Quantile Mediation Models: A Comparison of Methods for Assessing Mediation Across the Outcome Distribution

Abstract

Recent introduction of quantile regression methods to analysis of epidemiologic data suggests that traditional mean regression approaches may not suffice for some health outcomes such as Body Mass Index (BMI). In the same vein, the traditional mean-based approach to mediation modeling may not be sufficient to capture the potentially different mediating effects of behavioral interventions across the outcome distribution. By combining methods for estimating conditional quantiles with traditional mediation modeling techniques, mediation effects can be estimated for any quantile of the outcome distribution (so-called quantile mediation effects). Estimation and inference techniques for quantile mediation effects are compared through simulation studies, and recommendations are given. The quantile mediation methods are further compared with the traditional mean-based regression approaches to mediation analysis through analysis of data from Healthy Places, a trial that is examining the effects of the community-built environment on resident obesity risk. We found the magnitudes of indirect (mediating) effects of walkability on BMI and waist circumference were substantially larger for the upper quantiles compared with the median or mean. Results suggest that restricting the examination of mediation to the mean of the outcome distribution provides an incomplete picture of proposed mediating mechanisms and in some cases may miss important mediational relationships to outcomes.

Quantile causal mediation analysis allowing longitudinal data

“…Because many observational studies collect longitudinal data, we also allow the mediator and outcome variables to be repeated measurements. This work generalizes previous work on mediation models now allowing for quantile estimation and longitudinal data …”

“…To estimate these effects, we need to expand standard mediation methods and consider quantiles of mediators and outcomes as dependent variables. Mediation formulae based on quantiles of the outcome distribution have been derived . However, these formulae focuses mostly on mean changes in the mediator or do not explicitly define the causal estimands as functions of potential outcomes .…”

“…Mediation formulae based on quantiles of the outcome distribution have been derived . However, these formulae focuses mostly on mean changes in the mediator or do not explicitly define the causal estimands as functions of potential outcomes . In this manuscript, we define and derive the controlled direct and the indirect effects along the distribution of the outcome with 2 quantile regression models, one for the mediator and one for the outcome.…”

“…14,26 However, these formulae focuses mostly on mean changes in the mediator 14 or do not explicitly define the causal estimands as functions of potential outcomes. 26 In this manuscript, we define and derive the controlled direct and the indirect effects along the distribution of the outcome with 2 quantile regression models, one for the mediator and one for the outcome. We formalize our estimands using the potential outcome framework and allow for an exposure-mediator interaction in the model for the outcome.…”

Investigating causal relation between prenatal arsenic exposure and birthweight: Are smaller infants more susceptible?

“…Causal mediation modeling techniques can be combined with quantile regression to identify the causal association between prenatal arsenic exposure and birthweight in relation to gestational age across birthweight percentiles (also called quantile causal mediation analysis) (51). This method has been demonstrated previously in social science research (52). Using this modeling approach, we will be able to determine whether prenatal arsenic exposure effects birthweight via shortening gestation as well as intrauterine growth restriction and that whether infants at the tails of birthweight distribution are more susceptible to arsenic exposure.…”