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Parametric Survival Models - Princeton University

Parametric Survival ModelsGerm an Rodr 2001; revised Spring 2005, Summer 2010We consider briefly the analysis of Survival data when one is willing toassume a Parametric form for the distribution of Survival Survival NotationLetTdenote a continuous non-negative random variable representing sur-vival time, with probability density function (pdf)f(t) and cumulative dis-tribution function (cdf)F(t) = Pr{T t}. We focus on thesurvival func-tionS(t) = Pr{T > t}, the probability of being alive att, and the hazardfunction (t) =f(t)/S(t). Let (t) = t0 (u)dudenote the cumulative (orintegrated) hazard and recall thatS(t) = exp{ (t)}.

The Gompertz distribution is characterized by the fact that the log of the hazard is linear in t, so (t) = expf + tg and is thus closely related to the Weibull distribution where the log of the hazard is linear in logt. In fact, the Gompertz is a log-Weibull distribution. This distribution provides a remarkably close t to adult mortality in

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