Transcription of Parametric Survival Models - Princeton University
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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)}.
k(x) is the incomplete gamma function, de ned as I k(x) = Z x 0 k 1e xdx=( k): There is no closed-form expression for the survival function, but there are excellent algorithms for its computation. (R has a function called pgamma that computes the cdf and survivor function. This function calls kthe shape parameter and 1= the scale parameter.)
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