Survival Analysis, a Self-Learning Text

Chapter 1. The basic ideas are considered: like event, survival time, censoring, survival function, hazard function. Data layouts and some descriptive measures are discussed. The principles of confounding and interaction are discussed. In a multivariable example the similarities and differences between linear, logistic regression and survival regression and the concept of a hazard ratio are discussed. This chapter was overall clear. In this book the hazard is introduced as the instantaneous potential per unit time for the event to occur. The derivation of the relationship between the hazard function and the survival function is not given (the author finds it not important, since a computer can do the calculations), while the calculations are easy to perform. We also missed a warning that censoring should be independent of the occurrence of an event. Competing risks and left censoring are mentioned but not treated in detail. Chapter 2. This chapter is about Kaplan-Meier curves, the log-rank test and the Peto test. The proof of the Kaplan-Meier formula is difficult to follow, just because the author is so hard trying to make it easy to understand. The log-rank test and Peto test are clearly explained. Chapter 3. Here the Cox Proportional Hazards model is discussed. The chapter starts with the computer output of a rather complex example with a treatment effect, a confounder plus an interaction term. Hereafter the general model is discussed. The partial likelihood is discussed but the formula is not given. The interpretation of the coefficients is discussed using the data example. Somewhere in the midst of several examples, the general rule is given, which is confusing. Chapter 4. Four different ways of checking the assumptions of the Cox model are discussed: log-log plots, comparing observed with model survival curves, Schonfeld's goodness of fit test and time dependent covariate methods. Suggestions are given about how to proceed in practice. Overall this is a good chapter, although the part about log-log plots is too elaborate. Chapter 5 is about stratification in the Cox model. There is a discussion of when to use stratification (if the PH assumption does not hold), and the possibility of interaction between the stratification variables and the other predictors is considered, with statistical tests. In Chapter 6 time dependent covariates are discussed. A distinction is made between two different situations. The first situation is a variable that changes in time (like employment status, smoking status). The second situation is a variable that is constant in time, but its effect on the hazard changes in time, so that the proportional hazards assumption does not hold. By multiplying the variable by some function of time, the model can be improved.