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The aim of this work is to develop methods for studying the determinants ofmarriage incidence using marriage histories collected under two different typesof retrospective cross-sectional study designs. These designs are: sampling ofever married women before the cross-section, a prevalent cohort, and samplingof women irrespective of marital status, a general cross-sectional cohort.While retrospective histories from a prevalent cohort do not identify incidencerates without parametric modelling assumptions, the rates can be identifiedwhen combined with data from a general cohort. Moreover, education, a strongendogenous covariate, and marriage processes are correlated. Hence, they needto be modelled jointly in order to estimate the marriage incidence. For thispurpose, we specify a multi-state model and propose a likelihood-basedestimation method. We outline the assumptions under which a likelihoodexpression involving only marriage incidence parameters can be derived. This isof particular interest when either retrospective education histories are notavailable or related parameters are not of interest. Our simulation resultsconfirm the gain in efficiency by combining data from the two designs, whiledemonstrating how the parameter estimates are affected by violations of theassumptions used in deriving the simplified likelihood expressions. Two IndianNational Family Health Surveys are used as motivation for the methodologicaldevelopment and to demonstrate the application of the methods.

Estimation of marriage incidence rates by combining two cross-sectional retrospective designs: Event history analysis of two dependent processes