Journal of Data Science

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.

In randomized controlled trials, individual subjects experiencing recurrent events may display heterogeneous treatment effects. That is, certain subjects might experience beneficial effects, while others might observe negligible improvements or even encounter detrimental effects. To identify subgroups with heterogeneous treatment effects, an interaction survival tree approach is developed in this paper. The Classification and Regression Tree (CART) methodology (Breiman et al., 1984) is inherited to recursively partition the data into subsets that show the greatest interaction with the treatment. The heterogeneity of treatment effects is assessed through Cox’s proportional hazards model, with a frailty term to account for the correlation among recurrent events on each subject. A simulation study is conducted for evaluating the performance of the proposed method. Additionally, the method is applied to identify subgroups from a randomized, double-blind, placebo-controlled study for chronic granulomatous disease. R implementation code is publicly available on GitHub at the following URL: https://github.com/xgsu/IT-Frailty.