Meeting Brochure and registration form      SMDM Homepage

Saturday, 22 October 2005
57

OPTIMAL TIME TO INITIATE HIV THERAPY: A MARKOV DECISION PROCESS APPROACH

Steven M. Shechter, MS1, Matthew D. Bailey, PhD1, Andrew J. Schaefer, PhD1, Joyce C. Chang, PhD1, R. Scott Braithwaite, MD, MSc2, and Mark S. Roberts, MD, MPP1. (1) University of Pittsburgh, Pittsburgh, PA, (2) Yale University / VA Connecticut Healthcare System, West Haven, CT

Purpose:

Perhaps the most important unresolved question in HIV care is when to initiate highly active antiretroviral therapy for a HIV patient. We present a Markov decision process (MDP) model that considers the optimal time to start a patient on therapy as a function of the CD4 count.

Methods:

MDPs are mathematical techniques for solving stochastic, dynamic decision problems. They are applied to industrial engineering problems such as optimal machine replacement, in which periodic observations are made of a stochastic system and certain actions may be taken each period. This framework is well-suited to HIV therapy where physicians makes periodic observations of an asymptomatic patient and decide whether or not to start therapy. We model monthly observations of a patient's (categorized) CD4 count. The monthly probabilistic transitions from one CD4 category to other CD4 categories or death are based on a Markov model of the natural history of a patient's CD4 count. We estimated survival after starting therapy using a Weibull regression model with CD4 count as a covariate. With these two components, the MDP provides an analytic solution for the optimal pre-therapy treatment policy (i.e., start therapy or continue to wait) as a function of the CD4 category each month. MDPs have “structural properties”: provable statements indicating how the model will behave under specific conditions. These structural properties may provide insights concerning the actual process being modeled.

Results:

We created 5 CD4 categories: cat1: [0,50); cat2: [50,200); cat3: [200,350); cat4: [350, 500); cat5: [500, infinity). The Weibull-estimated post-therapy survival for each category was: 8.6, 10.0, 12.6, 15.9, and 20.1 years. We used a pre-therapy Markov transition probability matrix that implied the expected remaining life years of patients who never take therapy are: 3.9, 7.7, 10.9, 12.7, and 13.9 across categories. The solution of the MDP indicated that the optimal policy starts a patient on therapy when in cat1, waits when in cats2-4, and starts when in cat5. This resulted in expected remaining life years of: 8.6, 11.2, 15.2, 17.8, and 20.1.

Conclusion:

The data satisfied sufficient conditions to prove the optimal value vector was monotonically increasing in the CD4 category: higher CD4 categories resulted in higher expected remaining life years. However, the form of the optimal policy was not expected and requires further investigation.


See more of Poster Session I
See more of The 27th Annual Meeting of the Society for Medical Decision Making (October 21-24, 2005)