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Wei-Yann Tsai

2010-06-25
12:30:00 - 14:30:00

405 , Mathematics Research Center Building (ori. New Math. Bldg.)

Lecture 3:


Proportional Hazards Model is defined as h(t|z) = h0(t)exp bz, where where b is a p dimension unknown parameters that relates the covariate z to survival, h(t|z) is conditional hazard rate function give covariate z and h0(t)=h(t|z=0) is the baseline hazrd rate function. In addition, if T is continuous then Cox model can also be specified by S(t|z) = [S0(t)](exp bz).


Partial likelihood will be derived and be used to obtain the inference for the parameters b.


The following is a history review of partial likelihood estimation:


(1) 1972, Cox's original "conditional likelihood".


(2) Kalbfleisch and Prentice (1973). Marginal likelihood base on rank.


(3) Breslow (1974). Profile likelihood.


(4) Cox's "Partial likelihood" (1975).


Reading:


1. D.R. Cox (1972). Regression models and life-tables (with discussion), J. Roy. Statist. Soc. (B) 34, 187–220. (primary reading)


2. D.R. Cox (1975). Partial likelihood. Biometrika, 269-276. (secondary reading)


3. Breslow, N (1975). Covariance analysis of censored survival data. Biometrics, 89-99. (secondary reading)


4. JD Kalbfleisch, RL Prentice (1973). Marginal likelihoods based on Cox's regression and life model. Biometrika 60, 267-278. (secondary reading)


5. Tsiatis, A.A. (1981). A large sample study of Cox’s regression model. Ann. Statist. 93-108. (reading for PH.D. students)


6. PK Andersen, RD Gill(1982) Cox's regression model for counting processes: a large sample study. The Annals of Statistics, 1100-1120. (reading for PH.D. students)