Nonlinear Models for Medical Statistics

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ISBN: 9780198508120 | 0198508123
Cover: Hardcover
Copyright: 9/20/2001

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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 of statistical modelling and of generalized linear models. It begins with a general introduction to nonlinear models, comparing them to generalized linear models, descriptions of data handling and formula definition and a summary of 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 moleuclar genetics.

Basic concepts

(22)

Statistical modelling

(8)

Data-generating mechanisms

(2)

Probability models

(2)

Distributions

(2)

Regression functions

(2)

Limitations of generalized linear models

(6)

Definition

(1)

Choice of distribution

(1)

Regression functions

(1)

Dependent observations

(1)

Inference

(1)

Definitions of nonlinearity

(3)

Distribution and regression functions

(1)

Models with a linear part

(1)

Transformable linearity

(1)

Intrinsic and parameter-effects nonlinearity

(1)

Developing regression functions

(4)

Descriptive versus mechanistic models

(1)

Solving differential equations

(3)

Exercises

(1)

Practical aspects

(14)

Data

(4)

Response variables

(2)

Convariates

(2)

Specifying models

(2)

Software

(1)

Model components

(2)

Calculating the likelihood

(4)

Nonlinear optimization

(1)

Parametrization

(1)

Initial estimates

(1)

Checking convergence

(1)

Inference

(3)

Model selection

(1)

Likelihood regions

(1)

Goodness of fit

(1)

Exercises

(1)

Families of nonlinear regression functions

(12)

Growth curves

(5)

Polynomials

(1)

Exponential forms

(1)

Sigmoidal curves

(3)

Sums of exponentials

(3)

Compartment models

(2)

Diffusion models

(1)

Other nonlinear functions

(2)

Power functions

(1)

Cyclic functions

(1)

Change-point models

(1)

Exercises

(2)

Epidemiology

(24)

Studying natural populations

(2)

Goals

(1)

Designs

(1)

Ecological regression

(1)

Growth curves

(4)

Richards curve

(1)

Weight gains of pregnant women

(1)

Differences among women

(2)

Death rates

(2)

Log linear models

(1)

Malignant neoplasms

(1)

Overdispersion

(1)

Change points

(3)

Poisson process

(1)

The haemolytic uraemic syndrome study

(1)

Detecting a change point

(2)

A dynamic model

(1)

Recurrent epidemics

(7)

Epidemic models

(2)

Childhood infections

(2)

Infectious disease outbreaks

(2)

Micro-organism subtyping

(1)

Typing model

(1)

The Maine tuberculosis outbreak

(1)

Exercises

(4)

Clinical trials

(12)

Evaluating a new medication

(2)

Goals

(1)

Designs

(1)

Validity

(1)

Models

(1)

Response decline to a stable state

(8)

The azathioprine study

(1)

Asymptotic and polynomial curves

(6)

Conclusions

(1)

Exercises

(2)

Quality of life

(20)

Effects of medical treatment

(3)

Goals

(1)

Constructing event history models

(1)

Models for ordinal variables

(2)

Recurrent events

(2)

The bladder cancer study

(1)

Birth processes

(2)

Change of state

(3)

The adenosine deaminase study

(1)

Time-varying covariates

(2)

Transition probabilities

(3)

The peptic oesophagitis study

(2)

Ordinal regression

(1)

Random walks

(1)

Analysis of diary cards

(5)

The seasonal rhinitis study

(1)

Spells

(4)

Exercises

101

(4)

Pharmacokinetics

105

(36)

Studying drug concentration in the body

105

(8)

Goals

105

(1)

Compartment models

106

(4)

Statistical models

110

(3)

Parent drug and metabolite

113

(18)

The flosequinan study

113

(1)

Modelling the parent drug

114

(5)

Modelling the metabolite

119

(2)

Simulataneous modelling

121

(5)

Serial dependence

126

(4)

Conclusions

130

(1)

Repeated dosing

131

(4)

The propoxyphene study

131

(1)

Tracking patients

132

(3)

Exercises

135

(6)

Pharmacodynamics

141

(16)

Studying the effects of drugs on the body

141

(1)

Goals

141

(1)

Response variables

142

(1)

Continuous response

142

(4)

The gastric pH study

142

(1)

Regression functions

143

(1)

Gaussian copulas

143

(3)

Count response

146

(9)

The capsaicin cough challenge study

146

(4)

Overdispersed autoregression

150

(1)

Analysing the challenge-response curve

151

(2)

Conclusions

153

(2)

Exercises

155

(2)

Assays and formulations

157

(22)

Assays

157

(2)

Goals

157

(1)

Methods

158

(1)

Colorimetric enzyme assay

159

(2)

Assay methodology

159

(1)

Michaelis-Menten function

159

(1)

Analysis of the acid phosphatase assay

160

(1)

DNase assay

161

(3)

Generalized Michaelis-Menten fucntion

161

(2)

Analysis of the rat serum

163

(1)

Ames Salmonella microsome assay

164

(5)

Assay methodology

164

(2)

Mechanistic models

166

(2)

The International Programme on Chemical Safety study

168

(1)

Determining formulations

169

(5)

Developing delivery systems

169

(2)

Transport models

171

(1)

Pill dissolution rates

172

(2)

Exercises

174

(5)

Molecular genetics

179

(76)

Sequence analysis

179

(3)

Basic DNA structure

179

(1)

Sequencing methods

180

(1)

Alignment

181

(1)

Finding genes and their exons

182

(5)

The β-globin gene

183

(1)

Locating the gene

184

(1)

Locating the exons

185

(2)

Detecting locations of mutations

187

(3)

Mitochondrial DNA

187

(1)

Modelling mutation rates

188

(2)

Exercises

190

(3)

Appendices

A Data and model examples from R

193

(12)

A.1 Data

193

(1)

A.1.1 Data objects

193

(3)

A.1.2 Data methods

196

(2)

A.2 Models

198

(1)

A.2.1 Software

198

(1)

A.2.2 Probability distribution

198

(1)

A.2.3 Covariate dependence

199

(1)

A.2.4 General nonlinear specification

200

(2)

A.3 Likelihoods

202

(1)

A.3.1 A simple example

202

(1)

A.3.2 More complex cases

203

(2)

B Stochastic dependence structures

205

(24)

B.1 Random effects

205

(1)

B.1.1 Mixture models

205

(2)

B.1.2 Conjugate distributions

207

(1)

B.1.3 Other mixtures

207

(1)

B.2 Time dependence

208

(1)

B.2.1 Ordered dependence

208

(1)

B.2.2 Autoregression

209

(2)

B.3 Multivariate distributions with correlation matrices

211

(1)

B.3.1 Multivariate Student t distribution

211

(1)

B.3.2 Multivariate power-exponential distribution

212

(1)

B.3.3 Copulas

213

(1)

B.4 Dynamic models

214

(1)

B.4.1 Dynamic generalized linear models

214

(1)

B.4.2 General dynamic nonlinear models

215

(4)

B.5 Markov processes

219

(1)

B.5.1 Markov chains

219

(1)

B.5.2 Hidden Markov models

220

(1)

B.6 Duration data

221

(1)

B.6.1 Survival and intensity functions

222

(2)

B.6.2 Counting processes

224

(3)

B.6.3 Important special cases

227

(2)

C Data tables for the exercises

229

(26)

C.1 Gastric half-emptying times

229

(1)

C.2 Bacteriuria infections

230

(1)

C.3 Cases of lung cancer

231

(1)

C.4 Case-control study of asbestos

232

(1)

C.5 Rectal polyps

233

(4)

C.6 Recurrence of kidney infections

237

(1)

C.7 Mammary tumours

238

(2)

C.8 Skin papilloma in mice

240

(1)

C.9 Leuk &Aelig;mia clinical trial

241

(1)

C.10 Leuk &Aelig;mia patients

242

(1)

C.11 Breast cancer

243

(1)

C.12 Prednisolone concentrations

244

(1)

C.13 Indomethicin concentrations

245

(1)

C.14 Ephedrine concentrations

245

(1)

C.15 Blood glucose levels

246

(2)

C.16 Theophylline concentrations

248

(1)

C.17 Declomycin concentrations

249

(1)

C.18 Propoxyphene concentrations

250

(1)

C.19 Phenylbiguanide and blood pressure

251

(1)

C.20 ELISA for anticoronavirus

251

(1)

C.21 Cortisol radioimmunological assay

252

(1)

C.22 ELISA for allergens

252

(1)

C.23 Penicilin G and theophylline

253

(2)

Bibliography

255

(8)

Author index

263

(3)

Subject index

266

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Nonlinear Models for Medical Statistics

Summary

Table of Contents

Supplemental Materials

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