Problem with Cox regression Using drug dispensing data, I am trying to examine the association between proportion of days covered (PDC) by a drug and disease relapse. PDC is calculated by drug's supply divided by follow-up time. Events such as end of study and death are censored using Cox regression. Follow-up basically ends at disease relapse, death or end of study, whichever comes first. 
Example of patient:
Date: 1 Jan 2010 (hospital discharge), dispensed 30 days of drug
Date: 1 Feb 2010, dispensed 60 days
Date: 1 May 2010, dispensed 60 days
Disease relapse: 1 Aug 2010 (end of follow-up)
Duration of follow-up: 210 days (from 1 Jan to 1 Aug 2010)
PDC = (30 + 60 + 60) / 210 = 0.714
With the PDC, I divided the patients into PDC >=80% and PDC < 80%, and examine the rate of disease relapse. The HR associated with a category of PDC is derived using exposure information concurrent to the observed outcomes.
My results showed that a higher PDC (>=80%) is associated with higher HR (risk) of disease relapse, which does not make sense. I examined my data closer and found that those with disease relapse, appeared to have shorter follow-up time, which also tends to result in higher PDC values. This may be possible as the PDC usually becomes more accurate over a longer period of time. But in patients with the disease relapse, the follow-up time is cut and hence their PDC becomes higher, relative to those without relapse. 
Is there any way of handling this issue? I am not sure whether the PDC should be considered a time-varying covariate. Any help is appreciated. Thank you.
 A: Someone who dies within the time period covered by the first dispensed drug is automatically >=100%, right? So all early deaths may be misleading or at least not be able to tell you anything on your question (you have no idea whether they took the treatment and/or would have got new drug in time, but they are counted as having all their days covered). I also do not think you can get around that by looking at the period after the initially dispensed drug should have run out, because to an extent you run into the same problem after every single dispensing.
Additionally, it may just hard to keep up a good compliance with getting the treatment dispensed on time in the long run, but you don't get to the long-run unless you survive.
Furthermore, how is the treatment meant to be taken? Are you accounting for severity? E.g. if people that get better (or are less severe to start off with) stop taking the treatment (or get sloppy with getting more drug), you might get the observed association, too.
