Estimation and Inference for the Mediation Proportion

Abstract

In epidemiology, public health and social science, mediation analysis is often undertaken to investigate the extent to which the effect of a risk factor on an outcome of interest is mediated by other covariates. A pivotal quantity of interest in such an analysis is the mediation proportion. A common method for estimating it, termed the "difference method", compares estimates from models with and without the hypothesized mediator. However, rigorous methodology for estimation and statistical inference for this quantity has not previously been available. We formulated the problem for the Cox model and generalized linear models, and utilize a data duplication algorithm together with a generalized estimation equations approach for estimating the mediation proportion and its variance. We further considered the assumption that the same link function hold for the marginal and conditional models, a property which we term "g-linkability". We show that our approach is valid whenever g-linkability holds, exactly or approximately, and present results from an extensive simulation study to explore finite sample properties. The methodology is illustrated by an analysis of pre-menopausal breast cancer incidence in the Nurses' Health Study. User-friendly publicly available software implementing those methods can be downloaded from the last author's website (SAS) or from CRAN (R).

Keywords: mediation analysis; mediation proportion; proportion of treatment effect; the difference method.

Figure 1

Relative bias of the mediation proportion estimator under the logistic model as a function of the mediation proportion (p), the correlation between the exposure and the mediator (ρ), the number of expected cases (E(N_cases)) and the outcome rate (P(Y = 1)). The value of ${\beta }_1^{\ast }$ was taken to be log(1.5).

Figure 2

Relative bias of the mediation proportion estimator under the Cox model as a function of the mediation proportion (p), the correlation between the exposure and the mediator (ρ), the number of expected cases (E(N_cases)) and the event rate (P(δ = 1)). The value of ${\beta }_1^{\ast }$ was taken to be log(1.5).