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Large spatial datasets are typically modeled through a small set of knot locations; often these locations are specified by the investigator by arbitrary criteria. Existing methods of estimating the locations of knots assume their number is known a priori, or are otherwise computationally intensive. We develop a computationally efficient method of estimating both the location and number of knots for spatial mixed effects models. Our proposed algorithm, Threshold Knot Selection (TKS), estimates knot locations by identifying clusters of large residuals and placing a knot in the centroid of those clusters. We conduct a simulation study showing TKS in relation to several comparable methods of estimating knot locations. Our case study utilizes data of particulate matter concentrations collected during the course of the response and clean-up effort from the 2010 Deepwater Horizon oil spill in the Gulf of Mexico.
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In many applications researchers are typically interested in testing for inequality constraints in the context of linear fixed effects and mixed effects models. Although there exists a large body of literature for performing statistical inference under inequality constraints, user friendly statistical software for implementing such methods is lacking, especially in the context of linear fixed and mixed effects models. In this article we introduce CLME, a package in the R language that can be used for testing a broad collection of inequality constraints. It uses residual bootstrap based methodology which is reasonably robust to non-normality as well as heteroscedasticity. The package is illustrated using two data sets. The package also contains a graphical interface built using the shiny package.
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Objectives: Headache after aneurysmal subarachnoid hemorrhage (HASH) is common, severe, and often refractory to conventional treatments. Current treatment standards include medications including opioids, until the pain is mitigated. Peripheral nerve blocks (PNBs) may be an effective therapeutic option for HASH. We conducted a small before-and-after study of PNBs to determine safety, feasibility, and efficacy in treatment of HASH. Methods: We conducted a pilot before-and-after observational study and collected data for 5 patients in a retrospective control group and 5 patients in a prospective intervention PNB group over a 12-month period. All patients received a standard treatment of medications including acetaminophen, magnesium, gabapentin, dexamethasone and anti-spasmodics or anti-emetics as needed. Patients in the intervention group received bilateral greater occipital, lesser occipital, and supraorbital PNBs in addition to medications. The primary outcome was pain severity, measured by Numeric pain rating scale (NPRS). All patients were followed for 1 week following enrollment. Results: The mean ages in the PNB group and control group were 58.6 and 57.4, respectively. One patient in the control group developed radiographic vasospasm. Three patients in both groups had radiographic hydrocephalus and IVH, requiring external ventricular drain (EVD) placement. The PNB group had an average reduction in mean raw pain score of 2.76 (4.68, 1.92 p = 0.024), and relative pain score by 0.26 (0.48, 0.22 p = 0.026), compared to the control group. The reduction occurred immediately after PNB administration. Conclusion: PNB can be a safe, feasible and effective treatment modality for HASH. Further investigations with a larger sample size are warranted.
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There are many applications in which a statistic follows, at least asymptotically, a normal distribution with a singular or nearly singular variance matrix. A classic example occurs in linear regression models under multicollinearity but there are many more such examples. There is well-developed theory for testing linear equality constraints when the alternative is two-sided and the variance matrix is either singular or non-singular. In recent years there is considerable, and growing, interest in developing methods for situations in which the estimated variance matrix is nearly singular. However, there is no corresponding methodology for addressing one-sided, i.e., constrained or ordered alternatives. In this paper we develop a unified framework for analyzing such problems. Our approach may be viewed as the trimming or winsorizing of the eigenvalues of the corresponding variance matrix. The proposed methodology is applicable to a wide range of scientific problems and to a variety of statistical models in which inequality constraints arise. We illustrate the methodology using data from a gene expression microarray experiment obtained from the NIEHS' Fibroid Growth Study.
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The Association of Firearm and Toolmark Examiners recommends a minimum of two test fires be performed when an unknown firearm is submitted to a laboratory prior to doing a comparison with a cartridge case collected from a crime scene. Limited research has been performed to determine how many test fires are necessary to be representative of the match distribution of a firearm. Various makes and models of firearms comprising five calibers were tested using a hybrid equivalence test to determine how many cartridge cases were required to represent the match distribution of an unknown firearm based on both breech face and firing pin correlation scores from an IBIS® HeritageTM System. The same general trend was observed for each caliber of firearm where the equivalence percentage increased from 10 to 30 cartridge cases. Overall, 15 cartridge cases are sufficient for above an 80% probability of representing the full match distribution for an unknown firearm. To approach full equivalence, 25 cartridge cases are enough because 30 cartridge cases were not found to be significantly higher in equivalence percentage for any caliber of firearm tested.
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The severity of recent droughts in semiarid regions is increasingly attributed to anthropogenic climate change, but it is unclear whether these moisture anomalies exceed those of the past and how past variability compares to future projections. On the Mongolian Plateau, a recent decade-long drought that exceeded the variability in the instrumental record was associated with economic, social, and environmental change. We evaluate this drought using an annual reconstruction of the Palmer Drought Severity Index (PDSI) spanning the last 2060 years in concert with simulations of past and future drought through the year 2100 CE. We show that although the most recent drought and pluvial were highly unusual in the last 2000 years, exceeding the 900-year return interval in both cases, these events were not unprecedented in the 2060-year reconstruction, and events of similar duration and severity occur in paleoclimate, historical, and future climate simulations. The Community Earth System Model (CESM) ensemble suggests a drying trend until at least the middle of the 21st century, when this trend reverses as a consequence of elevated precipitation. Although the potential direct effects of elevated CO2 on plant water use efficiency exacerbate uncertainties about future hydroclimate trends, these results suggest that future drought projections for Mongolia are unlikely to exceed those of the last two millennia, despite projected warming.
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Many studies have been performed in recent years in the field of firearm examination with the goal of providing an objective method for comparisons of fired cartridge cases. No published research to support the number of test fires needed to represent the variability present within the impressions left on a cartridge case could be found. When a suspect firearm is submitted to a firearm examiner, typically two to four test fires are performed. The recovered cartridge cases are compared to each other to determine which characteristics from the firearm are reproducing, and then compared to any cartridge cases collected at a crime scene. The aim of this research was to determine the number of test fires examiners should perform when a suspect firearm is submitted to the lab to balance cartridge case acquisition time with performance accuracy. Each firearm in the IBIS® database at West Virginia University® is represented by approximately 100 fired cartridge case entries. Random samples of cartridge cases were taken separately from the breech face match score and firing pin match score lists. This subset was compared to the total match distribution of the firearm using a hybrid equivalence test to determine if the subset of similarity scores were statistically equivalent to the larger distribution of scores. For the sampled distribution to remain above 80% equivalent to the match distribution, a minimum of 15 cartridge cases should be used to model the match distribution, based on IBIS® scores. Thirty cartridge cases is a conservative estimate, allowing one to determine that the location and dispersion of the match and sampling distributions are equivalent with nearly 100% probability.
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Oxidative stress is elevated in numerous environmental exposures and diseases. Millions of dollars have been spent to try to ameliorate this damaging process using anti-oxidant therapies. Currently, the best accepted biomarker of oxidative stress is the lipid oxidation product 8-iso-prostaglandin F2α (8-iso-PGF2α), which has been measured in over a thousand human and animal studies. 8-iso-PGF2α generation has been exclusively attributed to nonenzymatic chemical lipid peroxidation (CLP). However, 8-iso-PGF2α can also be produced enzymatically by prostaglandin-endoperoxide synthases (PGHS) in vivo. When failing to account for PGHS-dependent generation, 8-iso-PGF2α cannot be interpreted as a selective biomarker of oxidative stress. We investigated the formation of 8-iso-PGF2α in rats exposed to carbon tetrachloride (CCl4) or lipopolysaccharide (LPS) using the 8-iso-PGF2α/PGF2α ratio to quantitatively determine the source(s) of 8-iso-PGF2α. Upon exposure to a 120mg/kg dose of CCl4, the contribution of CLP accounted for only 55.6±19.4% of measured 8-iso-PGF2α, whereas in the 1200mg/kg dose, CLP was the predominant source of 8-iso-PGF2α (86.6±8.0% of total). In contrast to CCl4, exposure to 0.5mg/kg LPS was characterized by a significant increase in both the contribution of PGHS (59.5±7.0) and CLP (40.5±14.0%). In conclusion, significant generation of 8-iso-PGF2α occurs through enzymatic as well as chemical lipid peroxidation. The distribution of the contribution is dependent on the exposure agent as well as the dose. The 8-iso-PGF2α/PGF2α ratio accurately determines the source of 8-iso-PGF2α and provides an absolute measure of oxidative stress in vivo.