Suppose we have a population $P$ that we are interested in. We want to track the onset of particular conditions (i.e. $A$, $B$ and $C$). Suppose that as blood pressure drops, these events occur. So $C$ is associated with a higher level drop of blood pressure. How would we use survival analysis to analyze this situation?
I was going to suggest competing risk models. There has been a recent revival of this subject because of its importance in medicine. Here is a very detailed article from Statistics in Medicne 2005 that is a nice tutorial with many references and software tools in R and SAS. I went to a conference where Jason Fine presented his work on competing risk and the Fine-Gray model. I think I mentioned it and Crowder's book in an answer to a previous question on CV. You can find Fine's two major papers and much more in the tutorial style article I gave in the link above.
It appears that Julien's link is a similar one to mine, also a tutorial covering competing risk but his has more references because it also includes multistate models but does not include all the references and software in my link. Oddly they are both tutorials for Statistics in Medicine.
Note: the link to Statistics in Medicine paper is not working any more, but the paper got cached on archive.org and can be found there. The paper is referenced as: Gichangi, A. & Vach, W. (2005). The analysis of competing risks data: A guided tour. Statistics in Medicine, but it does not seem to have appeared in Statistics in Medicine journal yet.