survival analysis and censoring
Dear Prof. Therneau, Many thanks for this,
On 3/13/08, Terry Therneau <therneau at mayo.edu> wrote:
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.
I'm still astonished that this is the explanation, but I've spent an hour playing with my little R code model and this is exactly the problem. Score 1 for solid maths and 0 for my intuition. Many Thanks, Geoff
Terry Therneau