Flexible parametric modeling of survival from age at death data: A mixed linear regression framework

Correspondence Etienne Rouby, Centre d'études Biologiques de Chizé, UMR 7372, Villiersen-Bois, France. Email: etienne.rouby@univ-lr.fr Abstract Many long-lived vertebrate species are under threat in the Anthropocene, but their conservation is hampered by a lack of demographic information to assess population long-term viability. When longitudinal studies (e.g., Capture-MarkRecapture design) are not feasible, the only available data may be cross-sectional, for example, stranding for marine mammals. Survival analysis deals with age at death (i.e., time to event) data and allows to estimate survivorship and hazard rates assuming that the cross-sectional sample is representative. Accommodating a bathtub-shaped hazard, as expected in wild populations, was historically difficult and required specific models. We identified a simple linear regression model with individual frailty that can fit a bathtub-shaped hazard, take into account covariates, allow goodness-of-fit assessments and give accurate estimates of survivorship in realistic settings. We first conducted a Monte Carlo study and simulated age at death data to assess the accuracy of estimates with respect to sample size. Secondly, we applied this framework on a handful of case studies from published studies on marine mammals, a group with many threatened and data-deficient species. We found that our framework is flexible and accurate to estimate survivorship with a sample size of 300. This approach is promising for obtaining important demographic information on data-poor species.