Decomposition of longitudinal disparities: an application to the fetal growth-singletons study

Addressing health disparities across demographic groups remains a critical challenge in public health, with significant gaps in understanding how these disparities evolve over time. This paper extends the traditional Peters-Belson decomposition to a longitudinal setting, focusing on the role of a single explanatory variable, referred to as a modifier, that captures complex interactions with other covariates. The proposed method partitions disparities into 3 components: (i) the portion associated with differences in the conditional distribution of covariates, evaluated under a common distribution of the modifier across groups; (ii) the portion arising from differences in the distribution of the modifier and its interactions with other covariates; and (iii) the unexplained disparity not accounted for by observed covariates. Rather than aggregating the first 2 components into one "explained disparity," the proposed method allows for a separate characterization of temporal patterns in disparities, distinguishing those that are unassociated with the modifier from those that are associated with it. We illustrate the method using a fetal growth study, examining disparities in fetal development trajectories across racial and ethnic groups during pregnancy.