An eight-state union history model with a transient phase after sexual debut and marriage

Age of entry into the population at risk and the following union sequences are essential inputs for demographic and sexually transmitted infection models. These inputs are usually estimated separately from retrospective reports and current-status marital state. We fit the full union history as one joint-model of eight-state competing continuous time Markov chain using Demographic and Health Survey data from four countries with one to six survey rounds each. The fitted intensities are therefore estimated against the same exposure, structually producing consistent estimates for the proportion in every state. To account for the high first-year marriage rate after sexual debut, the coincident reports of debut and marriage age, and the never-marrying group, we reparameterise flexible hazard functions as log hazards, add a transient phase after debut and after marriage. Our model fitted well to both age and duration domain in all four country. In the first years after debut, the rate of marriage is from 1.7 (95\% CI 1.0--2.9) times the later rate in Sierra Leone to 5.1 (95\% CI 4.7--5.5) times in Rwanda. The raised rate lasts on average from 1.2 (95\% CI 0.1--15.2) years in Sierra Leone to 3.5 (95\% CI 2.3--5.2) years in Malawi. By 27 years after marriage, the widowed proportion reaches 23.3\% (95\% CI 22.2--25.1) in Rwanda, compared to 0.7\% (95\% CI 0.2--6.5) at 29 years in S\~ao Tom\'e, where the later-union proportion is 52.3\% (95\% CI 43.9--66.4). The divorced proportion stays flat over duration since marriage, 12.9\% (95\% CI 12.3--13.5) at 19 years in Rwanda. The premarital interval is thus a mixture of a short and a long component which should be taken into account in demographic and transmission model. As early marriage is followed by faster replacement of the first union, a cross-sectional proportion divorced would understate the amount of dissolution. Our model provide a framework for estimating a complete set of union-history rates to be used in transmission or a fertility models.