Comparing Cox model with Competing Risk model

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I have a competing risk data where a patient may die from either AIDS or
Cancer. I want to compare the cox model for each of the event of interest
with a competing risk model. In the competing risk model the cumulative
incidence function is used directly.

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  If you do want to persue the Fine-Gray model I would suggest using
software that already exists.  Find the "Task Views" tab on CRAN, and
follow it to "survival" and then look at the competing risks section.
There is a lot to offer.  I would trust it more than rolling your own
function.

  As an aside, modeling the subdistribution function is ONE way of
dealing with competing risks, but not everyone thinks that it is the
best way to proceed.  The model corresponds to a biology that I find
unlikely, though it makes for nice math.  Since the alternative is
discussed in a vignette that I haven't-yet-quite-written we won't persue
that any further, however. :-)

Terry Therneau