13_AS_3_lec_a

# For a justication see km section 88 in conjunction

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online