Quantifying Direct and Indirect Effects through Joint Modeling of Terminal Events and Gap Times between Recurrent Events.

Joint models can describe the relationship between recurrent and terminal events. Typically, recurrent events are modeled using the total time scale, assuming constant covariate effects on each recurrent event. However, modeling the gap time between recurrent events could allow varying covariate effects and offer greater flexibility and accuracy. For instance, in HIV-infected patients, the intervals between the first occurrence of opportunistic infections (OIs) may follow a different distribution compared to later OIs. However, limited research has focused on mediation analysis using joint modeling of gap times and survival time. In this work, we propose a novel joint modeling approach that studies the mediation effect of recurrent events on survival outcomes by modeling the recurrent events by gap time. This allows us to handle cases where the first occurrence of a recurrent event behaves differently from subsequent events. Additionally, we use a relaxed "sequential ignorability" assumption to address unmeasured confounding. Simulation studies demonstrate that our model performs well in estimating both model parameters and mediation effects. We apply our method to an AIDS study to evaluate the comparative effectiveness of two treatments and the effect of baseline CD4 counts on overall survival, mediated by recurrent opportunistic infections modeled through gap times.