Note: Cover -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- Glossary and notation -- Index of data sets -- 1: Data, preliminary analyses and mechanistic models -- 1.1 Introduction -- 1.2 Aspects of toxicology -- 1.3 Examples -- 1.4 Preliminary graphical representations -- 1.5 Mechanistic models -- 1.6 Interpolation and extrapolation -- 1.7 Discussion -- 1.8 Exercises and complements -- 2: Maximum-likelihood fitting of simple models -- 2.1 The likelihood surface and non-linear optimization -- 2.2 The method-of-scoring for the logit model -- 2.3 The connection with iterated weighted regression -- generalized linear models -- 2.4 Hand calculation and using tables -- 2.5 The chi-square goodness-of-fit test -- heterogeneity -- 2.6 Minimum chi-square estimation -- 2.7 Estimating the dose for a given mortality -- 2.7.1 Using the delta method -- 2.7.2 Using Fieller's Theorem -- 2.7.3 The likelihood-ratio interval -- 2.7.4 Comparing the likelihood-ratio and Fieller intervals -- 2.8 Maximum-likelihood estimation for logistic regression -- 2.9 Making comparisons -- 2.10 Testing for trend in proportions -- 2.11 Discussion -- 2.12 Exercises and complements -- 3: Extensions and alternatives -- 3.1 Introduction -- 3.2 Natural or control mortality -- EM algorithm and mixture models -- 3.3 Wadley's problem -- use of controls -- 3.4 Influence and diagnostics -- 3.5 Trichotomous responses -- 3.6 Bayesian analysis -- 3.7 Synergy and antagonism -- 3.8 Multivariate bioassays -- 3.9 Errors in dose measurement -- 3.10 Discussion -- 3.11 Exercises and complements -- 4: Extended models for quantal assay data -- 4.1 Introduction -- 4.2 The Aranda-Ordaz asymmetric model -- 4.3 Extended symmetric models -- 4.4 Transforming the dose scale -- 4.5 Additional models and procedures -- goodness of link -- 4.5.1 Other models -- 4.5.2 Goodness of link. , 4.6 Safe dose evaluation -- 4.7 Discussion -- 4.8 Exercises and complements -- 5: Describing time to response -- 5.1 Introduction and data -- 5.2 Descriptive methods -- 5.2.1 The MICE index -- 5.2.2 Polynomial growth curves -- 5.3 The stochastic model of Puri and Senturia -- 5.3.1 A mechanistic model -- 5.3.2 Fitting end-point mortality data -- 5.3.3 The Diggle-Gratton extension -- 5.3.4 A method of conditional mean and zero-frequency -- 5.3.5 The case β ≠ 0 -- 5.4 Multi-event models -- 5.5 Survival analysis -- 5.5.1 A mixture model for the flour-beetle data -- 5.5.2 The case of no long-term survivors -- 5.6 Non-monotonic response -- 5.7 Discussion -- 5.8 Exercises and complements -- 6: Over-dispersion -- 6.1 Extra-binomial variation -- 6.1.1 The beta-binomial model -- 6.1.2 Fitting the beta-binomial model -- 6.1.3 Tarone's test -- 6.1.4 The possibility of bias -- 6.2 Making comparisons in the presence of extra-binomial variation -- 6.2.1 An example involving treatment versus control -- 6.2.2 Comparing alternative test procedures -- 6.3 Dose-response with extra-binomial variation -- 6.3.1 The basic beta-binomial model -- 6.3.2 Describing variation through the parameter θ (or ρ) -- 6.4 The quasi-likelihood approach -- 6.5 Overdispersion versus choice of link function -- 6.5.1 Binomial examples -- 6.5.2 Wadley's problem with over-dispersion -- 6.6 Additional models -- 6.6.1 The correlated-binomial model -- 6.6.2 Mixtures of binomials -- outliers and influence -- 6.6.3 Comparison of models -- 6.6.4 Logistic-normal-binomial and probit-normal-binomial models -- 6.6.5 Modelling the effect of litter-size -- 6.7 Additional applications -- 6.7.1 Urn-model representations -- ant-lions -- 6.7.2 The beta-geometric distribution -- fecundability -- 6.7.3 Analysis of variance -- 6.7.4 Incorporating historical control information -- 6.8 Discussion. , 6.9 Exercises and complements -- 7: Non-parametric and robust methods -- 7.1 Introduction -- 7.2 The pool-adjacent-violators algorithm -- ABERS estimate -- 7.3 The Spearman-Kärber estimate of the ED50 -- 7.4 Trimming -- 7.4.1 Trimmed Spearman-Kärber -- 7.4.2 Trimmed logit -- 7.5 Robustness and efficiency -- 7.5.1 Asymptotic variance and the Spearman-Kärber estimate -- 7.5.2 L, M and R estimators -- 7.5.3 Influence curve robustness -- 7.5.4 Efficiency comparisons -- 7.6 Alternative distribution-free procedures -- 7.6.1 Sigmoidal constraint -- 7.6.2 Density estimation -- 7.7 Discussion -- 7.8 Exercises and complements -- 8: Design and sequential methods -- 8.1 Introduction -- 8.2 Optimal design -- 8.3 The up-and-down experiment -- 8.4 The Robbins-Monro procedure -- 8.4.1 Introduction -- 8.4.2 Wu's logit-MLE method -- 8.5 Sequential optimization -- 8.6 Comparison of methods for ED100p estimation -- 8.7 Discussion -- 8.8 Exercises and complements -- Appendices -- A Approximation procedures -- B GLMs and GLIM -- C Bordering Hessians -- D Asymptotically equivalent tests of hypotheses -- E Computing -- F Useful addresses -- G Solutions and comments for selected exercises -- References -- Author index -- Subject index.