  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.
