Latent Class Dynamic Mediation Model with Application to Smoking Cessation Data

Abstract

Traditional mediation analysis assumes that a study population is homogeneous and the mediation effect is constant over time, which may not hold in some applications. Motivated by smoking cessation data, we propose a latent class dynamic mediation model that explicitly accounts for the fact that the study population may consist of different subgroups and the mediation effect may vary over time. We use a proportional odds model to accommodate the subject heterogeneities and identify latent subgroups. Conditional on the subgroups, we employ a Bayesian hierarchical nonparametric time-varying coefficient model to capture the time-varying mediation process, while allowing each subgroup to have its individual dynamic mediation process. A simulation study shows that the proposed method has good performance in estimating the mediation effect. We illustrate the proposed methodology by applying it to analyze smoking cessation data.

Keywords: Bayesian inference; dynamic mediation; latent class; time-varying coefficients.

Figure 1:

Directed graph of latent class dynamic mediation model for intensive longitudinal data. Boxes represent observed variables: Z = (Z₁, …, Z_p)^T are p-dimensional covariates; X_t, M_t, and Y_t are the predictor, mediator and outcome at time t. In the smoking cessation example, they are the measured levels of negative mood, positive smoking outcome expectancies, and smoking urge, respectively. Circles represent unobserved constructs that underlie the latent classes and heterogeneity of the observed variables: C represents latent class membership; α_l(t), γ_l(t), β_l(t), δ_l(t), τ_l(t) are the class-specific time-varying parameters that are related to the mediation process, conditional on the latent class C = l; ${\sigma }_{\xi l}^2$, ${\sigma }_{1l}^2$, ${\sigma }_{\zeta l}^2$, ${\sigma }_{2l}^2$ are the class-specific time-invariant variance components that are related to the mediation process, conditional on the latent class C = l. The probability of belonging to a latent class is modeled as a function of baseline covariates Z.

Figure 2:

The estimated mediation effect of positive smoking outcome expectancies on the relationship between negative affect and smoking urge for two subgroups. The shade shows the 95% credible interval.

Figure 3:

The estimated proportion of mediation effects of the positive smoking outcome expectancies on the relationship between negative affect and smoking urge out of total effects of the negative affect on smoking urge for two subgroups. The blue line indicates the “non-mediated subgroup” and the black line indicates the “mediated subgroup”.

Figure 4:

Distribution of posterior predictive check statistics T(y, θ) and T(m, θ). Red line indicates the statistics calculated based on the observed data.