Nonlinear Models in Medical Statistics
This text provides an introduction to the use of nonlinear models in medical statistics, It is a practical text rather than a theoretical one and assumes a basic knowledge in statistical modelling and of generalized linear models.The book first provides a general introduction to nonlinear models, comparing them to generalized linear models. It describes data handling and formula definition and summarises the principal types of nonlinear regression formulae. there is an emphasis on techniques for non-normal data.Following chapters provide detailed examples of applications in various areas of medicine, epidemiology, clinical trials, quality of life, pharmokinetics, pharmacodynamics, assays and formulations, and molecular genetics.The book concludes with appendicies describing data handling and model formulae in more detail, and given ways of modelling dependencies in repeated measurements, and data for the exercises.
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Families of nonlinear regression functions
Quality of life
Assays and formulations
A Data and model examples from R
B Stochastic dependence structures
allow analysis appropriate assay assumption autoregression baseline censoring clinical trials compared compartment model complex concentration constant corresponding cough counts covariates data-generating mechanism dependence describe disease dispersion Equation example exponential flosequinan gamma distribution gene given growth curve hidden Markov models indicate individual profiles intensity function involves likelihood function Lindsey linear models link function location parameter log likelihood log normal distribution logistic mean measured metabolite mixing distribution model Section models fitted multivariate distributions mutation negative binomial negative binomial distribution nonlinear models nonlinear regression º º observations obtained optimization overdispersion parameter estimates parent drug patients pharmacokinetics placebo plotted in Figure Poisson population possible probability distribution propoxyphene protein random effects response variable sequence statistical stochastic time-varying covariates tion transformation treatment types unknown parameters usually values variance vector Weibull Weibull distribution whereas zero