TAUS: Target-Age Unified Survival. Survival analysis without assuming proportional hazards or parameterising the survival function

ABSTRACT Standard survival analysis methods often rely on the assumption of proportional hazards (PH) or parameterisations of the survival function that might not be appropriate for wild populations. To enable survival analysis without these modelling constraints, we developed an approach that combines the Kaplan-Meier estimator with conditional probability theory to compute age-specific probabilities of survival up to some target age of choice τ. Marginalising this probability over the age distribution of the population yields Oτ, the probability that a randomly sampled individual of unknown age will outlive the target age τ. Notably, the value for τ is set by the analyst 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 model provided a valid description of survival patterns in all cases. Its richer output also allowed finer analysis of survival differences between populations. The TAUS model is also available as an R package (https://github.com/casasgomezuribarri/TAUS). This new approach to survival analysis without PH or parametric assumptions allows the comparison of survival probabilities across 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 Competing Interest Statement The authors have declared no competing interest.