For a justication see km section 88 in conjunction

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Unformatted text preview: Cox Regression Model Estimation of the full survival function Estimation of the survival function To estimate the survival function S (t ; Z ) with covariate vector Z based on a Cox model λ(t ; Z ) = λo (t ) exp{β Z T }) we need not only to fit a proportional hazards model (Cox model) to the data, and obtain the partial maximum likelihood estimates of the parameters β , but also to estimate the baseline cumulative hazard rate t Λo (t ) = 0 λo (s )ds . Note that S (t ) = e − 34/45 t 0 T λ0 (s )e β Z ds = S0 (t )e where S0 (t ) is the baseline survival function. βZ T , Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model Estimation of the full survival function Estimate of the baseline cumulative hazard rate Λ0 (t ) Breslow’s estimator of the baseline cumulative hazard rate Λ0 (t ) is ˆ Λ0 (t ) = tj ≤t dj , T i ∈R (tj ) exp{bZi } where b is the partial maximum likelihood estimate of β . (for a justification, see K&M, section 8.8, in conjunction with Technical Note 2 on page 258) Finally, since ˆ ˆ S0 (t ) = exp{−Λ0 (t )} we have 35/45 T ˆ ˆ S (t ) = S0 (t )exp(bZ ) . Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model Diagnostics for the Cox regression model 1 Introduction 2 Main assumption...
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This document was uploaded on 04/03/2014.

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