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HSRP 734: Advanced Statistical Methods July 10, 2008

Objectives. Describe the Kaplan-Meier estimated survival curveDescribe the log-rank testUse SAS to implement . Kaplan-Meier Estimate of Survival Function S(t). The Kaplan-Meier estimate of the survival function is a simple, useful and popular estimate for the survival function.This estimate incor

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HSRP 734: Advanced Statistical Methods July 10, 2008

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    1. HSRP 734: Advanced Statistical Methods July 10, 2008

    2. Objectives Describe the Kaplan-Meier estimated survival curve Describe the log-rank test Use SAS to implement

    3. Kaplan-Meier Estimate of Survival Function S(t) The Kaplan-Meier estimate of the survival function is a simple, useful and popular estimate for the survival function. This estimate incorporates both censored and noncensored observations Breaks the estimation problem down into small pieces

    4. Kaplan-Meier Estimate of the Survival Function S(t) For grouped survival data, Let interval lengths Lj become very small – all of length L=Dt and let t1, t2, … be times of events (survival times)

    5. Kaplan-Meier Estimate of the Survival Function S(t) 2 cases to consider in the previous equation Case 1. No event in a bin (interval) does not change — which means that we can ignore bins with no events

    6. Kaplan-Meier Estimate of the Survival Function S(t) Case 2. yj events occur in a bin (interval) Also: nj persons enter the bin assume any censored times that occur in the bin occur at the end of the bin

    7. Kaplan-Meier Estimate of the Survival Function S(t) So, as Dt ? 0, we get the Kaplan- Meier estimate of the survival function S(t) Also called the “product-limit estimate” of the survival function S(t) Note: each conditional probability estimate is obtained from the observed number at risk for an event and the observed number of events (nj-yj) / nj

    8. Kaplan-Meier Estimate of Survival Function S(t) We begin by Rank ordering the survival times (including the censored survival times) Define each interval as starting at an observed time and ending just before the next ordered time Identify the number at risk within each interval Identify the number of events within each interval Calculate the probability of surviving within that interval Calculate the survival function for that interval as the probability of surviving that interval times the probability of surviving to the start of that interval

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