A Growth-Curve Model Approach to Multivariate Quantal Bioassay

Carter, E. M.; Hubert, J. J.

doi:10.2307/2530913

“…This is also the case for the models of Mayer et al [4] (two-step linear regression approach for very small effects) or Van Wijk and Kraaij [5] (extended log-logistic model). Carter and Hubert [6] used a multivariate regression and have shown that, in practice, an inverse time model is appropriate.…”

Section: Expressing Lc50 As a Function Of Timementioning

confidence: 99%

Modeling Explicitly and Mechanistically Median Lethal Concentration as a Function of Time for Risk Assessment

Bonnomet

¹

,

Duboudin

²

,

Magaud

³

et al. 2002

Environ Toxicol Chem

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A mechanistic model that explains how toxic effects depend on the duration of exposure has been developed. Derived from the dynamic energy budget (DEB)tox model, it expresses the hazard rate as a function of the toxic concentration in the organism. Using linear approximations in accordance with the general simplifications made in DEBtox, the concentration that induces x% of lethality (LCx) and in particular the lethal concentration 50% (LC50) are expressed explicitly as functions of time. Only three parameters are required: an asymptotic effect concentration, a time constant, and an effect velocity. More sophisticated (but still analytic) models are possible, describing more complex toxicity patterns such as an increase of sensitivity with time or, conversely, an adaptation. These models can be fitted to the common and widespread LC50 endpoints available from the literature for various aquatic species and chemicals. The interpretation of the values assigned to the parameters will help explain the toxicity processes and standardize toxicity values from different sources for comparisons.

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“…Reinsel (1982) extended the univariate growth curve model to the multivariate case, where several response variables are measured over multiple time points. The multivariate growth curve model enables us to examine relationships between different response variables (also see Carter & Hubert, 1984;Lundbye-Christensen, 1996;Nummi & MOtt6nen, 2000). Another recent extension is to impose reduced-rank restrictions on the univariate growth curve model, motivated by the fact that the mathematical structure of the growth curve model is akin to that of the reduced-rank regression model (Albert & Kshirsagar, 11993;Reinsel & Velu, 1998, pp.…”

Section: Introductionmentioning

confidence: 99%

A multivariate reduced-rank growth curve model with unbalanced data

Hwang

¹

,

Takane

²

2004

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show abstract

“…This is also the case for the models of Mayer et al [4] (two‐step linear regression approach for very small effects) or Van Wijk and Kraaij [5] (extended log‐logistic model). Carter and Hubert [6] used a multivariate regression and have shown that, in practice, an inverse time model is appropriate.…”

Section: Methods and Derivation Of An Alternative Approachmentioning

confidence: 99%

Modeling explicitly and mechanistically median lethal concentration as a function of time for risk assessment

Bonnomet

¹

,

Duboudin

²

,

Magaud

³

et al. 2002

Enviro Toxic and Chemistry

View full text Add to dashboard Cite

A mechanistic model that explains how toxic effects depend on the duration of exposure has been developed. Derived from the dynamic energy budget (DEB)tox model, it expresses the hazard rate as a function of the toxic concentration in the organism. Using linear approximations in accordance with the general simplifications made in DEBtox, the concentration that induces x% of lethality (LCx) and in particular the lethal concentration 50% (LC50) are expressed explicitly as functions of time. Only three parameters are required: an asymptotic effect concentration, a time constant, and an effect velocity. More sophisticated (but still analytic) models are possible, describing more complex toxicity patterns such as an increase of sensitivity with time or, conversely, an adaptation. These models can be fitted to the common and widespread LC50 endpoints available from the literature for various aquatic species and chemicals. The interpretation of the values assigned to the parameters will help explain the toxicity processes and standardize toxicity values from different sources for comparisons.

show abstract

A Growth-Curve Model Approach to Multivariate Quantal Bioassay

Cited by 25 publications

References 16 publications

Modeling Explicitly and Mechanistically Median Lethal Concentration as a Function of Time for Risk Assessment

Modeling Explicitly and Mechanistically Median Lethal Concentration as a Function of Time for Risk Assessment

A multivariate reduced-rank growth curve model with unbalanced data

Modeling explicitly and mechanistically median lethal concentration as a function of time for risk assessment

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