Mediation Analysis for Censored Survival Data Under an Accelerated Failure Time Model

Abstract

Recent advances in causal mediation analysis have formalized conditions for estimating direct and indirect effects in various contexts. These approaches have been extended to a number of models for survival outcomes including accelerated failure time models, which are widely used in a broad range of health applications given their intuitive interpretation. In this setting, it has been suggested that under standard assumptions, the “difference” and “product” methods produce equivalent estimates of the indirect effect of exposure on the survival outcome. We formally show that these two methods may produce substantially different estimates in the presence of censoring or truncation, due to a form of model misspecification. Specifically, we establish that while the product method remains valid under standard assumptions in the presence of independent censoring, the difference method can be biased in the presence of such censoring whenever the error distribution of the accelerated failure time model fails to be collapsible upon marginalizing over the mediator. This will invariably be the case for most choices of mediator and outcome error distributions. A notable exception arises in case of normal mediator–normal outcome where we show consistency of both difference and product estimators in the presence of independent censoring. These results are confirmed in simulation studies and two data applications.

Systemic inflammation and the relationship between periodontitis, edentulism, and all‐cause mortality: A 17‐year prospective cohort study

“…Mediation analysis with time‐to‐event outcomes can be performed using Cox proportional hazard models, but this approach is suitable only for studying rare events (<10%) (Lapointe‐Shaw et al, 2018). In the current study, events (deaths) equated to 32.1% of the cohort, so we performed mediation analysis utilizing AFT models (Fulcher et al, 2017; Burgos Ochoa et al, 2020). The analysis revealed a statistically significant mediation effect of CRP; however, the proportion of the total effect that was mediated was small (10%) and the amount of the total effect that remained after adjustment for the mediator (the direct effect) was large.…”

A survival mediation model with Bayesian model averaging

“…Tchetgen 27 proposed a theory pertaining to estimation of natural direct and indirect effects with marginal structural Cox proportional hazards and additive hazards models. Fulcher et al 28 discussed the effect of censoring and truncation with respect to "product" and "difference" methods used to estimate the mediation effect under the accelerated failure time model. Lin et al 29 described the methodology for estimating mediation effects under a time-varying survival model.…”

In-Sample Hazard Forecasting Based on Survival Models with Operational Time

“…The model is still widely used and adapted to new problems in medical research. A recent modification of the AFT model has been introduced in Li and Jin (2018) and recent applications include AIDS research (Fulcher et al 2017) and cancer research (Cho et al 2018) among many others.…”