The register extract I use here covers the period between 1990 and 2005. The information from the Register of Deaths and the Migration Register are given on a daily basis, meaning that the exact day of the event is known. The information from the Family Register, the Education Register and the Income Register is only updated annually, which means that the data are based on the individual’s status at January 1 of each year during the observation period.
The variables personal identification number of the partner, wealth, municipality of residence, and citizenship were coded as time-varying covariates. The covariate age gap to the spouse is also time-varying but was computed from existing variables. My data set includes only people aged 50 and over. At these advanced ages, education is unlikely to change, so this approach should give approximately the same results. The remaining variables, marital status, date of migration, and type of migration, as well as date of birth and date of death, were used to define the time periods under risk.
The variable sex is a time-constant covariate by nature, while education was assumed to be time-constant despite its inherently time-varying nature
The base population of my analysis is all married people aged 50 years and older living in Den. There are three ways for individuals to enter the study: (1) being married and 50 years old or older on January 1, 1990; (2) being married and becoming 50 years old between ; and (3) immigrating to Den, and being married, and being 50 years or older.
There are five possible ways to exit the study: (1) dying between ; (2) divorcing between ; (3) becoming widowed between ; (4) being alive on ; and (5) emigrating from Den.
Methods
I apply hazard regression models to examine the influence of the age gap to the spouse on the individual’s mortality. Hazard regression, also called event-history analysis or survival analysis, represents the most suitable analytical framework for studying the time-to-failure distribution of events of individuals over their life course. The general proportional hazards regression model is expressed by
Since the failure event in our analysis is the death of the individual, the baseline hazard of our model h0(t) is age, measured as time since the 50th birthday. It is assumed to follow a Gompertz distribution, defined as
where ? and ?0 are ancillary parameters that control the shape of the baseline hazard. The Gompertz distribution, proposed by Benjamin Gompertz in 1825, has been widely used by demographers to model human mortality data. The exponentially increasing hazard of the Gompertz distribution is a useful approximation for ages between 30 and 95. For younger ages, mortality tends to differ from the exponential curve due to infant and accident mortality. For advanced ages, the increase in the risk of death tends to decelerate so that the Gompertz model overestimates mortality at these ages (Thatcher, Kannisto, and Vaupel 1998). I Doorgaan met assume that the impact of this deceleration on my results is negligible because the number of married people over age 95 is extremely low.
Therefore, all regression models were calculated for females and males separately. It should be noted that the male and female models do not necessarily include the same individuals. If both spouses are aged 50 or older, a couple is included in all models. If only the husband is 50 years or older, a couple is included only in the male models. Correspondingly, a couple is only included in the female models if the wife is 50 years or older and the husband is 49 years or younger.