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Dose–response regressions for algal growth and similar continuous endpoints: Calculation of effective concentrations

We derive equations for the effective concentration giving 10% inhibition (EC10) with 95% confidence limits for probit (log‐normal), Weibull, and logistic dose–response models on the basis of experimentally derived median effective concentrations (EC50s) and the curve slope at the central point (50% inhibition). For illustration, data from closed, freshwater algal assays are analyzed using the green alga Pseudokirchneriella subcapitata with growth rate as the response parameter. Dose–response regressions for four test chemicals (tetraethylammonium bromide, musculamine, benzonitrile, and 4‐4‐(trifluoromethyl)phenoxy‐phenol) with ranges of representative slopes at 50% response (0.54–2.62) and EC50s (2.20–357 mg/L) were selected. Reference EC50s and EC10s with 95% confidence limits using probit or Weibull models are calculated by nonlinear regression on the whole dataset using a dose–response regression program with variance weighting and proper inverse estimation. The Weibull model provides the best fit to the data for all four chemicals. Predicted EC10s (95% confidence limits) from our derived equations are quite accurate; for example, with 4‐4‐(trifluoromethyl)phenoxy‐phenol and the probit model, we obtain 1.40 (1.22–1.61) mg/L versus 1.40 (1.20‐1.64) mg/L obtained from the nonlinear regression program. The main advantage of the approach is that EC10 or ECx (where x = 1–99) can be predicted from well‐determined responses around EC20 to EC80 without experimental data in the low‐ or high‐response range. Problems with the estimation of confidence interval for EClow,x (concentration predicted to cause x% inhibition) from algal growth inhibition also are addressed. Large confidence intervals may be the result of experimental error and lack of a well‐defined reference response value.