Multistate approach for stochastic interventions on a time-to-event mediator in the presence of competing risks: A new R command within the CMAverse R package

To the Editor: CMAverse is the most comprehensive R package for reproducible causal mediation analysis.1 It now includes a new command, cmest_multistate, for scenarios represented by Figure A where the mediator and the outcome are competing time-to-events, which arise in biomedical and social sciences, such as bone marrow transplantation,2 health economics,3 and aging research.4 The cmest_multistate command is based on a multistate approach that jointly models a time-to-event mediator and a time-to-event outcome.5 Two causal estimands are proposed: RD (residual disparity), the difference in probability of surviving beyond time s between the exposed group (A = 1) and the unexposed group (A = 0), had the time to mediator (M) distribution g been fixed to that of the unexposed group, and SD (shifting distribution effect), the difference in probability of surviving beyond time s for the exposed group, had the time to mediator distribution been changed to that of the unexposed group. They can be expressed as follows:FIGURE.: A, Directed acyclic graph of the conditional independence assumptions of the exposure (A), the mediator (M), the outcome (S), and the baseline covariates (C). B, Multistate model representation of the three transitions of interest, where an individual could transit from the baseline state to the mediator event (transition 1), then from the mediator event to the outcome event (transition 3), or directly transit from the baseline state to the outcome event without experiencing the mediator event (transition 2). C, Bootstrap mean (in circle) and 95% confidence intervals for RDs (in black) and SDs (in gray), overlayed with theoretical values (in triangle), across time points 0.1, 0.5, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0.RDs=P(Sg0>s|A=1,C)−P(Sg0>s|A=0,C) SDs=P(Sg1>s|A=1,C)−P(Sg0>s|A=1,C), where S is the time to outcome, C is the baseline covariate vector, and ga=G(Mc)(A=a) is a random draw from the time to mediator distribution in group A = a, a stochastic intervention on the mediator. These effects are particularly relevant in health disparities settings where exposures are complex social constructions that cannot be intervened.6,7 Multistate modeling captures the following scenarios for transitions between the baseline state (0), the mediator (1), and the outcome (2): The individual (a) experiences the mediator event, then the outcome event, (b) experiences the outcome event only, and at this time is censored for the mediator event, (c) is censored for both the mediator event and the outcome event, (d) experiences the mediator event but is censored for the outcome event. Under the multistate modeling framework, RDs and SDs can be expressed in terms of transition-specific hazards and cumulative hazards.5 They are computed using the mstate package8 assuming transition-specific semi-parametric Cox proportional hazards models, where baseline hazards are estimated nonparametrically. Confidence intervals are obtained by parallel-computed nonparametric bootstrap. Assuming no unmeasured mediator–outcome confounders, the approach delivers estimates with causal interpretation. Identifiability assumptions are explained in depth in Valeri et al.5 We illustrate the validity of cmest_multistate on a simulated dataset by comparing its outputs with the theoretical values. The dataset (n = 1000) is simulated from the following Cox proportional hazards models for transition 1 (0→1), transition 2 (0→2), and transition 3 (1→2), represented in Figure B: λ01(t|A,C1,C2)=λ010ea1A+a2C1+a3C2=1.5⋅e1.9A+0.2C1+0.5C2 λ02(t|A,C1,C2)=λ020eb1A+b2C1+b3C2=1⋅eA−0.5C1−0.3C2 λ12(t|A,M,C1,C2)=λ120ec1A+c2M+c3C1+c4C2=0.8⋅e0.55A−0.15M−0.1C1−0.2C2, where λ..0 are constant baseline hazards, C1 is a Bernoulli covariate (P = 0.6), and C2 is a normal covariate with mean 1 and standard deviation 1. Time for transition 1 (tM) and time for transition 2 (tS) are first separately generated. If tM < tS, both event indicators δM and δS are set to 1 (event). Otherwise, δM and δS are set to 0 (censored) and 1, respectively. If tM < tS, tS is regenerated including M as an additional covariate. The time to censoring is independently generated using a uniform distribution, and δS is updated accordingly. Estimated means and 95% confidence intervals from 1000 bootstrap samples are plotted in Figure C, along with the corresponding theoretical values. Figure C indicates that cmest_multistate achieves low bias and successfully covers the theoretical values. We believe that the new command will contribute to health disparities research in areas where competing risks are prevalent. Under stronger no unmeasured confounding assumptions, such as no unmeasured exposure-outcome/exposure-mediator/exposure-induced mediator–outcome confounders, cmest_multistate can be used to estimate natural direct and natural indirect effects and be of interest to broader scientific settings. In future works, we aim to allow for time-varying confounders and more flexible modeling options.REFERENCES 1. Shi B, Choirat C, Coull BA, VanderWeele TJ, Valeri L. CMAverse: a suite of functions for reproducible causal mediation analyses. Epidemiology. 2021;32:e20–e22. Cited Here | Google Scholar 2. Klein JP, Shu Y. Multi-state models for bone marrow transplantation studies. Stat Methods Med Res. 2002;11:117–139. Cited Here | Google Scholar 3. Williams C, Lewsey JD, Mackay DF, Briggs AH. 2017. Estimation of survival probabilities for use in cost-effectiveness analyses: a comparison of a multi-state modeling survival analysis approach with partitioned survival and Markov decision-analytic modeling. Med Decis Making. 2017;37:427–439. Cited Here | Google Scholar 4. Johnson AL, Nystrom NC, Piper ME, et al. Cigarette smoking status, cigarette exposure, and duration of abstinence predicting incident dementia and death: a multistate model approach. J Alzheimers Dis. 2021;80:1013–1023. 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