Survival Analysis of Loblolly Pine Trees With Spatially Correlated Random Effects

Loblolly pine, a native pine species of the southeastern United States, is the most-planted species for commercial timber. Predicting survival of loblolly pine following planting is of great interest to researchers in forestry science as it is closely related to the yield of timber. Data were collected from a region-wide thinning study, where permanent plots, located at 182 sites ranging from central Texas east to Florida and north to Delaware, were established in 1980–1981. One of the main objectives of this study was to investigate the relationship between the survival of loblolly pine trees and several important covariates such as age, thinning types, and physiographic regions, while adjusting for spatial correlation among different sites. We use a semiparametric proportional hazards model to describe the effects of covariates on the survival time, and incorporate the spatial random effects in the model to describe the spatial correlation among different sites. We apply the expectation-maximization (EM) algorithm to estimate the parameters in the model and conduct simulations to validate the estimation procedure. We also compare the proposed method with existing methods through simulations and discussions. Then we apply the developed method to the large-scale loblolly pine tree survival data and interpret the results. We conclude this article with discussions on the advantages of the proposed method, major findings of data analysis, and directions for future research. Supplementary materials for this article are available online.

火炬松（Loblolly pine）是美国东南部的本土松树种，也是商业用材林种植量最大的树种。预测火炬松栽植后的存活率备受林业科学领域研究者关注，因其与木材产量密切相关。本数据集源自一项区域尺度间伐试验，研究团队于1980—1981年在182个样点布设了固定样地，这些样点的分布范围从得克萨斯州中部向东延伸至佛罗里达州，向北至特拉华州。该研究的主要目标之一，是探究火炬松存活率与树龄、间伐类型、地貌区域等多项重要协变量之间的关联，并校正不同样点间的空间相关性。我们采用半参数比例风险模型（semiparametric proportional hazards model）刻画协变量对存活时间的影响，并在模型中纳入空间随机效应以描述不同样点间的空间相关性。我们使用期望最大化算法（expectation-maximization，EM）估计模型参数，并通过模拟实验验证该估计流程。此外，我们通过模拟实验与讨论将所提方法与现有方法进行对比。随后将所开发的方法应用于大规模火炬松存活数据集，并对分析结果进行解读。本文最后讨论了所提方法的优势、数据分析的主要发现以及未来研究方向。本文的补充材料可在线获取。