlo simulations to evaluate the accuracy of three methods (maximum likelihood (MLE) and Markov Chain Monte Carlo estimates (Bayesian) of the no-effect concentration (NEC) model and Piecewise regression) in estimating true and apparent thresholds in survival experiments with datasets having different slopes, background mortalities, and experimental designs. Datasets were generated with models that include a threshold parameter (NEC) or not (log-logistic). Accuracy was estimated using root-mean square errors (RMSEs), and RMSE ratios were used to estimate the relative improvement in accuracy by each design and method. All methods had poor performances in shallow and intermediate curves, and accuracy increased with the slope of the curve. The EC5 was generally the most accurate method to estimate true and apparent thresholds, except for steep curves with a true threshold. In that case, the EC5 underestimated the threshold, and MLE and Bayesian estimates were more accurate. In most cases, information criteria weights did not provide strong evidence in support of the true model, suggesting that identifying the true model is a difficult task. Piecewise regression was the only method where the information criteria weights had high support for the threshold model; however, the rate of spurious threshold model selection was also high. Even though thresholds are an attractive concept from a regulatory and practical point of view, threshold estimates, under the experimental conditions evaluated in this work, should be carefully used in survival analysis or when there are any biological reasons to support the existence of a threshold.

Introducing the No‐Significant‐Effect Concentration

“…Expanding the range of models that can be used is very simple within the Bayesian framework using the currently available packages in R. Indeed, this is already being achieved in two recently developed C-R packages (Fisher et al, 2020(Fisher et al, , 2023 https://github.com/open-AIMS/bayesnec). The Bayesian approach also has two other advantages in C-R modeling, previously noted by Krull (2020): (1) direct inclusion of uncertainty in the estimates, which can be drawn directly from the posterior distribution, and (2) the fact that prior information can be adjusted by using expert elicitation, information from the literature, or previous experiments. Even when weakly informative priors are used, their inclusion in the model-fitting process can contribute to the accuracy of the method and improve the stability of model fitting (Krull, 2020).…”

“…The Bayesian approach also has two other advantages in C‐R modeling, previously noted by Krull (2020): (1) direct inclusion of uncertainty in the estimates, which can be drawn directly from the posterior distribution, and (2) the fact that prior information can be adjusted by using expert elicitation, information from the literature, or previous experiments. Even when weakly informative priors are used, their inclusion in the model‐fitting process can contribute to the accuracy of the method and improve the stability of model fitting (Krull, 2020).…”

Methods for estimating no‐effect toxicity concentrations in ecotoxicology

“…The NEC is typically estimated using a threshold model (Fox, 2008(Fox, , 2010Pires et al, 2002) and represents the maximum concentration for which there is no response for a given species, thereby providing a toxicity measure that is ideal for incorporation into SSDs aimed at estimating protective concentrations of contaminants. Although the NEC is considered the preferred measure for inclusion into SSDs in at least some jurisdictions (Warne et al, 2018), CR data do not necessarily exhibit abrupt threshold-like responses, and applying a threshold model in this case will lead to poor outcomes (Krull, 2020). This phenomenon has occurred in our own work, where at times attempts to fit a threshold model have failed using standard packages such as drc in R (Ritz et al, 2015) or, when it does fit successfully, may yield values that are higher than even the EC10 (Negri et al, 2021).…”