The usual approach for Cox regression is to use twice the log likelihood-ratio statistic, which is referred to in this paper as R2, and the chi-square. This paper is concerned with higher-order expansions that involve the second and third order terms. The statistic for such expansions is R* = (1/R)log(R/U), where the quantity U is difficult to calculate. An approximation U~, by Skovgaard, is suggested as a method to approximate U. The author uses the functions “glim” and “nls,” which are found in S-plus, a well-known statistical package.

Implement Skovgaard’s algorithm for generalized linear and nonlinear regression models is the objective of the paper. The author presents this in four sections and an appendix. The first section is an introduction. The second section develops the approximate statistic proposed by Skovgaard. The third section develops the algorithm for generalized linear regression models, and the fourth section develops the algorithm for nonlinear regression models, and includes an example of hormone-receptor assay results from a mammary tumor. The appendix provides the code to let the computer do the work.

The usual approach to life tables and Kaplan-Meier censored data is to use twice the log likelihood-ratio, and the chi-square statistic with a linear regression model. The author provides an approach that allows readers to include higher order terms and still have the benefit of a statistic with which to test hypotheses. In addition the author relates this to a popular statistical package, S-plus, and provides the code to accomplish the approximation. I recommend this paper.