National Wildlife Health Center, United States Geological Survey 6006 Schroeder Road, Madison, Wisconsin, 53711.
Wildlife Biology Program and Avian Science Center, College of Forestry and Conservation, University of Montana Montana, 59812.
Ecol Evol. 2015 Feb;5(3):769-80. doi: 10.1002/ece3.1399. Epub 2015 Jan 17.
Event-time or continuous-time statistical approaches have been applied throughout the biostatistical literature and have led to numerous scientific advances. However, these techniques have traditionally relied on knowing failure times. This has limited application of these analyses, particularly, within the ecological field where fates of marked animals may be unknown. To address these limitations, we developed an integrated approach within a Bayesian framework to estimate hazard rates in the face of unknown fates. We combine failure/survival times from individuals whose fates are known and times of which are interval-censored with information from those whose fates are unknown, and model the process of detecting animals with unknown fates. This provides the foundation for our integrated model and permits necessary parameter estimation. We provide the Bayesian model, its derivation, and use simulation techniques to investigate the properties and performance of our approach under several scenarios. Lastly, we apply our estimation technique using a piece-wise constant hazard function to investigate the effects of year, age, chick size and sex, sex of the tending adult, and nesting habitat on mortality hazard rates of the endangered mountain plover (Charadrius montanus) chicks. Traditional models were inappropriate for this analysis because fates of some individual chicks were unknown due to failed radio transmitters. Simulations revealed biases of posterior mean estimates were minimal (≤ 4.95%), and posterior distributions behaved as expected with RMSE of the estimates decreasing as sample sizes, detection probability, and survival increased. We determined mortality hazard rates for plover chicks were highest at <5 days old and were lower for chicks with larger birth weights and/or whose nest was within agricultural habitats. Based on its performance, our approach greatly expands the range of problems for which event-time analyses can be used by eliminating the need for having completely known fate data.
事件时间或连续时间统计方法在整个生物统计学文献中都有应用，并导致了许多科学进展。然而，这些技术传统上依赖于知道失效时间。这限制了这些分析的应用，特别是在生态领域，标记动物的命运可能是未知的。为了解决这些限制，我们在贝叶斯框架内开发了一种综合方法来估计未知命运下的危险率。我们将已知命运的个体的失效/生存时间和间隔censored 的时间与未知命运的个体的信息结合起来，并对检测未知命运的动物的过程进行建模。这为我们的综合模型提供了基础，并允许必要的参数估计。我们提供贝叶斯模型及其推导，并使用模拟技术在几种情况下研究我们的方法的性质和性能。最后，我们使用分段常数危险函数来应用我们的估计技术，以研究年份、年龄、雏鸟大小和性别、养育成年个体的性别以及筑巢栖息地对濒危山鹬（Charadrius montanus）雏鸟死亡率危险率的影响。由于一些个体雏鸟的无线电发射器失效，传统模型不适合这种分析。模拟结果表明，后验均值估计的偏差最小（≤4.95%），后验分布表现符合预期，随着样本量、检测概率和生存率的增加，估计值的均方根误差（RMSE）减小。我们确定了山鹬雏鸟的死亡率危险率在<5 天时最高，而出生体重较大或巢位于农业栖息地的雏鸟的死亡率危险率较低。基于其性能，我们的方法通过消除对完全已知命运数据的需求，大大扩展了可以使用事件时间分析的问题范围。
