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This text introduces up-to-date statistical methods for survival data analysis in medicine and genetics. Along with classical results, it presents new developments in interval censoring, statistical diagnostics with time-dependent outcomes, analysis of ultrahigh-dimensional data sets, cure rate models, and repeated measure data. Suitable for both graduate students and biomedical researchers, the text covers applications in cancer studies, medical diagnosis, genetics, and genomics. It provides R code and example data sets online.