6. Effects of Exposure on Prevalence and Cumulative Relative Risk: Direct and Indirect Effects in a Recursive Hazard Model

Abstract

This paper outlines decomposition methods for assessing how exposure affects prevalence and cumulative relative risk. Let x denote a vector of exogenous covariates and suppose that a single dimension of time t governs two event processes T(1) and T(2). If the occurrence of the event T(1) determines entry into the risk of the event T(2), then subgroup variation in T(1) will affect the prevalence T(2), even if subgroups in the population are otherwise identical. Although researchers often acknowledge this phenomenon, the literature has not provided procedures to assess the magnitude of an exposure effect of T(1) on the prevalence of T(2). We derive decompositions that assess how variation in exposure generated by direct and indirect effects of the covariates x affect measures of absolute and relative prevalence of T(2). We employ a parametric but highly flexible specification for baseline hazard for the T(1) and T(2) processes and use the resulting parametric proportional hazard model to illustrate the direct and indirect effects of family structure when T(1) is age at first sexual intercourse and T(2) is age at a premarital first birth for data on a cohort of nonhispanic white U.S. women.