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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 ˆ R ( t ) = 1- ˆ F ( t ) where ˆ 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 ˆ R ( t ) = braceleftBigg 1 if t < t 1 producttext i : t i ≤ t parenleftBig 1- d i n i parenrightBig...
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This note was uploaded on 07/22/2011 for the course STA 4502 taught by Professor Staff during the Spring '08 term at University of Florida.
- Spring '08