Models for the estimation of a ‘no effect concentration’

The use of a no effect concentration (NEC), instead of the commonly used no observed effect concentration (NOEC), has been advocated recently. In this article models and methods for the estimation of an NEC are proposed and it is shown that the NEC overcomes many of the objections to the NOEC. The NEC is included as a threshold parameter in a non-linear model. Numerical methods are then used for point estimation and several techniques are proposed for interval estimation (based on bootstrap, profile likelihood and asymptotic normality). The adequacy of these methods is empirically confirmed by the results of a simulation study. The profile likelihood based interval has emerged as the best method. Finally the methodology is illustrated with data obtained from a 21 day Daphnia magna reproduction test with a reference substance, 3,4-dichloroaniline (3,4-DCA), and with a real effluent. Copyright © 2002 John Wiley & Sons, Ltd.

[1]  K. Liang,et al.  Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests under Nonstandard Conditions , 1987 .

[2]  Helmut Küchenhoff.  An Exact Algorithm for Estimating Breakpoints in Segmented Generalized Linear Models , 1997 .

[3]  Elizabeth Southerland,et al.  Technical Support Document for Water Quality-based Toxics Control , 1991 .

[4]  Chris Gennings,et al.  Threshold Models for Combination Data from Reproductive and Developmental Experiments , 1995 .

[5]  J. Hoekstra,et al.  Alternatives for the no‐observed‐effect level , 1993 .

[6]  P. Feder.  The Log Likelihood Ratio in Segmented Regression , 1975 .

[7]  R. Ribeiro,et al.  A Daphnia magna first-brood chronic test: An alternative to the conventional 21-Day chronic bioassay? , 1999, Ecotoxicology and environmental safety.

[8]  D. A. Williams,et al.  The comparison of several dose levels with a zero dose control. , 1972, Biometrics.

[9]  Sebastiaan A.L.M. Kooijman,et al.  Some statistical properties of estimates of no-effect concentrations , 1996 .

[10]  Silvapulle Mj.  On testing for threshold values. , 1991 .

[11]  C. Cox,et al.  Threshold dose-response models in toxicology. , 1987, Biometrics.

[12]  J. Shao,et al.  The jackknife and bootstrap , 1996 .

[13]  K Ulm,et al.  A statistical method for assessing a threshold in epidemiological studies. , 1991, Statistics in medicine.

[14]  P. Chapman,et al.  A warning: NOECs are inappropriate for regulatory use , 1996 .

[15]  Mark Crane,et al.  Asking the right questions: ecotoxicology and statistics , 1996, Ecotoxicology.

[16]  Sebastiaan A.L.M. Kooijman,et al.  An alternative for NOEC exists, but the standard model has to be abandoned first , 1996 .

[17]  Charles W. Dunnett,et al.  New tables for multiple comparisons with a control. , 1964 .

[18]  Roland Fisch,et al.  Report of the OECD Workshop on Statistical Analysis of Aquatic Toxicity Data , 1998 .

[19]  R. Kühn,et al.  Results of the harmful effects of water pollutants to Daphnia magna in the 21 day reproduction test , 1989 .

[20]  Sebastiaan A.L.M. Kooijman,et al.  Analysis of toxicity tests on Daphnia survival and reproduction , 1996 .