Well I don't know any specific technique from time series applied to medicine. However actuarial science (contingency and survival theory)  has a lot of aplicattions to medicine such as fitting parametric and non parametric (life tables) model to asses this problem. You can have a look to survival theory. 

Here you can download great book about this topic:

http://www.google.cz/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&uact=8&ved=0ahUKEwj6ybP-loLLAhVFtQ8KHY-VAZEQFgg-MAQ&url=http%3A%2F%2Fdisciplinas.stoa.usp.br%2Fpluginfile.php%2F183701%2Fmod_folder%2Fcontent%2F0%2FHosmer%2520D.W.%2C%2520Lemeshow%2520S.%2520Applied%2520Survival%2520Analysis.pdf%3Fforcedownload%3D1&usg=AFQjCNG-4mEAa1Jrwc6k1lCgM3bfN8oV9g&bvm=bv.114733917,d.bGQ

Time series analysis is applied to many different problems in medicine. Try e.g. to searching for *time series" at PubMed: https://www.ncbi.nlm.nih.gov/pubmed/?term=%22time+series%22. As alluded to in the answers above, the perhaps most prominent use that springs to mind is the use of time series models to forecast mortality.

Dear Dimitri:

First let us know what you want to do o respond (the research question), because the time series o actual methods are usually applied when the main objective is to evaluate the time elapsed between two events, for instance, the time elapse between the first diagnosis and the occurrence of some complications, recovering health, or death. As you will see the basic data her are the occurrence dates.