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Survival Models - Princeton University

Chapter 7 Survival ModelsOur final chapter concerns Models for the analysis of data which have threemain characteristics: (1) the dependent variable or response is the waitingtimeuntil the occurrence of a well-defined event, (2) observations arecen-sored, in the sense that for some units the event of interest has not occurredat the time the data are analyzed, and (3) there are predictors orexplanatoryvariables whose effect on the waiting time we wish to assess or control. Westart with some basic The Hazard and Survival FunctionsLetTbe a non-negative random variable representing the waiting time untilthe occurrence of an event. For simplicity we will adopt the terminologyof Survival analysis, referring to the event of interest as death and to thewaiting time as Survival time, but the techniques to be studied have muchwider applicability. They can be used, for example, to study age at marriage,the duration of marriage, the intervals between successive births to a woman,the duration of stay in a city (or in a job), and the length of life.

2 CHAPTER 7. SURVIVAL MODELS It will often be convenient to work with the complement of the c.d.f, the survival function S(t) = PrfT tg= 1 F(t) = Z 1 t f(x)dx; (7.1) which gives the probability of being alive just before duration t, or more generally, the probability that the event of interest has not occurred by duration t. 7.1.2 The Hazard ...

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