Modeling Clustered Survival Times of Loblolly Pine with Time-dependent Covariates and Shared Frailties

Tree mortality is an important component of forest tree and stand growth models, which provide decision support for forest managers. Mortality patterns, however, are highly variable and difficult to describe. Despite numerous investigations aimed at developing tree survival models, there are still important gaps that need to be filled. This paper used a large-scale repeated measure dataset collected from permanent sample plots established in 1980/81 across the natural range of loblolly pine (Pinus taeda L.) in the Piedmont, Atlantic Coastal Plain and Gulf Coastal Plain physiographic regions of the US. The primary objective of this study was to explain the survival of loblolly pine trees using time-varying covariates such as diameter at breast height, total tree height, crown ratio, stand age, stand basal area, and dominant height. In this paper, individual-tree mortality was described using a semiparametric proportional hazards regression model. Shared frailty models were used to account for unobserved heterogeneity not explained by the observed covariates. Our investigation involved developing a modeling comparison procedure, predicting mortality based on a frailty model, and quantifying the predictive ability for tree mortality. The survival model developed using a large scale database provides further understanding of mortality trends in planted stands of loblolly pine. The survival model will enable forest managers to more accurately specify initial planting density, thinning schedules, and other management interventions.