Extensions of the proportional hazards loglikelihood for censored survival data

The semi-parametric approach to the analysis of proportional hazards survival data is relatively new, having been initiated in 1972 by Sir David Cox, who restricted its use to hypothesis tests and confidence intervals for fixed effects in a regression setting. Practitioners have begun to diversify applications of this model, constructing residuals, modeling the baseline hazard, estimating median failure time, and analyzing experiments with random effects and repeated measures. The main purpose of this thesis is to show that working with an incompletely specified loglikelihood is more fruitful than working with Cox's original partial loglikelihood, in these applications. In Chapter 2, we show that the deviance residuals arising naturally from the partial loglikelihood have difficulties detecting outliers. We demonstrate that a smoothed, nonparametric baseline hazard partially solves this problem. In Chapter 3, we derive new deviance residuals that are useful for identifying the shape of the baseline hazard. When these new residuals are plotted in temporal order, patterns in the residuals mirror patterns in the baseline hazard. In Chapter 4, we demonstrate how to analyze survival data having a split-plot design structure. Using a BLUP estimation algorithm, we produce hypothesis tests for fixed effects, and estimation procedures for the fixed effects and random effects

Aboveground Total and Green Biomass of Dryland Shrub Derived from Terrestrial Laser Scanning

Sagebrush (Artemisia tridentata), a dominant shrub species in the sagebrush-steppe ecosystem of the western US, is declining from its historical distribution due to feedbacks between climate and land use change, fire, and invasive species. Quantifying aboveground biomass of sagebrush is important for assessing carbon storage and monitoring the presence and distribution of this rapidly changing dryland ecosystem. Models of shrub canopy volume, derived from terrestrial laser scanning (TLS) point clouds, were used to accurately estimate aboveground sagebrush biomass. Ninety-one sagebrush plants were scanned and sampled across three study sites in the Great Basin, USA. Half of the plants were scanned and destructively sampled in the spring (n = 46), while the other half were scanned again in the fall before destructive sampling (n = 45). The latter set of sagebrush plants was scanned during both spring and fall to further test the ability of the TLS to quantify seasonal changes in green biomass. Sagebrush biomass was estimated using both a voxel and a 3-D convex hull approach applied to TLS point cloud data. The 3-D convex hull model estimated total and green biomass more accurately (R2 = 0.92 and R2 = 0.83, respectively) than the voxel-based method (R2 = 0.86 and R2 = 0.73, respectively). Seasonal differences in TLS-predicted green biomass were detected at two of the sites (p \u3c 0.001 and p = 0.029), elucidating the amount of ephemeral leaf loss in the face of summer drought. The methods presented herein are directly transferable to other dryland shrubs, and implementation of the convex hull model with similar sagebrush species is straightforward

Remote sensing of sagebrush canopy nitrogen

This paper presents a combination of techniques suitable for remotely sensing foliar Nitrogen (N) in semiarid shrublands – a capability that would significantly improve our limited understanding of vegetation functionality in dryland ecosystems. The ability to estimate foliar N distributions across arid and semi-arid environments could help answer process-driven questions related to topics such as controls on canopy photosynthesis, the influence of N on carbon cycling behavior, nutrient pulse dynamics, and post-fire recovery. Our study determined that further exploration into estimating sagebrush canopy N concentrations from an airborne platform is warranted, despite remote sensing challenges inherent to open canopy systems. Hyperspectral data transformed using standard derivative analysis were capable of quantifying sagebrush canopy N concentrations using partial least squares (PLS) regression with an R2 value of 0.72 and an R2 predicted value of 0.42 (n=35). Subsetting the dataset to minimize the influence of bare ground (n=19) increased R2 to 0.95 (R2 predicted=0.56). Ground-based estimates of canopy N using leaf mass per unit area measurements (LMA) yielded consistently better model fits than ground-based estimates of canopy N using cover and height measurements. The LMA approach is likely a method that could be extended to other semiarid shrublands. Overall, the results of this study are encouraging for future landscape scale N estimates and represent an important step in addressing the confounding influence of bare ground, which we found to be a major influence on predictions of sagebrush canopy N from an airborne platform