Partially hidden Markov model for time-varying principal stratification in HIV prevention trials

It is frequently of interest to estimate the intervention effect that adjusts for post-randomization variables in clinical trials. In the recently completed HPTN 035 trial, there is differential condom use between the three microbicide gel arms and the No Gel control arm, so that intention to treat (ITT) analyses only assess the net treatment effect that includes the indirect treatment effect mediated through differential condom use. Various statistical methods in causal inference have been developed to adjust for post-randomization variables. We extend the principal stratification framework to time-varying behavioral variables in HIV prevention trials with a time-to-event endpoint, using a partially hidden Markov model (pHMM). We formulate the causal estimand of interest, establish assumptions that enable identifiability of the causal parameters, and develop maximum likelihood methods for estimation. Application of our model on the HPTN 035 trial reveals an interesting pattern of prevention effectiveness among different condom-use principal strata.