Background: Time-to-event data with multiple time scales are observed in many epidemiological and clinical studies. While models that allow for simultaneous consideration of multiple time scales for the hazard of an event have been proposed, their use is still not wide-spread in applied research. One reason for this might be the lack of convenient statistical software to estimate such models. Here we introduce the R-package TwoTimeScales. The package provides tools to estimate models for hazards that vary smoothly over two time scales, including proportional hazards models with such a two-dimensional baseline hazard. Extensions to competing risks models are implemented as well. Methodology is based on two-dimensional smoothing with P-splines. Results: We demonstrate the features of the R-package by analysing a freely available dataset containing post-surgery follow-up data on patients with breast cancer. We present two examples, a proportional hazards regression and a competing risks problem. Besides estimation, we illustrate the plotting utilities of the package. Conclusion: The R-package TwoTimeScales can be easily used to fit flexible hazard models with two time scales, allowing new perspectives in the analysis of time-to-event data with multiple time scales.

Despite the well-documented health disadvantages of single motherhood, research on single fathers' health remains limited owing to scarce data on this growing population. The influence of life course factors, such as partnership history and timing, on single parents' health is also understudied. Using high-quality register data on the total Danish population, this study (1) compares the mortality risk of single and partnered parents and (2) investigates heterogeneity in single parents' mortality by considering pathways into single parenthood, repartnering, child age, and episode length. Results show that single fathers have the highest all-cause mortality risk of all parent groups. Cause-specific analyses suggest that they are at especially high risk of dying by suicide or substance abuse. Mortality rates are higher for mothers entering single parenthood through being unpartnered than through partnership loss. Repartnering mitigates the negative effects of single parenthood. Mothers experiencing single parenthood when their youngest child was aged 1‒5 have lower mortality risk than peers who became single mothers of teenagers. The length of time spent as a single parent does not influence mortality. These findings highlight considerable diversity in parents' longevity and underscore the need for further attention to the health disadvantages of single fathers.

Competing risks models can involve more than one time scale. A relevant example is the study of mortality after a cancer diagnosis, where time since diagnosis but also age may jointly determine the hazards of death due to different causes. Multiple time scales have rarely been explored in the context of competing events. Here, we propose a model in which the cause-specific hazards vary smoothly over two times scales. It is estimated by two-dimensional P-splines, exploiting the equivalence between hazard smoothing and Poisson regression. The data are arranged on a grid so that we can make use of generalised linear array models for efficient computations. The R-package TwoTimeScales implements the model. As a motivating example we analyse mortality after diagnosis of breast cancer and we distinguish between death due to breast cancer and all other causes of death. The time scales are age and time since diagnosis. We use data from the Surveillance, Epidemiology and End Results (SEER) program. In the SEER data, age at diagnosis is provided with a last open-ended category, leading to coarsely grouped data. We use the two-dimensional penalised composite link model to ungroup the data before applying the competing risks model with two time scales.

Hazard models are the most commonly used tool to analyse time-to-event data. If more than one time scale is relevant for the event under study, models are required that can incorporate the dependence of a hazard along two (or more) time scales. Such models should be flexible to capture the joint influence of several times scales and nonparametric smoothing techniques are obvious candidates. P-splines offer a flexible way to specify such hazard surfaces, and estimation is achieved by maximizing a penalized Poisson likelihood. Standard observations schemes, such as right-censoring and left-truncation, can be accommodated in a straightforward manner. The model can be extended to proportional hazards regression with a baseline hazard varying over two scales. Generalized linear array model (GLAM) algorithms allow efficient computations, which are implemented in a companion R-package.

Event history models are based on transition rates between states and, to define such hazards of experiencing an event, the time scale over which the process evolves needs to be identified. In many applications, however, more than one time scale might be of importance. Here we demonstrate how to model a hazard jointly over two time dimensions. The model assumes a smooth bivariate hazard function, and the function is estimated by two-dimensional P-splines. We provide an R-package TwoTimeScales for the analysis of event history data with two time scales. As an example, we model transitions from cohabitation to marriage or separation simultaneously over the age of the individual and the duration of the cohabitation. We use data from the German Family Panel (pairfam) and demonstrate that considering the two time scales as equally important provides additional insights about the transition from cohabitation to marriage or separation.

Background: Certain migration contexts that may help clarify immigrants' health needs are understudied, including the order in which married individuals migrate. Research shows that men, who are healthier than women across most populations, often migrate to a host country before women. Using Danish register data, we investigate descriptive patterns in the order that married men and women arrive in Denmark, as well as whether migration order is related to overnight hospitalizations. Methods: The study base includes married immigrants who lived in Denmark between January 1, 1980 and December 31, 2014 (N = 13,680). We use event history models to examine the influence of spousal migration order on hospitalizations. Results: The order that married individuals arrive in Denmark is indeed highly gendered, with men tending to arrive first, and varies by country of origin. Risk of hospitalization after age 50 does not depend on whether an individual migrated before, after, or at the same time as their spouse among either men or women. However, among those aged 18+, men migrating before their wives are more likely to experience hospitalizations within the first 5 years of arrival. Conclusions: These findings provide the first key insights about gendered migration patterns in Denmark. Although spousal order of migration is not related to overnight hospitalization among women, our findings provide preliminary evidence that men age 18+ who are first to arrive experience more hospitalization events in the following 5 years. Future research should explore additional outcomes and whether other gendered migration contexts are related to immigrants' health.

Background: Women earn less than men at most career stages. Explanations for a gender gap in wages include gender differences in the allocation of household and domestic work. At the family level, a marital age difference is an important shared characteristic that might play a role in determining a woman’s career trajectory, and, therefore, her income. Since women tend to marry older men, we investigate whether women whose husbands are older have lower incomes than women whose husbands are the same age or younger. Objective: This study investigates whether the age gap between a woman and her partner was associated with her income in Denmark in 2010. Methods: We use data on Danish female twin pairs in 2010. Our design includes samples within twin pairs (n = 4,716) and pooled twin samples (n = 13,354) to account for differences in early household environments and uses unconditional quantile regression to model the association between the age gap and the woman's income. Results: We find a statistically significant association between the marital age gap and the woman's income. The form of this association appears to be complex and varies across the income and age gap distribution. However, the magnitude of the estimated effects is small in economic terms. Conclusions: These results suggest that the marital age gap is unlikely to be an important determinant of a woman’s income, at least in Denmark. Contribution: To our knowledge, this is the first study that explores the association between marital age differences and a woman's earnings using a twin design and high-quality register data.

ObjectivesTo explore temporal trends and individual-level determinants of hospital deaths at ages 50 and older in Denmark from 1980 to 2014. DesignIndividual-level register-based retrospective study. SettingDenmark, 1980 to 2014. ParticipantsAll deaths that occurred in Denmark from 1980 to 2014 among individuals 50 years or older (N = 1 834 437), extracted from population registers. MeasurementsA death was defined as a hospital death if the individual was admitted to the hospital as an inpatient and the date of discharge from the hospital is equal to the date of death. ResultsThe percentage of hospital deaths decreased in both sexes (all ages combined, men: 56% to 44%; women: 49% to 39%) and at ages 50 to 79, remained almost unchanged at ages 80 to 89, and increased in the oldest age group (90+ men: 27% to 32%; women: 18% to 24%). We observed increasing trends of hospital deaths for three groups, people 90 years and older, dying from respiratory diseases, and who had terminal hospitalizations lasting 1 to 3 days. Subanalysis of all hospital deaths according to length of the terminal hospitalizations suggests that the overall reduction of hospital deaths might be driven by a reduction in hospitalizations that were longer than 1 week. Persons who are married, have middle or high income, have a history of hospitalizations in the year before death, or die because of respiratory diseases have higher odds of dying in a hospital. ConclusionResults provide evidence that Danes 50 years and older are increasingly dying outside the hospital context. We find three age-specific patterns in the proportion of hospital deaths. Changes in healthcare and social systems implemented in Denmark during the observation period may underlie the broader reduction in hospital deaths in the country. J Am Geriatr Soc 67:471-476, 2019.