Thought I'd try to do a little modeling of these failure rates. I do think that the question regarding failure approaching 100% is not if, but when. But 'when' is still a very important question. I think it is many years away.
In the discussion below, I'll use weeks as a convenient time interval.
Assumptions:
1) there are two populations of people who start a given PI: those who already have resistant strains, and those who don't.
2) there is a constant mutation rate. This implies that the conditional probability of a resistant strain developing during any particular week, conditioned on it not having developed by the beginning of that week, is constant over time.
3) the mutation rate is proportional to the viral load.
Under these assumptions, we should see the following characteristics of PI resistance:
a) there should be a relatively high initial failure rate as the population with resistant strains is likely to fail quickly.
b) IF the viral load is constant, then the time-to-failure (yes, I'm an engineer) for the other population should be exponentially distributed. This means that a patient's probability of NOT failing treatment during a given N-week period remains constant, and is of the form p=exp(-rN) --- we don't know what r is, but my assumptions say it is proportional to the viral load. A very rough guess says that for the patients in the Agouron study, at 48 weeks, it is in the vicinity of .002.
c) It seems reasonable to expect viral load to decrease over time in compliant patients, until such time as the resistant strain shows up. So, the longer a patient responds, the better their chances to keep responding. BTW, I've asked AGPH what "responding" really means in their annual report. No answer yet. But I still don't see any evidence that it is inevitable that failure rates will approach 100% in 1, 5, or even 20 years. More than enough time for a whole slew of new drugs to appear.
d) Conversely, non-compliant patients have a risk of increasing their r values sharply for brief periods of time.
The sensitivity of the assays is critically important. It would be helpful to know whether the viral load really does continue dropping, or hovers around 499 copies. Not to mention the effects of "reservoirs."
All are welcome to pick apart, or hopefully, extend this model. I'll start: as time goes on, the first population will make up a greater and greater proportion of the total, so any PI which has been widely used will become less and less effective in supposedly PI-naive patients.
DISCLAIMERS: 1. The above is a bit disorganized. Too bad. It's meant to stimulate discussion, not to be a thorough analysis. 2. In case it is not embarrassingly obvious, I know next to nothing about biochemistry, epidemiology, virology, etc. etc. and it's quite possible that one or more of my assumptions is absolutely ludicrous. I'm sure someone will let me know, gently, if this is the case. |
