We illustrate 2 techniques for estimating age-specific hazards with wildlife telemetry data: Siler's (Ecology 60:750-757, 1979) competing risk model fit using maximum likelihood and a penalized likelihood estimate that only assumes the hazard varies smoothly with age. In most telemetry studies, animals enter at different points in time (and at different ages), leading to data that are left-truncated. In addition, death times may only be known to occur within an interval of time (interval-censoring). Observations may also be right-censored (e. g., due to the end of the study, radio-collar failure, or emigration from the study area). It is important to consider the observation process, since the contribution of each individual's data to the likelihood will depend on whether data are left-truncated or censored. We estimate age-specific hazards using telemetry data collected in two Phases during a 13-year study of white-tailed deer (Odocoileus virginianus) in northern Minnesota. The hazards estimated from the two methods were similar for the full data set that included 302 adults and 76 neonates (followed since or shortly after birth). However, estimated hazards for early-aged individuals differed considerably for subsets of the data that did not include neonates. We discuss the advantages and disadvantages of these two modeling approaches and also compare the estimators using a short simulation study.
Bibliographical noteFunding Information:
Acknowledgments Our study was supported by the Minnesota Department of Natural Resources, Division of Fisheries and Wildlife, with supplemental funding provided by the Minnesota Environmental and Natural Resources Trust Fund, Minnesota Deer Hunters Association, and the Special Projects Foundation of the Minneapolis Big Game Club. The Cass County Land Department, the U. S. Forest Service, Potlatch Corporation, and Blandin Paper Company provided valuable cooperation. We gratefully acknowledge the assistance of D. W. Kuehn, B. A. Sampson, and about 145 field biology interns. We thank M. R. Riggs for helpful comments on an earlier draft.
- Maximum likelihood
- Penalized likelihood
- Siler hazard
- White-tailed deer