time dependency of Cox regression

array chip wrote:

Hi,

How can I specify a Cox proportional hazards model
with a covariate which i believe its strength on
survival changes/diminishes with time? The value of
the covariate was only recorded once at the beginning
of the study for each individual (e.g. at the
diagnosis of the disease), so I do not have the time
course data of the covariate for any given individual.
For example, I want to state at the end of the
analysis that the hazard ratio of the covariate is 6
at the beginning, decrease to 3 after 2 years and
decrease to 1.5 after 5 years.

If you fit a Cox model with the fixed covariate, plot(cox.zph(model)) will 
show you an estimate of how the log hazard ratio changes over time, with 
pointwise confidence intervals.

If you want more precise estimates and confidence intervals you can split 
up your covariate into a set of time-dependent covariates.

If you wanted a time period for each year up to 6 years you would make 6 
time dependent covariates, looking like

  x 0 0 0 0 0
  0 x 0 0 0 0
  0 0 x 0 0 0
  0 0 0 x 0 0
  0 0 0 0 x 0
  0 0 0 0 0 x

and have (up to) six records per person.  The survSplit() function in the 
survival package will do the splitting, you then need to set the 
appropriate terms to zero and fit the model.

 	-thomas