Randomized interventional effects in semicompeting risks

TL;DR

The randomized interventional approach to time-to-event outcomes, where both intermediate and terminal events are subject to right censoring, is extended and matched unrelated donor transplantation is preferable in terms of survival rates under the use of post-transplantation PTCy GVHD prophylaxis for lymphoma patients.

Abstract

In clinical studies, the risk of the primary (terminal) event may be modified by intermediate events, resulting in semicompeting risks. To study the treatment effect on the terminal event mediated by the intermediate event, researchers wish to decompose the total effect into direct and indirect effects. In this article, we extend the randomized interventional approach to time-to-event outcomes, where both intermediate and terminal events are subject to right censoring. We envision a random draw for the intermediate event process from a reference distribution, either marginally over time-varying confounders or conditionally given the observed history. We present the identification formula for interventional effects. We also discuss some variants of the identification assumptions. We estimate the treatment effects using nonparametric maximum likelihood estimation and propose a sensitivity analysis. We study the effect of matched unrelated donor versus haploidentical donor on death mediated by relapse in a hematopoietic cell transplantation study with graft-versus-host disease (GVHD) as the time-varying confounder. We find that matched unrelated donor transplantation is preferable in terms of survival rates under the use of post-transplantation PTCy GVHD prophylaxis for lymphoma patients.

Figures (3)

• Figure 1: A graph illustrating the events. Red lines indicate the paths to deliver treatment effect on the intermediate event, and green lines indicate the paths to deliver treatment effect on the terminal event. Baseline confounders are omitted for simplicity.
• Figure 2: Directed acyclic graphs (DAGs) for the counting processes. In the left figure, the counting processes are at the natural level. In the right figure, the counting process of the intermediate event is replaced by the draw $G(\cdot)$. The black arrows to $G(\cdot)$ represent deterministic relationships, in that the draw of $G(t)$ is only meaningful if $G(t^-)=\tilde{N}_2(t^-)=0$. Colored arrows represent that the treatment affects the hazards (intensities). The gray $U_1$ is an unobserved confounder within the $L(\cdot)$ process, and the gray $U_2$ is an unobserved confounder between $L(\cdot)$ and $\tilde{N}_1(\cdot)$. Baseline confounders are omitted for simplicity.
• Figure 3: Estimated cumulative incidence functions of death associated with Haplo-HCT, MUD-HCT, and in the counterfactual worlds; estimated interventional effects and conditional interventional effects. The solid lines are $F(t;z)$, and the dashed lines are $F(t;z,z)$: they are very close to each other. Confidence intervals are obtained by bootstrapping. Upper: model without frailty; Lower: model with frailty.

Theorems & Definitions (3)

• Theorem 1
• Remark 1
• Remark 2