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

Spatial trends of breast and prostate cancers in the United States between 2000 and 2005

<p>Abstract</p> <p>Background</p> <p>Breast cancer in females and prostate cancer in males are two of the most common cancers in the United States, and the literature suggests that they share similar features. However, it is unknown whether the occurrence of these two cancers at the county level in the United States is correlated. We analyzed Caucasian age-adjusted county level average annual incidence rates for breast and prostate cancers from the National Cancer Institute and State Cancer Registries to determine whether there was a spatial correlation between the two conditions and whether the two cancers had similar spatial patterns.</p> <p>Results</p> <p>There was a significant correlation between breast and prostate cancers by county (r = 0.332, p < 0.001). This relationship was more pronounced when we performed a geographically-weighted regression (GWR) analysis (r = 0.552) adjusting for county unemployment rates. There was variation in the parameter estimates derived with the GWR; however, the majority of the estimates indicted a positive association. The strongest relationship between breast and prostate cancer was in the eastern parts of the Midwest and South, and the Southeastern U.S. We also observed a north-south pattern for both cancers with our cluster analyses. Clusters of counties with high cancer incidence rates were more frequently found in the North and clusters of counties with low incidence rates were predominantly in the South.</p> <p>Conclusion</p> <p>Our analyses suggest breast and prostate cancers cluster spatially. This finding corroborates other studies that have found these two cancers share similar risk factors. The north-south distribution observed for both cancers warrants further research to determine what is driving this spatial pattern.</p

Estrogen receptor positive breast cancers and their association with environmental factors

<p>Abstract</p> <p>Background</p> <p>Epidemiological studies to assess risk factors for breast cancer often do not differentiate between different types of breast cancers. We applied a general linear model to determine whether data from the Surveillance, Epidemiology, and End Results Program on annual county level age-adjusted incidence rates of breast cancer with and without estrogen receptors (ER+ and ER-) were associated with environmental pollutants.</p> <p>Results</p> <p>Our final model explained approximately 38% of the variation in the rate of ER+ breast cancer. In contrast, we were only able to explain 14% of the variation in the rate of ER- breast cancer with the same set of environmental variables. Only ER+ breast cancers were positively associated with the EPA's estimated risk of cancer based on toxic air emissions and the proportion of agricultural land in a county. Meteorological variables, including short wave radiation, temperature, precipitation, and water vapor pressure, were also significantly associated with the rate of ER+ breast cancer, after controlling for age, race, premature mortality from heart disease, and unemployment rate.</p> <p>Conclusions</p> <p>Our findings were consistent with what we expected, given the fact that many of the commonly used pesticides and air pollutants included in the EPA cancer risk score are classified as endocrine disruptors and ER+ breast cancers respond more strongly to estrogen than ER- breast cancers. The findings of this study suggest that ER+ and ER- breast cancers have different risk factors, which should be taken into consideration in future studies that seek to understand environmental risk factors for breast cancer.</p

Correlations between meteorological parameters and prostate cancer

<p>Abstract</p> <p>Background</p> <p>There exists a north-south pattern to the distribution of prostate cancer in the U.S., with the north having higher rates than the south. The current hypothesis for the spatial pattern of this disease is low vitamin D levels in individuals living at northerly latitudes; however, this explanation only partially explains the spatial distribution in the incidence of this cancer. Using a U.S. county-level ecological study design, we provide evidence that other meteorological parameters further explain the variation in prostate cancer across the U.S.</p> <p>Results</p> <p>In general, the colder the temperature and the drier the climate in a county, the higher the incidence of prostate cancer, even after controlling for shortwave radiation, age, race, snowfall, premature mortality from heart disease, unemployment rate, and pesticide use. Further, in counties with high average annual snowfall (>75 cm/yr) the amount of land used to grow crops (a proxy for pesticide use) was positively correlated with the incidence of prostate cancer.</p> <p>Conclusion</p> <p>The trends found in this USA study suggest prostate cancer may be partially correlated with meteorological factors. The patterns observed were consistent with what we would expect given the effects of climate on the deposition, absorption, and degradation of persistent organic pollutants including pesticides. Some of these pollutants are known endocrine disruptors and have been associated with prostate cancer.</p

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

Improving Computational Efficiency in Identifying Parsimonious Statistical Models

Many authors have argued that identifying parsimonious statistical models (those that are neither overfit nor underfit) while considering curvature and/or interaction terms among predictors is inadvisable because of the huge number of potential models. For example, the complete second order model set will contain models for consideration where k is the number of predictors in the model. To address this difficulty, we present a stepwise algorithm, developed for the R statistical environment, in which the number of considered models is quadratic in k. This is in contrast with conventional stepwise model selection functions (e.g., StepAIC and step) which consider a model set cubic in k. Our new approach, termed Greedy, uses one of 3 measures of statistical parsimony for its model set, the Akaike information criterion (AIC), the Bayesian information criterion (BIC), and its predicted residual error sum of squares (PRESS) statistic. We found that, when considering large and/or high dimensional datasets, the Greedy algorithm identified the same optimal (minimum AIC) model as conventional stepwise approaches, or one with essentially equal parsimony, while having dramatically smaller computational run times

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