Time-varying mediation analysis for incomplete data with application to DNA methylation study for PTSD

DNA methylation (DNAm) has been shown to mediate causal effects from traumatic experiences to post-traumatic stress disorder (PTSD). However, the scientific question about whether the mediation effect changes over time remains unclear. In this paper, we develop time-varying structural equation models to identify cytosine-phosphate-guanine (CpG) sites where DNAm mediates the effect of trauma exposure on PTSD, and to capture dynamic changes in mediation effects. The proposed methodology is motivated by the Detroit Neighborhood Health Study (DNHS) with high-dimensional and longitudinal DNAm measurements. To handle the non-monotone missing DNAm in the dataset, we propose a novel Longitudinal Multiple Imputation (LMI) method utilizing dependency among repeated measurements, and employ the generalized method of moments to integrate the multiple imputations. Simulations confirm that the proposed method outperforms existing approaches in various longitudinal settings. In DNHS data analysis, our method identifies several CpG sites where DNAm exhibits dynamic mediation effects. Some of the corresponding genes have been shown to be associated with PTSD in the existing literature, and our findings on their time-varying effects could deepen the understanding of the mediation role of DNAm on the causal path from trauma exposure to PTSD risk. ### Competing Interest Statement The authors have declared no competing interest.