Quantifying Direct and Indirect Effects Through Joint Modeling of Terminal Events and Gap Times Between Recurrent Events
Pub. online: 1 April 2026
Type: Statistical Data Science
Open Access
Open Access
Received
24 July 2025
24 July 2025
Accepted
3 March 2026
3 March 2026
Published
1 April 2026
1 April 2026
Abstract
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.
Supplementary material
Supplementary MaterialSupplementary Material Sections I-IV mentioned in the main text are provided as a pdf supplement file. Data supporting the findings of this paper can be requested as described in the data availability statement on page 5 of the Supplementary Material. The SAS and R codes for the simulation and data analysis of this paper are available at https://github.com/nfang-cloud/Joint_Model_Gap_Time.
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