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.