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Unformatted text preview: Chapter 7: Analysis of Censored Data 1. Estimating the Survival Function Censored Data T : the survival time of an experimental unit * the exact value might not be known * sometimes it is only known that T exceeds some threshold suppose that the true life time T 1 ,...,T n iid F with F continous observations are X i = min ( T i ,C i ) where C i is the censoring time Example 1 Kaplan-Meier Estimate the survival function (the reliability function) R ( t ) = Pr ( T > t ) = 1- F ( t ) no censoring R ( t ) = 1- F ( t ) where F ( t ) is the empirical cdf censored data: Kaplan-Meier estimate * data x i : uncensored x + i : censored * notations t 1 < t 2 < t D : the distinct event times that are observed n i : number of observations that are known to have survived t i or longer d i : number of events at t i i = 1 , 2 ,...,D * Kaplan-Meier estimate R ( t ) = braceleftBigg 1 if t < t 1 producttext i : t i t parenleftBig 1- d i n i parenrightBig...
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- Spring '08