Nonlinear Models in Medical Statistics. (Book Reviews)
Gasser, Theo, Journal of the American Statistical Association
J. K. LINDSEY. New York: Oxford University Press, 2001. ISBN 0-19-850812-3. vi + 280 pp. $65.00 (H).
This book is not a standard textbook on nonlinear models, but rather a collection of case studies. A brief introduction into concepts of statistical modeling is provided in the first three chapters, and Appendix B gives a brief overview of some special topics relevant to the book. This material does not, however, replace a solid knowledge of regression modeling and generalized linear modeling. As the title indicates, the examples come from the medical field, mainly from clinical epidemiology or drug development. Thus, they do not cover the variety of applications found in biomedicine. Applications in physiology and in other basic sciences are completely lacking.
The datasets, available at the author's home page, are indispensable for this kind of book. The analysis is based on the R package, which is freely available. A chapter-by-chapter summary follows.
1. Basic Concepts (22 pages)
This small chapter gives a brief introduction to generalized linear models and nonlinear models. The author considers generalized linear models to be nonlinear in a way, because linear estimation methods no longer work. Many statisticians would consider these to be true generalizations of the ordinary linear models used when there is a continuous outcome. In my view, the author is overly alarmist regarding simple approaches to modeling that disregard some complexities in the data. Often the problem at stake or the quality of the data may justify a simple approach to modeling. One might, for example, be justified in disregarding heteroscedasticity and using unweighted least squares.
2. Practical Aspects (14 pages)
This chapter starts with relatively straightforward topics, such as storing data appropriately when the number and locations of times varies from subject to subject. It discusses ways to improve maximizing the likelihood, such as reparameterizing, constraining parameters, and choosing initial estimates. The author advocates model selection and assessing goodness of fit via the log likelihood, and the Akaike information criterion (AIC) in particular.
3. Families of Nonlinear Regression Functions (11 pages)
This chapter begins by introducing classes of models for describing growth curves, then covers sums of exponentials, and, as special cases, cyclic functions and changepoint models. Evidently, this is hardly exhaustive in covering the topic.
4. Epidemiology (24 pages)
The epidemiologic case studies deal with relatively classical (descriptive) epidemiology. The first example involves weight gain in 10 pregnant women, measured repeatedly. Although the analysis via growth curves seems appropriate, neither clear goals nor clear conclusions are given. The model for death rates for in fluoridated and nonfluoridated cities is perhaps a bit less convincing. The subsequent changepoint problem might be better cast in a hypothesis-testing framework. The case study on recurrent epidemics, on the other hand, is close to an ideal modeling example.
5. Clinical Trials (12 pages)
A rationale for conducting clinical trials is given first. Only one example is analyzed: improving the condition of multiple sclerosis patients (n = 48). The goals and the conclusions here are more clearly stated than in Chapter 4.
6. Quality of Life (20 pages)
Here various models for event-history data are studied using data from a number of clinical trials, After recurrent events, change-of-state and transition probabilities are treated using birth processes, mixture distributions, intensity functions with time-varying covariates, ordinal regression, and random walk. This gives a relatively good picture of some relevant biostatistical models for typical datasets. …