Direct and Indirect Effects in a Survival Context

Abstract

A cornerstone of epidemiologic research is to understand the causal pathways from an exposure to an outcome. Mediation analysis based on counterfactuals is an important tool when addressing such questions. However, none of the existing techniques for formal mediation analysis can be applied to survival data. This is a severe shortcoming, as many epidemiologic questions can be addressed only with censored survival data. A solution has been to use a number of Cox models (with and without the potential mediator), but this approach does not allow a causal interpretation and is not mathematically consistent. In this paper, we propose a simple measure of mediation in a survival setting. The measure is based on counterfactuals, and measures the natural direct and indirect effects. The method allows a causal interpretation of the mediated effect (in terms of additional cases per unit of time) and is mathematically consistent. The technique is illustrated by analyzing socioeconomic status, work environment, and long-term sickness absence. A detailed implementation guide is included in an online eAppendix (http://links.lww.com/EDE/A476).

Understanding mechanisms: opening the “black box” in observational studies

“…The traditional way was performed in accord with an earlier study applying the same data, where the degree of reduction in rate ratios in models including the covariate were interpreted as a corresponding degree of mediation through that factor (24). The results of the counterfactual analysis were qualitatively in accordance with the mediating effect in ordinary Cox regression analysis, but the quantitative effect was stronger (17).…”

“…This approach is well suited for causal mediation analysis (16). Dynamic path analysis is an alternative for estimating direct and indirect effects (17,20,23). This method is particularly useful when time-to-event is the outcome, ie, in survival analysis (17,20).…”

“…One interesting possibility that has gained increased attention recently is to estimate direct and indirect effects in mediation analysis. Assessing the role of an intermediate between exposure and outcome -a mediator -could be considered as a way to open risk factor epidemiology's "black box", thereby improving the mechanistic understanding of an exposure-outcome relationship (15 (17). One realistic and interesting possibility is that the mediator might be more accessible for intervention than the exposure and therefore more valuable from a preventive point of view (15).…”

“…Dynamic path analysis is an alternative for estimating direct and indirect effects (17,20,23). This method is particularly useful when time-to-event is the outcome, ie, in survival analysis (17,20). Lange & Hansen (17) estimated the mediating role of the physical work environment on the relationship between SES and sickness absence.…”

“…Lange & Hansen (17) estimated the mediating role of the physical work environment on the relationship between SES and sickness absence. Two methods were compared: one traditional where Cox models with and without the covariate (work environment) were compared, and the other in a counterfactual analysis where exposure (SES) and covariates were time-dependent, modeling the rate using the the Aalen additive hazard model (17). The traditional way was performed in accord with an earlier study applying the same data, where the degree of reduction in rate ratios in models including the covariate were interpreted as a corresponding degree of mediation through that factor (24).…”