This nicely written monograph deals with the statistical analysis of right-censored lifetime data, when the population under study may contain some immunes. In mathematical terms, the unknown lifetime distribution is allowed to have some positive mass \(1-p\) at infinity. The authors discuss parametric and nonparametric methods to estimate or test hypotheses about \(p\), the fraction of susceptibles in the population. For this, the most important properties of the Kaplan-Meier estimator and likelihood methods for censored data are reviewed. The methodology is applied to several data sets. Since most of the material presented has not been available in textbook form, this book is highly recommended to both applied statisticians and theoretically oriented researchers in survival analysis.