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Non-Parametric Estimation in Survival Models

Non-Parametric Estimation in Survival Models Germ an Rodr guez Spring, 2001; revised Spring 2005. We now discuss the analysis of Survival data without parametric assump- tions about the form of the distribution. 1 One Sample: Kaplan-Meier Our first topic is Non-Parametric Estimation of the Survival function. If the data were not censored, the obvious estimate would be the empirical Survival function n = 1. X. S(t) I{ti > t}, n i=1. where I is the indicator function that takes the value 1 if the condition in braces is true and 0 otherwise. The estimator is simply the proportion alive at t. Estimation with Censored Data Kaplan and Meier (1958) extended the estimate to censored data. Let t(1) < t(2) < .. < t(m). denote the distinct ordered times of death (not counting censoring times). Let di be the number of deaths at t(i) , and let ni be the number alive just before t(i).

1.2 Non-parametric Maximum Likelihood The K-M estimator has a nice interpretation as a non-parametric maximum likelihood estimator …

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