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Obsidian | Level 7

I have a general question about competing risk calculations and how they are presented in LIFETEST.  My dataset contains data on hospitalized patients undergoing cancer treatment.  Measurements are taken on patient survival vs death due to disease vs death due to treatment toxicity. This data is not too different from Example 74.4 in the LIFETEST procedure documentation in SAS/STAT 15.1. 


Why is the comparison done in terms of a cumulative incidence function (CIF) instead of some kind of survival curve?  Can the CIFs be translated somehow into a kind of cause-specific survival function?


The group I will be presenting to is used to seeing survival analysis in terms of the traditional survival curve sloping down and to the right.  I need to give a compelling reason why is it correct instead to use CIFs which slope up and to the right.  


My understanding is that one purpose of doing a competing risk LIFETEST procedure is to enable the analyst to test the hypothesis that two or more CIFs differ based on values of a stratification variable.  This requires Gray's test instead of the Log-Rank test.  So is it  possible that the cause-specific CIFs could be statistically different while the all-cause survival curves may not? 


I have read some of the literature on this and I'm trying to see if my understanding is correct.  Thanks for any input you may have. 


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