Identifying and Estimating Causal Direct Effects Under Unmeasured Confounding

Abstract

Causal mediation analysis provides techniques for defining and estimating effects that may be endowed with mechanistic interpretations. With many scientific investigations seeking to address mechanistic questions, causal direct and indirect effects have garnered much attention. The natural direct and indirect effects, the most widely used among such causal mediation estimands, are limited in their practical utility due to stringent identification requirements. Accordingly, considerable effort has been invested in developing alternative direct and indirect effect decompositions with relaxed identification requirements. Such efforts often yield effect definitions with nuanced and challenging interpretations. By contrast, relatively limited attention has been paid to relaxing the identification assumptions of the natural direct and indirect effects. Motivated by a secondary aim of a recent non-randomized vaccine prospective cohort study (NCT05168813), we present a set of relaxed conditions under which the natural direct effect is identifiable in spite of unobserved baseline confounding of the exposure-mediator pathway; we use this result to investigate the effect mediated by putative immune correlates of protection. Relaxing the commonly used but restrictive cross-world counterfactual independence assumption, we discuss strategies for evaluating the natural direct effect in non-randomized settings that arise in the analysis of vaccine studies. We revisit prior studies of semi-parametric efficiency theory to demonstrate the construction of flexible, multiply robust estimators of the natural direct effect and discuss efficient estimation strategies that do not place restrictive modeling assumptions on nuisance functions.

Figures (5)

• Figure 1: Directed acyclic graph (DAG) corresponding to SCM \ref{['SEM']}. We depict the endogenous variables with circles and exogenous variables with rectangles. For the sake of visual economy, we write all exogenous variables under the common set of exogenous factors $U$.
• Figure 2: DAG with unmeasured confounders $V$ affecting both exposure ($A$) and mediators ($Z$) but with no direct path between $V$ and the outcome ($Y$), reflecting Assumptions \ref{['ass:no-V-to-Y']} and \ref{['ass:equalE']}. The direct effect of $A$ on $Y$ is denoted via a dotted line, and the indirect effect through $Z$ with a dashed line. The lack of direct path between $V$ and $Y$ is emphasized through the red dotted rectangle. We depict the observed variables with circles and unobserved variables with rectangles, omitting $U$ from the graph for the sake of visual economy.
• Figure 3: Simulation study: Impact of unmeasured exposure--mediator confounding. The dashed horizontal lines represent the desired asymptotic values of each metric. These values are zero for bias and variance, one for the normalized MSE, and 0.95 for coverage of 95% Wald-type CIs. The dashed line for the normalized MSE corresponds to the asymptotic efficiency bound when there is no unmeasured confounding $(\gamma=0)$.
• Figure 4: Simulation study: Application in a vaccine prospective cohort study. The dashed lines indicate the desired asymptotic values of each metric, as in Figure \ref{['fig:sim-results']}. The One-Step and TMLE estimators correspond to the estimators that explicitly estimate the two-phase sampling mechanism. The One-Step (Obs. Weights) and TMLE (Obs. Weights) estimators correspond to the estimators that incorporate the two-phase sampling weights as observations weights.
• Figure 5: Application in the CoVPN 3008 study. Test statistic $t$ (y-axis) measuring the degree of deviation from $H_0$ versus plausible more protective (to left) and less protective (to right) total $\psi_\text{RR}$ values (x-axis). The red vertical dashed line corresponds to the value of $\psi_\text{RR}$ considered as $H_0$ in our primary analysis. The horizontal dashed line corresponds to the null hypothesis of no protective effect.

Theorems & Definitions (10)

• Theorem 1
• Corollary 1
• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof
• Lemma 4
• proof