Applied Survival Analysis: Regression Modeling of Time to Event Data.

The authors of the classical book Applied Logistic Regression (1989) have published a second applied textbook: Applied Survival Analysis. It covers an up-to-date description of the methods used in analysing time to event data. The book focuses on practical applications and not on mathematical theory and proofs. Beyond descriptive methods and parametric models, 80% of the book deals with the proportional hazards model, which is probably the most applied model in modern survival analysis. Hosmer and Lemeshow assume that the reader has a basic knowledge of methods of linear and/or logistic regression analysis. The idea is, not to show all basics of regression analysis, but the application of the proportional hazards model based on this knowledge. In doing so, the authors can direct to analogies in other models and do not have to introduce the theory of estimating and testing in regression analysis. Thus, the book is an ideal textbook for people with knowledge of regression analysis who want to become acquainted with the methods of survival analysis. The authors put great emphasis on the interpretation of each step of the calculation and their consequences on the analysis. Hence the book is a helpful guide and advisor for analysing datasets. A further advantage is the detailed interpretation of the results of the models. This also makes the book understandable for people who want to get into survival analysis without deep knowledge of other regression methods. The authors present very well the main points involved when analysing a regression model. Those who are interested in principal and mathematical basics of survival analysis have to look for other sources of information. Thus the word ‘applied’ in the title of the book is very well chosen by the authors although the reader should be willing to understand the basic formulas. Every method presented in the book is completed with a real-world example for supporting the learning process. The datasets used in the examples can be downloaded from an FTP-server and analysed for a better understanding of the calculation steps. In addition, Hosmer and Lemeshow give some advice on how to use the statistical software packages STATA, BMDP, SAS, S-Plus. Each chapter ends with tests to check the knowledge acquired. However, the test solutions are missing. Giving the results of these tests would probably have gone beyond the scope of this book but could have been supplied via the FTP-server. The bibliography provides a source of further investigation into the field of survival analysis and gives a good overview of the recent literature. After a short preface and an introduction to censoring mechanisms, univariate analysis such as the Kaplan-Meier method is described. The proportional hazards model and the estimation of the regression coefficients is introduced in Chapter 3. Chapter 4 shows the possibilities for interpretation of a fitted regression model. Different strategies and difficulties of interpretation are illustrated by examples. Chapter 5 covers variable selection. The basic idea and the problems of variable selection—how to identify the most suitable regression model—are presented. First, Hosmer and Lemeshow describe a technique, which is based on the contentional meaning of the variables, bivariate and multiple models. The authors dedicate a large part of this chapter to the question of how to include variables into the model. Among others, the fractional polynomials from Royston and Altman are described. In a second step the inclusion of interactions in the model is examined. This chapter is rounded off by mentioning the stepwise selection and the best subset selection, which probably are the most commonly used automatic methods for variable selection. The calculation of the model should not be realized without examining the adequacy of the model. In Chapter 6, the authors describe methods for checking the conditions of the model, especially the proportionality of hazards and the goodness of fit, before they present and interpret the final model. Extending methods are presented in the next three chapters. In Chapter 7, methods based on the proportional hazard model are described. Hosmer and Lemeshow cover considerations of time dependant covariates—covariates with changing influence on survival probabilities in time—and they give hints on more extensive literature. In Chapter 8, parametric regression models are presented alternatively to the proportional hazard model. A great advantage in using such models is the complete specification of the model. It leads to a better prediction of survival times. However, more specific assumptions of the underlying survival process have to be made. Chapter 9 introduces further developments in the field of survival analysis in recent times. In each of these three chapters Hosmer and Lemeshow give a brief introduction and then refer to more far-reaching literature. Since new aspects in survival analysis are more and more presented in the scientific literature, the reader of this book gets a good overview of these new aspects going beyond the proportional hazard model. In summary it may be said that this book is very readable. Because of the above-mentioned detailed interpretation of the analysing steps and the description of corresponding pitfalls it can be recommended to all those who are about to use such models as well as to those who have already worked with them but want to revise their procedures.