Cox model with additional info on the baseline

1. Cox model with additional info on the baseline Empirical Likelihood analysis of Cox proportional hazards regression model Mai Zhou Dept. of Statistics, University of Kentucky

2. Empirical Likelihood allows the statistician to employ likelihood methods, without having to pick a parametric family of distributions for the data. --- Owen • Empirical Likelihood allows for hypothesis testing and confidence region construction without an information/variance estimator.

3. For n observations, • independent, from the empirical likelihood is • EL(F) = Where

4. Censored Observations • For a right censored observation • The likelihood contribution is • For a left censored observation the contribution is • Interval censored:

5. Truncated observations For a left truncated observation (often referred toas delayed entry) : (entry time, survival time) = • The likelihood contribution is • If the survival time is right censored, then the likelihood contribution is

6. R = Gnu S/Splus http://cran.us.r-project.org + many add-on packages A Package for empirical likelihood with censored/truncated data Contributed package – emplik • Does Empirical likelihood ratio tests for mean or weighted hazard, based on left-truncated, right censored or left, right, doubly censored data.

7. Tests hypothesis of the form: with right, left, doubly censored data. Or with left-truncated, right censored data.

8. Emplik package also include Owen’s function elm( ) ported to R. > library(emplik) > el.cen.EM(x, d, fun=gfun, mu=62) • where x = survival times , d= censoring status, fun = predefined gfun (if ‘fun’ is left out, then fun=t, by default). mu = 62. One of the output is -2LLR =