TAUS: Target-Age Unified Survival. Survival Analysis Without Assuming Proportional Hazards or Parameterising the...

Standard survival analyses often assume proportional hazards (PH) or impose parametric survival functions that poorly represent real populations. Ecological applications are further limited by missing age data. Since standard survival methods estimate probabilities of survival at birth, this introduces an important survivorship bias. To circumvent these modelling constraints, we developed a method that combines the Kaplan-Meier estimator with conditional probability theory to compute age-specific probabilities of survival up to some target age of choice $\tau$ . Marginalising this probability over the age distribution of the population yields $O_{\tau }$ , the probability that a randomly sampled individual of unknown age will outlive the target age $\tau$ . Notably, $\tau$ is set for each group independently, which allows accounting for differences in pace of life across populations. We tested its application using a simulation study and two real-world datasets, and compared its performance against that of Cox PH and parametric survival models. The PH assumption was violated in the three examples, rendering the Cox PH models inappropriate. Parametric models offered a better alternative, but the best parametric fit missed at least some key survival patterns in all examples. The TAUS method provided a valid description of survival patterns in all cases. Its output also allowed finer analysis of survival differences between populations. The TAUS method is also available as an R package (https://github.com/casasgomezuribarri/TAUS). This new method, free of the PH and parametric assumptions, allows the comparison of survival probabilities between populations with different age structures and rates of pace of life. This makes it suitable for a wide range of ecological applications, including in population viability analysis, epidemiology, or life-history theory.