[R] survival analysis and censoring

[Terry Therneau]

  In your particular case I don't think that censoring is an issue, at least not 
for the reason that you discuss.  The basic censoring assumption in the Cox 
model is that subjects who are censored have the same future risk as those who 
were a. not censored and b. have the same covariates.  
   The real problem with informative censoring are the covaraites that are not 
in the model; ones that I likely don't even know exist.  Assume for instance 
that some unknown exposure X, Perth sunlight say, makes people much more likely 
to get both of the outcomes.  Assume further that it matters, i.e., the study 
includes a reasonable number of people with and without this exposure.  Then 
someone who has an early heart attack actually has a higher risk of colorectal 
cancer than a colleague of the same age/sex/followup who did not have a heart 
attack, the reason being that the HA guy is more likely to be from Perth.
   
   Your simulation went wrong by not actually accounting for time.  You created 
an outcome table for CC & HD and added a random time vector to it.  If someone 
would have had CC at 2 years and now has HD at 1 year, you can't just change the 
status to make them censored at 2.  The gambling analogy would be kicking 
someone out of the casino just before they win -- it does odd things to the 
odds.
       Terry Therneau