A Generalization of the Probit and Logit Methods for Dose Response Curves

1976/12/01 by Ross L. Prentice · 407 citations
Biochemistry, Genetics and Molecular Biology · Decision Sciences · Mathematics · #Carcinogens and Genotoxicity Assessment #Exponential function #Extreme value theory #Gamma distribution #Generalization #Generalized extreme value distribution #Kurtosis #Logistic distribution #Logistic regression #Logit #Mathematical analysis #Mathematics #Optimal Experimental Design Methods #Probit #Probit model #Skewness #Statistical Methods in Clinical Trials #Statistics

paper · doi:10.2307/2529262

published in Biometrics 32(4), 761 (Oxford University Press)

openalex publication_date 1976/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

The relationship between response probability and dosage in quantal response bioassay is modelled using a four parameter class. In addition to location and scale quantities the model includes two shape parameters that essentially index skewness and heaviness of tails of the dose-response curve. The class of models includes such special cases as the logistic, normal, extreme minimum value, extreme maximum value, double exponential, exponential and reflected exponential distribution functions. Score tests are derived for logistic and normal hypotheses and certain submodels are discussed for which the model fitting is computationally convenient. The data of Bliss (1935) illustrates the potential improvement over usual methods in the estimation of critical dose levels.

Cited by

• A Robust Bayesian Random Effects Model for Nonlinear Calibration Problems
• Parallelism in Neurodegenerative Biomarker Tests: Hidden Errors and the Risk of Misconduct
• Bayesian Analysis of Binary and Polychotomous Response Data
• Prior Distributions for the Bradley-Terry Model of Paired Comparisons
• MAGNET-KG: Maximum-Entropy Geometric Networks for Temporal Knowledge Graphs: Theoretical Foundations and Mathematical Framework
• Categorical Data Analysis Using a Skewed Weibull Regression Model
• Detection and serotyping of pneumococci in community acquired pneumonia patients without culture using blood and urine samples. [europepmc]
• LFG-500, a newly synthesized flavonoid, induces apoptosis in human ovarian carcinoma SKOV3 cells with involvement of the reactive oxygen species-mitochondria pathway. [europepmc]
• Enhanced Cytotoxic Activity of Mitochondrial Mechanical Effectors in Human Lung Carcinoma H520 Cells: Pharmaceutical Implications for Cancer Therapy. [europepmc]
• Leveraging Mathematical Modeling to Quantify Pharmacokinetic and Pharmacodynamic Pathways: Equivalent Dose Metric. [europepmc]
• Categorical Data Analysis Using a Skewed Weibull Regression Model. [europepmc]
• Improvement of Bobrovsky-Mayor-Wolf-Zakai Bound. [europepmc]
• Skewed logit model for analyzing correlated infant morbidity data. [europepmc]
• The ElonginB/C-Cullin5-SOCS-Box-Complex Is a Potential Biomarker for Growth Hormone Disorders. [europepmc]
• Bioanalytical screening of low levels of dioxins and dioxin-like PCBs in pig meat (pork) for checking compliance with EU maximum and action levels using highly sensitive "third generation" recombinant H4L7.5c2 rat hepatoma cells. [europepmc]
• Benzoic Acid and Its Hydroxylated Derivatives Suppress Early Blight of Tomato ( Alternaria solani ) via the Induction of Salicylic Acid Biosynthesis and Enzymatic and Nonenzymatic Antioxidant Defense Machinery. [europepmc]
• Evidence for the Role of CYP51A and Xenobiotic Detoxification in Differential Sensitivity to Azole Fungicides in Boxwood Blight Pathogens. [europepmc]
• Bayesian and Classical Inference for the Generalized Log-Logistic Distribution with Applications to Survival Data. [europepmc]
• Benzimidazole Derivatives Suppress Fusarium Wilt Disease via Interaction with ERG6 of Fusarium equiseti and Activation of the Antioxidant Defense System of Pepper Plants. [europepmc]
• Comparative Study of Three Biological Control Agents and Two Conventional Fungicides against Coriander Damping-off and Root Rot Caused by Rhizoctonia solani . [europepmc]
• Hydroxylated Cinnamates Enhance Tomato Resilience to Alternaria alternata , the Causal Agent of Early Blight Disease, and Stimulate Growth and Yield Traits. [europepmc]
• Non-proteinogenic amino acids mitigate oxidative stress and enhance the resistance of common bean plants against Sclerotinia sclerotiorum . [europepmc]
• A new statistical distribution via the Phi-4 equation with its wide-ranging applications. [europepmc]
• Ornithine enhances common bean growth and defense against white mold disease via interfering with SsOAH and diminishing the biosynthesis of oxalic acid in Sclerotinia sclerotiorum . [europepmc]

Related

• Semiparametric logistic regression with unknown sizes, and its application to bioassays
• Monotonic Nonparametric Dose Response Model
• Equivalence of dose response curves
• Modeling Biphasic, Non-Sigmoidal Dose-Response Relationships: Comparison of Brain-Cousens and Cedergreen Models for a Biochemical Dataset
• Bayesian Model-Averaged Benchmark Dose Analysis Via Reparameterized Quantal-Response Models