### 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 non-hispanic white U.S. women.

Original language | English (US) |
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Pages (from-to) | 185-232 |

Number of pages | 48 |

Journal | Sociological methodology |

Volume | 39 |

Issue number | 1 |

DOIs | |

State | Published - Aug 1 2009 |

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### ASJC Scopus subject areas

- Sociology and Political Science