Sensitivity Plots for Confounder Bias in the Single Mediator Model

Abstract

Background Causal inference continues to be a critical aspect of evaluation research. Recent research in causal inference for statistical mediation has focused on addressing the sequential ignorability assumption; specifically, that there is no confounding between the mediator and the outcome variable. Objectives This article compares and contrasts three different methods for assessing sensitivity to confounding and describes the graphical depiction of these methods. Design Two types of data were used to fully examine the plots for sensitivity analysis. The first type was generated data from a single mediator model with a confounder influencing both the mediator and the outcome variable. The second was data from an actual intervention study. With both types of data, situations are examined where confounding has a large effect and a small effect. Subjects The nonsimulated data were from a large intervention study to decrease intentions to use steroids among high school football players. We demonstrate one situation where confounding is likely and another situation where confounding is unlikely. Conclusions We discuss how these methods could be implemented in future mediation studies as well as the limitations and future directions for these methods.

The Combined Effects of Measurement Error and Omitting Confounders in the Single-Mediator Model

“…Given that there may be multiple omitted confounders that exert their influences at different times and the true effects of each confounder are likely unknown, values to be used in these equations can be chosen based upon many different criteria. For example, values can be found by using the theoretical relation between a specific omitted variable and the included variables, by using prior research where the confounder was measured and included in a similar model, or by selecting values to examine the amount of bias in b and c′ that would result from omitting a confounder with specific effects (e.g., positive medium effects) on M and Y (see also Cox et al, 2014). Values of reliability used in the equations to assess how measurement error affects mediation analysis can be obtained from published studies and other prior information or by assessing how different hypothetical reliability values affect results.…”

“…Multiple methods to adjust for confounding when measures of confounders are available including principal stratification (Jo, 2008) and inverse probability weighting (Coffman & Zhong, 2012). In addition, multiple authors have explored methods to investigate the sensitivity of results to confounding (Cox, Kisbu-Sakarya, Miočević, & MacKinnon, 2014; Imai, Keele, & Yamamoto, 2010; Imai & Yamamoto, 2013; Liu et al, 2013; MacKinnon & Pirlott, 2015; VanderWeele, 2008, 2010, 2013). …”

Confounding in statistical mediation analysis: What it is and how to address it.

“…method (Mauro, 1990), the correlated residuals method (Imai, Keele, & Tingley, 2010), and VanderWeele’s method (VanderWeele, 2010). A thorough review of these three methods with R and SAS syntax to conduct them can be found in Cox et al (2014) and additional approaches to sensitivity analysis can be found in le Cessie (2016) and Albert and Wang (2015). We will focus on the L.O.V.E.…”

Statistical Approaches for Enhancing Causal Interpretation of the M to Y Relation in Mediation Analysis

“…Formulas for calculating a new mediated effect for different values of the correlation of a confounder and Y and the confounder and M are described in Cox, Kisbu-Sakarya, Miocevic, and MacKinnon (2013). As demonstrated in Figure S3 for the dissonance data example, a correlation of anxiety and dissonance of .54 and a correlation of anxiety and attitude of .60 would reduce the observed mediated effect to zero.…”