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

Abstract

Mediation analysis requires a number of strong assumptions be met in order to make valid causal inferences. Failing to account for violations of these assumptions, such as not modeling measurement error or omitting a common cause of the effects in the model, can bias the parameter estimates of the mediated effect. When the independent variable is perfectly reliable, for example when participants are randomly assigned to levels of treatment, measurement error in the mediator tends to underestimate the mediated effect, while the omission of a confounding variable of the mediator to outcome relation tends to overestimate the mediated effect. Violations of these two assumptions often co-occur, however, in which case the mediated effect could be overestimated, underestimated, or even, in very rare circumstances, unbiased. In order to explore the combined effect of measurement error and omitted confounders in the same model, the impact of each violation on the single-mediator model is first examined individually. Then the combined effect of having measurement error and omitted confounders in the same model is discussed. Throughout, an empirical example is provided to illustrate the effect of violating these assumptions on the mediated effect.

Genetically Informative Mediation Modeling Applied to Stressors and Personality-Disorder Traits in Etiology of Alcohol Use Disorder

“…Note, however, that these desirable power characteristics are not present to a comparable extent in all conceivable applications; for example, there is no biometric information in the exposure of randomized experiments because it is a purely environmental variable, by definition (i.e., forced by the experimenter; cf. Fritz et al 2016). In what follows, we use a model comparison criterion instead of null-hypothesis testing as it is a more suitable tool (see Methods), but the gains in power are nevertheless present implicitly.…”

“…When such “systemic” confounders are observed, researchers could add them as covariates to the biometric mediation model in a direct analogy to non-biometric mediation models or try developing an inverse probability weighted version of the model (Coffman and Zhong, 2012). Furthermore, researchers have developed techniques to investigate effects of omitted (systemic) variables and these could be used to estimate ‘plausible’ and/or ‘possible’ limits of confounding (Fritz et al, 2016; Imai et al, 2010; Mauro, 1990). Such sensitivity analyses investigate whether the parameter values required for change in sign or statistical significance of a model parameter of interest are mathematically possible and otherwise plausible.…”

“…If desired, one could extend this line of thought to a theoretical investigation of inferential effects of complex combinations of unobserved errors and omitted variables in different biometric components (cf. Fritz et al 2016). These further developments go beyond the present aim of establishing a useful connection between the basic mediation model and the twin design.…”

Comparing Models of Change to Estimate the Mediated Effect in the Pretest–Posttest Control Group Design

“…Unreliable measures of the mediator and dependent variables can substantially bias estimates of the mediated effect in most cases but the pattern of results can be complicated and even counter-intuitive in some cases (Fritz, Kenny, & MacKinnon, 2016; Hoyle & Kenny, 1999). In general, measurement error in the mediator leads to a reduced mediated effect and consequently an inflated direct effect in the single mediator model with linear relations.…”

Did you get any help? A post-hoc secondary analysis of a randomized controlled trial of psychoeducation for patients with antisocial personality disorder in outpatient substance abuse treatment programs

“…Indeed, in the present study, the effect of random assignment on perceived help (i.e., the a coefficient) and the association between perceived help and days abstinent (i.e., the b coefficient), were strong. However, this must be interpreted with great caution, as it is possible that third variables confounded the mediator and the dependent variable, a situation which could bias the estimate of the indirect effect [44]. Clearly, larger trials are needed to address potential mechanisms of action, including mediation through perceived help.…”