Survival Analysis of Loblolly Pine Trees With Spatially Correlated Random Effects

Abstract

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.

• Cox model
• EM algorithm
• Forestry
• Spatial frailty
• Time-dependent covariates
• Time-to-event data

Additional information

Notes on contributors

Jie Li

Jie Li is Assistant Professor (E-mail: [email protected])

Yili Hong

Yili Hong is Associate Professor (E-mail: [email protected]),Department of Statistics, Virginia Tech, Blacksburg, VA 24061.

Ram Thapa

Ram Thapa is Research Scientist (E-mail: [email protected])

Harold E. Burkhart

Harold E. Burkhart is University Distinguished Professor (E-mail: [email protected]), Department of Forest Resources and Environmental Conservation, Virginia Tech, Blacksburg, VA 24061.