Survival analysis is what you do when the outcome is a time to an event and some of your subjects have not had the event yet. That single wrinkle — censoring — breaks ordinary regression, and the field is the set of tools built to work around it.
State the prerequisite honestly, because it is the thing that most often goes wrong. This material assumes a course in probability and a working command of linear and logistic regression, including likelihood. If you do not have that, no ordering of survival texts will rescue you, which is why this path opens with two books that let you check rather than discover it halfway through a Cox model.
Checking the background
Statistical models is A. C. Davison's single-volume treatment of likelihood, generalised linear models and — usefully — survival data. If its chapters on likelihood inference read comfortably, you are ready. If they do not, work through it first.
Regression Modeling Strategies teaches the modelling craft the survival texts assume and rarely teach: splines, why not to select variables the way you were probably taught, validation, calibration. Frank Harrell applies all of it directly to Cox models, and these habits are far easier to acquire before you meet a new model class than after. Our record is the current second edition.
A first course
Survival Analysis: A Self-Learning Text is the gentlest entry in the field: Kleinbaum and Klein walk through every derivation with the answers on the facing page. Start here even if you find the format patronising. Our record is the second edition; buy the third, which adds competing risks and parametric models.
Applied Survival Analysis Using R is Dirk Moore's short, current, code-first companion. Read it in parallel rather than after — the theory sticks far better once you have fitted the model, and his coverage of the survival package is the practical half Kleinbaum leaves out.
Event History and Survival Analysis is Paul Allison's very short social-science entry, and a useful corrective if the medical framing of everything else does not match your data. It is unusually clear on discrete-time methods and is the standard reference for repeated events.
Survival analysis using the SAS system belongs on your shelf only if your workplace runs SAS, which much of pharma and clinical research still does. It is the practical reference for PROC LIFETEST and PROC PHREG. Our record is the first edition; the second is current.
The four standard applied texts
Modelling Survival Data in Medical Research is the best written of the four and the one to read cover to cover: model checking, parametric alternatives to Cox, sample size calculation, all worked on real trials. Our record is the 1994 first edition and Collett has been through four, with substantial differences — buy current.
Applied survival analysis is Hosmer and Lemeshow bringing to survival data the model-building discipline their logistic regression book made standard, which makes it the natural sequel to Harrell. Our record is the first edition; the second, subtitled Regression Modeling of Time-to-Event Data, is current.
Survival analysis, under that bare display title, is Klein and Moeschberger — the reference the others cite, and where you look up left truncation, interval censoring or a counting-process derivation. It is the full text in its first edition; the second is the one in print.
Statistical methods for survival data analysis is Elisa Lee, and it is here for one thing: the most methodical treatment of the parametric distributions — exponential, Weibull, log-normal, gamma — that the Cox-centric books skim. The current edition is co-authored with John Wang.
Four standard texts is more than most readers need. Collett is the one to read through; treat the other three as references and buy by question.
Where proportional hazards fails
Modeling survival data is Therneau and Grambsch, by the author of the R survival package: residuals, functional form, time-dependent effects, frailty, written by the person who implemented them. It is the most useful book here for diagnosing a model that is quietly wrong. The display title in our catalogue is truncated.
Analysis of Multivariate Survival Data is Hougaard on correlated failure times — paired organs, families, recurrent events — and the most complete treatment of frailty distributions anywhere. Reach for it when your observations are not independent, which is more often than the standard texts admit.
Dynamic regression models for survival data is Martinussen and Scheike on Aalen's additive hazards model and time-varying coefficients: the principled alternative when proportional hazards fails, rather than a patch on it. Mathematically the hardest book on the path, with counting processes and martingales throughout.
Applied Longitudinal Analysis closes on the neighbouring field, because joint models of longitudinal measurements and time-to-event are where a great deal of current applied work sits, and Fitzmaurice, Laird and Ware is the standard text for the repeated-measures half of that problem. The ordered path, with what each stage expects you to be able to do, is at /paths/pt_ai_survival-analysis.
