Simulation study of characteristics of statistical estimators of inhibition concentration

Statistical estimators of the concentrations associated with specified leve ls of reproductive toxicity in the aquatic organism Ceriodaphnia dubia are presented and compared. The first estimator, the ICp or inhibition concentr ation approach, was based on a nonparametric estimation routine that assume d responses monotonically declined with increasing concentrations. This est imator also assumed that linear interpolation between mean responses associ ated with consecutive concentration groups was reasonable. The second estim ator, the RIp or reproductive inhibition concentration approach, was based on a parametric concentration-response model. This model assumed that the n umber of young is a Poisson or negative, binomially distributed, random var iable, and that the mean number of young could be modeled using an exponent ial term involving a polynomial in the test concentrations. Confidence inte rvals for both these estimators were obtained using variants of a bootstrap resampling procedure. The properties of these estimators, namely bias, mea n squared error, and coverage probabilities, were compared in a Monte Carlo simulation study. The results from this study suggested that over a broad range of realistic conditions, the confidence intervals associated with the ICp estimator failed to maintain nominal coverage probabilities, whereas t he confidence intervals associated with the RIp estimator performed as nomi nally stated under most conditions. Finally, correct specification of the m odel concentration-response pattern was observed to be important for estima ting inhibition concentrations with small bias and variability.