Third-variable effect analysis with multilevel additive models

Abstract

Third-variable effect refers to the effect transmitted by third-variables that intervene in the relationship between an exposure and a response variable. Third-variable effect analysis has been broadly studied in many fields. However, it remains a challenge for researchers to differentiate indirect effect of individual factor from multiple third-variables, especially when the involving variables are of hierarchical structure. Yu et al. (2014) defined third-variable effects that were consistent for all different types of response (categorical or continuous), exposure, or third-variables. With these definitions, multiple third-variables can be considered simultaneously, and the indirect effects carried by individual third-variables can be separated from the total effect. In this paper, we extend the definitions of third-variable effects to multilevel data structures, where multilevel additive models are adapted to model the variable relationships. And then third-variable effects can be estimated at different levels. Moreover, transformations on variables are allowed to present nonlinear relationships among variables. We compile an R package mlma , to carry out the proposed multilevel third-variable analysis. Simulations show that the proposed method can effectively differentiate and estimate third-variable effects from different levels. Further, we implement the method to explore the racial disparity in body mass index accounting for both environmental and individual level risk factors.

Communication and COVID-19 Physical Distancing Behavior Among Dutch Youth

“…Both relations were estimated simultaneously in the mlma package for multi-level mediation (Yu & Li, 2020a, 2020b, however, without the covariates. Statistical relevance of the paths was determined based on bootstrapped confidence intervals and we established mediation when the confidence interval of the indirect relation via one of the psychosocial determinants did not include 0.…”

Multilevel mediation analysis on time-to-event outcomes: Exploring racial/ethnic disparities in breast cancer survival in California

“…Based on the definitions of third-variable effects byRef. 35, we derive the direct and indirect effects based on models (1), (2), and (4). In the following, f ′( x ) denotes the first derivative of function f on the random variable X and realized at X = x .…”

“…The R package mlma was developed by Yu et al 35 and has been updated to deal with time-to-event outcomes (versions 6.0-0 and after). In functions provided by the package, users need to specify potential mediator(s), predictor(s), outcome(s), covariate(s), and their transformation functions.…”

“…Finally, the function boot.mlma uses the bootstrap method in the multilevel third-variable analysis to generate the variance and confidence interval estimations. 35 The generic functions summary and plot help summarize the estimation results (estimates, variances, and confidence intervals) and depict relationships among variables.…”

“…34 proposed to use Bayesian mediation analysis to deal with hierarchical databases. Yu and Li 35 extended the definitions of third-variable effects (mediation or confounding effects) to multilevel data structures and proposed to use multilevel additive models to fit variable relationships. Using their method, the effects from multilevel paths relating exposure(s) through third-variable(s) to outcome(s) can be estimated.…”