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
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