Hidden Markov models for settings with interval-censored transition times and uncertain time origin: application to HIV genetic analyses

The simplicity and flexibility of Markov models make them appealing for investigations of the acquisition of HIV drug-resistance mutations, whose presence can define specific Markov states. Because the exact time of acquiring a mutation is not observed during clinical research studies on HIV infection, it is important that methods for fitting such models accommodate interval-censored transition times. Furthermore, many such studies include patients with extensive treatment experience prior to the onset of the studies. Therefore, the virus in these patients may have already acquired resistance mutations by study entry. Retrospective data regarding the time on treatment, which is often known or known with error, provide information about the acquisition rates before the start of a study. Finally, variability in the genetic sequences of circulating HIV creates uncertainty in the Markov states. This paper considers approaches to fitting Markov models to data with interval-censored transition times when the time origin and the Markov states are known with error. The methods were applied to AIDS Clinical Trial Group protocol 398, a randomized comparison of mono- versus dual-protease inhibitor use in heavily pretreated patients. We found that the estimated rates of acquiring certain classes of mutations depended on the presence of others, and that the precision of these estimates can be considerably improved by inclusion of retrospective data.