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Joint Models for Investigating Fertility and Mortality Rates
Marie Böhnstedt, Jutta Gampe, Maciej Danko, Aleksandra Danko (Landesamt für Landwirtschaft, Lebensmittelsicherheit und Fischerei, Mecklenburg-Vorpommern, Rostock, Deutschland); in Zusammenarbeit mit Hein Putter (Leiden University, Medical Center, Niederlande)
Fertility and mortality are interdependent processes. Dependence may be in the direction of increased mortality due to the costs of reproduction, or it may be in the opposite direction due to individual capacities that allow for high levels of reproduction to go along with lower mortality. Understanding these mechanisms is essential in biodemography.
When the patterns of age-specific fertility and mortality for some species are unknown and need to be estimated, this interdependence introduces some extra complications in the statistical approach: The terminal event (death) is not independent of the recurrent event process (reproduction); conversely, fertility constitutes an internal time-varying covariate process for survival. So-called joint models (i.e., for the recurrent event process and the survival process) are thus required to produce unbiased estimates of age-specific fertility rates and death rates. Such models also allow us to assess the dependence between the two processes.
In this project, we developed strategies to estimate the rates of recurrent events and the hazard of death jointly when information on the recurrent event process is available as the number of events in given time intervals (rather that the exact event times). A joint frailty model with an additional dependence parameter that captures positive but also negative dependence between the processes was fitted. Covariates may affect both rates of the joint model. We also developed a score test for dependence before fitting the complex joint model.
The approach was applied to data for Eleutheria dichotoma derived from experiments in the Institute’s former Laboratory of Evolutionary Biodemography, where reproductive outcomes were recorded as individual interval-counts of produced offspring. The model has clearly shown a negative dependence, i.e., higher reproductive rates going along with lower mortality.
This model is not limited to biodemographic applications but can be used whenever a recurrent event process, observed as interval counts, and a possibly dependent terminal event is to be studied.
Biodemography, Statistics and Mathematics
Biometrical Journal. accepted. (2020)