Causal mediation analysis with a latent mediator

Abstract

Health researchers are often interested in assessing the direct effect of a treatment or exposure on an outcome variable, as well as its indirect (or mediation) effect through an intermediate variable (or mediator). For an outcome following a nonlinear model, the mediation formula may be used to estimate causally interpretable mediation effects. This method, like others, assumes that the mediator is observed. However, as is common in structural equations modeling, we may wish to consider a latent (unobserved) mediator. We follow a potential outcomes framework and assume a generalized structural equations model (GSEM). We provide maximum-likelihood estimation of GSEM parameters using an approximate Monte Carlo EM algorithm, coupled with a mediation formula approach to estimate natural direct and indirect effects. The method relies on an untestable sequential ignorability assumption; we assess robustness to this assumption by adapting a recently proposed method for sensitivity analysis. Simulation studies show good properties of the proposed estimators in plausible scenarios. Our method is applied to a study of the effect of mother education on occurrence of adolescent dental caries, in which we examine possible mediation through latent oral health behavior.

Keywords: Factor analysis; Measurement error; Mediation formula; Monte Carlo EM algorithm; Structural equations model.

Figure 1

(a) Standard mediation model: X, exposure; M, observed mediator; Y, final response. (b) Latent mediator model: X, exposure; U, unobserved mediator; Z₁, …, Z_M, observed intermediate variables; Y, final response.

Figure 2

Sensitivity analysis for dental data. ML estimates from hybrid model of direct (left panel) and indirect (right panel) effects versus sensitivity parameter, ϕ. Solid line, estimates; dotted lines, lower and upper 95% confidence interval bounds.