### 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) |
---|---|

Pages (from-to) | 185-232 |

Number of pages | 48 |

Journal | Sociological Methodology |

Volume | 39 |

Issue number | 1 |

DOIs | |

State | Published - Aug 2009 |

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### ASJC Scopus subject areas

- Sociology and Political Science

### Cite this

**Effects of exposure on prevalence and cumulative relative risk : Direct and indirect effects in a recursive hazard model.** / Wu, Lawrence L.; Martin, Steven P.

Research output: Contribution to journal › Article

*Sociological Methodology*, vol. 39, no. 1, pp. 185-232. https://doi.org/10.1111/j.1467-9531.2009.01212.x

}

TY - JOUR

T1 - Effects of exposure on prevalence and cumulative relative risk

T2 - Direct and indirect effects in a recursive hazard model

AU - Wu, Lawrence L.

AU - Martin, Steven P.

PY - 2009/8

Y1 - 2009/8

N2 - 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 T1 and T2. If the occurrence of the event T1 determines entry into the risk of the event T2, then subgroup variation in T1 will affect the prevalence T2, 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 T1 on the prevalence of T2. 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 T2. We employ a parametric but highly flexible specification for baseline hazard for the T 1 and T2 processes and use the resulting parametric proportional hazard model to illustrate the direct and indirect effects of family structure when T1 is age at first sexual intercourse and T2 is age at a premarital first birth for data on a cohort of non-hispanic white U.S. women.

AB - 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 T1 and T2. If the occurrence of the event T1 determines entry into the risk of the event T2, then subgroup variation in T1 will affect the prevalence T2, 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 T1 on the prevalence of T2. 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 T2. We employ a parametric but highly flexible specification for baseline hazard for the T 1 and T2 processes and use the resulting parametric proportional hazard model to illustrate the direct and indirect effects of family structure when T1 is age at first sexual intercourse and T2 is age at a premarital first birth for data on a cohort of non-hispanic white U.S. women.

UR - http://www.scopus.com/inward/record.url?scp=69149099604&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=69149099604&partnerID=8YFLogxK

U2 - 10.1111/j.1467-9531.2009.01212.x

DO - 10.1111/j.1467-9531.2009.01212.x

M3 - Article

VL - 39

SP - 185

EP - 232

JO - Sociological Methodology

JF - Sociological Methodology

SN - 0081-1750

IS - 1

ER -