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

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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‐Mark‐Recapture 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.

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