What time is it? Choice of time origin and scale in extended proportional hazards models

The analysis of telemetry data offers many unique challenges due to both the observation process and the complexity of the underlying system (e.g., risk of mortality may be influenced by both age and a wide range of environmental variables). Although semi-parametric proportional hazards (SPPH) models have been proposed for analyzing ecological data, recent applications have failed to address the importance of choosing an appropriate time origin and scale for analysis. We compared models fit to a long-term deer (Odocoileus spp.) survival data set using three alternative survival timescales: age, time since start of study, and time since 6 June (with a seasonally recurrent timescale). Temporal variability in risk resulted from multiple sources (e.g., changes in hunting pressure, winter severity), and the risk of mortality varied nonlinearly with age (highest risk for young and older individuals). Age-varying hazards were represented well using regression splines, but temporal variability was more difficult to model using parametric assumptions. Annual survival estimates using the three timescales differed considerably. The model using a study-based timescale most closely tracked temporal patterns in risk. Given the difficulties in modeling temporal variability using parametric assumptions, we recommend this approach over an age-based or recurrent timescale when using SPPH models to evaluate the impact of large (naturally occurring or experimental) disturbances or to estimate annual age-specific survival rates. Lastly, we discuss the strengths and limitations of SPPH models relative to fully parametric approaches.