Title: Decomposition of Longitudinal Disparities: an Application to the Fetal Growth-Singletons Study

Abstract: Addressing health disparities among different demographic groups is a key challenge in public health. Despite many efforts, there is still a gap in understanding how these disparities unfold over time. Our paper focuses on this overlooked longitudinal aspect, which is crucial in both clinical and public health settings. In this paper, we introduce a longitudinal disparity decomposition method that decomposes disparities into three components: the explained disparity linked to differences in the exploratory variables' conditional distribution when the modifier distribution is identical between majority and minority groups, the explained disparity that emerges specifically from the unequal distribution of the modifier and its interaction with covariates, and the unexplained disparity. The proposed method offers a dynamic alternative to the traditional Peters-Belson decomposition approach, tackling both the potential reduction in disparity if the covariate distributions of minority groups matched those of the majority group and the evolving nature of disparity over time. We apply the proposed approach to a fetal growth study to gain insights into disparities between different race/ethnicity groups in fetal developmental progress throughout the course of pregnancy.