977 resultados para Classical orthogonal polynomials of a discrete variable


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Gastrointestinal stromal tumors (GIST) represent 80% of sarcoma arising from the GI tract. The inciting event in tumor progression is mutation of the kit or, rarely, platelet derived growth factor receptor-α (PDGFR) gene. These mutations encode ligand independent, constitutively active proteins: Kit or PDGFR. ^ These tumors are notoriously chemo and radio resistant. Historically, patients with advanced disease realized a median overall survival of 9 months. However, with modern management of GIST with imatinib mesylate (Novartis), a small molecule inhibitor of the Kit, PDGFR, and Abl tyrosine kinases, patients now realize a median overall survival greater than 30 months. However, almost half of patients present with surgically resectable GIST and the utility of imatinib in this context has not been prospectively studied. Also, therapeutic benefit of imatinib is variable from patient to patient and alternative targeted therapy is emerging as potential alternatives to imatinib. Thus, elucidating prognostic factors for patients with GIST in the imatinib-era is crucial to providing optimal care to each particular patient. Moreover, the exact mechanism of action of imatinib in GIST is not fully understood. Therefore, physicians find difficulty in accurately predicting which patient will benefit from imatinib, how to assess response to therapy, and the time at which to assess response. ^ I have hypothesized that imatinib is tolerable and clinically beneficial in the context of surgery, VEGF expression and kit non-exon 11 genotypes portend poor survival on imatinib therapy, and imatinib's mechanism of action is in part due to anti-vascular effects and inhibition of the Kit/SCF signaling axis of tumor-associated endothelial cells. ^ Results herein demonstrate that imatinib is safe and increases the duration of disease-free survival when combined with surgery. Radiographic and molecular (namely, apoptosis) changes occur within 3 days of imatinib initiation. I illustrate that non-exon 11 mutant genotypes and VEGF are poor prognostic factors for patients treated with imatinib. These findings may allow for patient stratification to emerging therapies rather than imatinib. I show that imatinib has anti-vascular effects via inducing tumor endothelial cell apoptosis perhaps by abrogation of the Kit/SCF signaling axis. ^

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Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

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Interaction effect is an important scientific interest for many areas of research. Common approach for investigating the interaction effect of two continuous covariates on a response variable is through a cross-product term in multiple linear regression. In epidemiological studies, the two-way analysis of variance (ANOVA) type of method has also been utilized to examine the interaction effect by replacing the continuous covariates with their discretized levels. However, the implications of model assumptions of either approach have not been examined and the statistical validation has only focused on the general method, not specifically for the interaction effect.^ In this dissertation, we investigated the validity of both approaches based on the mathematical assumptions for non-skewed data. We showed that linear regression may not be an appropriate model when the interaction effect exists because it implies a highly skewed distribution for the response variable. We also showed that the normality and constant variance assumptions required by ANOVA are not satisfied in the model where the continuous covariates are replaced with their discretized levels. Therefore, naïve application of ANOVA method may lead to an incorrect conclusion. ^ Given the problems identified above, we proposed a novel method modifying from the traditional ANOVA approach to rigorously evaluate the interaction effect. The analytical expression of the interaction effect was derived based on the conditional distribution of the response variable given the discretized continuous covariates. A testing procedure that combines the p-values from each level of the discretized covariates was developed to test the overall significance of the interaction effect. According to the simulation study, the proposed method is more powerful then the least squares regression and the ANOVA method in detecting the interaction effect when data comes from a trivariate normal distribution. The proposed method was applied to a dataset from the National Institute of Neurological Disorders and Stroke (NINDS) tissue plasminogen activator (t-PA) stroke trial, and baseline age-by-weight interaction effect was found significant in predicting the change from baseline in NIHSS at Month-3 among patients received t-PA therapy.^

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In Part One, the foundations of Bayesian inference are reviewed, and the technicalities of the Bayesian method are illustrated. Part Two applies the Bayesian meta-analysis program, the Confidence Profile Method (CPM), to clinical trial data and evaluates the merits of using Bayesian meta-analysis for overviews of clinical trials.^ The Bayesian method of meta-analysis produced similar results to the classical results because of the large sample size, along with the input of a non-preferential prior probability distribution. These results were anticipated through explanations in Part One of the mechanics of the Bayesian approach. ^

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Complex diseases such as cancer result from multiple genetic changes and environmental exposures. Due to the rapid development of genotyping and sequencing technologies, we are now able to more accurately assess causal effects of many genetic and environmental factors. Genome-wide association studies have been able to localize many causal genetic variants predisposing to certain diseases. However, these studies only explain a small portion of variations in the heritability of diseases. More advanced statistical models are urgently needed to identify and characterize some additional genetic and environmental factors and their interactions, which will enable us to better understand the causes of complex diseases. In the past decade, thanks to the increasing computational capabilities and novel statistical developments, Bayesian methods have been widely applied in the genetics/genomics researches and demonstrating superiority over some regular approaches in certain research areas. Gene-environment and gene-gene interaction studies are among the areas where Bayesian methods may fully exert its functionalities and advantages. This dissertation focuses on developing new Bayesian statistical methods for data analysis with complex gene-environment and gene-gene interactions, as well as extending some existing methods for gene-environment interactions to other related areas. It includes three sections: (1) Deriving the Bayesian variable selection framework for the hierarchical gene-environment and gene-gene interactions; (2) Developing the Bayesian Natural and Orthogonal Interaction (NOIA) models for gene-environment interactions; and (3) extending the applications of two Bayesian statistical methods which were developed for gene-environment interaction studies, to other related types of studies such as adaptive borrowing historical data. We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions (epistasis) and gene by environment interactions in the same model. It is well known that, in many practical situations, there exists a natural hierarchical structure between the main effects and interactions in the linear model. Here we propose a model that incorporates this hierarchical structure into the Bayesian mixture model, such that the irrelevant interaction effects can be removed more efficiently, resulting in more robust, parsimonious and powerful models. We evaluate both of the 'strong hierarchical' and 'weak hierarchical' models, which specify that both or one of the main effects between interacting factors must be present for the interactions to be included in the model. The extensive simulation results show that the proposed strong and weak hierarchical mixture models control the proportion of false positive discoveries and yield a powerful approach to identify the predisposing main effects and interactions in the studies with complex gene-environment and gene-gene interactions. We also compare these two models with the 'independent' model that does not impose this hierarchical constraint and observe their superior performances in most of the considered situations. The proposed models are implemented in the real data analysis of gene and environment interactions in the cases of lung cancer and cutaneous melanoma case-control studies. The Bayesian statistical models enjoy the properties of being allowed to incorporate useful prior information in the modeling process. Moreover, the Bayesian mixture model outperforms the multivariate logistic model in terms of the performances on the parameter estimation and variable selection in most cases. Our proposed models hold the hierarchical constraints, that further improve the Bayesian mixture model by reducing the proportion of false positive findings among the identified interactions and successfully identifying the reported associations. This is practically appealing for the study of investigating the causal factors from a moderate number of candidate genetic and environmental factors along with a relatively large number of interactions. The natural and orthogonal interaction (NOIA) models of genetic effects have previously been developed to provide an analysis framework, by which the estimates of effects for a quantitative trait are statistically orthogonal regardless of the existence of Hardy-Weinberg Equilibrium (HWE) within loci. Ma et al. (2012) recently developed a NOIA model for the gene-environment interaction studies and have shown the advantages of using the model for detecting the true main effects and interactions, compared with the usual functional model. In this project, we propose a novel Bayesian statistical model that combines the Bayesian hierarchical mixture model with the NOIA statistical model and the usual functional model. The proposed Bayesian NOIA model demonstrates more power at detecting the non-null effects with higher marginal posterior probabilities. Also, we review two Bayesian statistical models (Bayesian empirical shrinkage-type estimator and Bayesian model averaging), which were developed for the gene-environment interaction studies. Inspired by these Bayesian models, we develop two novel statistical methods that are able to handle the related problems such as borrowing data from historical studies. The proposed methods are analogous to the methods for the gene-environment interactions on behalf of the success on balancing the statistical efficiency and bias in a unified model. By extensive simulation studies, we compare the operating characteristics of the proposed models with the existing models including the hierarchical meta-analysis model. The results show that the proposed approaches adaptively borrow the historical data in a data-driven way. These novel models may have a broad range of statistical applications in both of genetic/genomic and clinical studies.

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The Greenland Ice Sheet Project 2 (GISP2) core can enhance our understanding of the relationship between parameters measured in the ice in central Greenland and variability in the ocean, atmosphere, and cryosphere of the North Atlantic Ocean and adjacent land masses. Seasonal (summer, winter) to annual responses of dD and deuterium excess isotopic signals in the GISP2 core to the seesaw in winter temperatures between West Greenland and northern Europe from A.D. 1840 to 1970 are investigated. This seesaw represents extreme modes of the North Atlantic Oscillation, which also influences sea surface temperatures (SSTs), atmospheric pressures, geostrophic wind strength, and sea ice extents beyond the winter season. Temperature excursions inferred from the dD record during seesaw/extreme NAO mode years move in the same direction as the West Greenland side of the seesaw. Symmetry with the West Greenland side of the seesaw suggests a possible mechanism for damping in the ice core record of the lowest decadal temperatures experienced in Europe from A.D. 1500 to 1700. Seasonal and annual deuterium excess excursions during seesaw years show negative correlation with dD. This suggests an isotopic response to a SST/ land temperature seesaw. The isotopic record from GISP2 may therefore give information on both ice sheet and sea surface temperature variability. Cross-plots of dD and d show a tendency for data to be grouped according to the prevailing mode of the seesaw, but do not provide unambiguous identification of individual seesaw years. A combination of ice core and tree ring data sets may allow more confident identification of GA and GB (extreme NAO mode) years prior to 1840.

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The genus Hinia is divided in 4 subgenera; other subgenera are not represented in the area studied. It was possible to find criteria for a better discrimination of the highly variable species H. (Hinia) schlotheimi and H. (Hinia) turbinella. The species "fuchsi" has been placed in the synonymy of H. (Hinia) turbinella. The species H. (Hinia) schlotheimi (BEYRICH) and H. (Telasco) schroederi (KAUTSKY) have been united under the name H. (Hinia) schlotheimi. The easily distinguishable species H. (Tritonella) tenuistriata and H. (Hinia) sulcata belong to two different genera. H. (Tritonella) cimbrica andersoni of the Viol- and Katzheide-Beds (Reinbek-stage) is separable from the population found in the Hemmoor-stage, it turned out to be a valuable guide subspecies for the Reinbek-stage. The species H. (Tritonella) serraticosta, H. (Tritonella) catulli, H. (Hinia) holsatica, and H. (Telasco) syltensis are all similar in respect to shape and ornamentation. Criteria have been found for a better discrimination of these species. The species contabulata, effusa and seminodifera described by SPEYER (1864), turned out to be contogenetic stages of H. (Tritonella) pygmaea. H. (Tritonella) cavata, previously described from the Tertiary of the North sea area, was proven to be absent from the area investigated. The forms described under that name, belong to H. (Tritonella) woodwardi.

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The Albian/Cenomanian strata in Hole 530A are organically richer than are the post-Cenomanian strata. Organic matter is thermally immature and appears to be of dominantly marine origin with either variable levels of oxidation or variable amounts of terrestrial input. Geochemical data alone cannot establish whether the black shales present in Hole 530A represent deposition within a stagnant basin or within an expanded oxygen-minimum layer

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Experimental phase relations were used to assess the role of volatiles and crustal level fractional crystallization in the petrogenesis of lavas from Hole 839B in the central Lau Basin. Melting experiments were performed on Sample 135-839B-15R-2, 63-67 cm, at 1 atm, anhydrous, and 2 kbar, H2O-saturated (~6 wt% H2O in the melt) to determine the influence of variable pressure and H2O content on phase appearances, mineral chemistry, and liquid line of descent followed during crystallization. The effects of H2O are to depress the liquidus by ~100°C, and to suppress crystallization of plagioclase and orthopyroxene relative to olivine and high-Ca clinopyroxene. At 1 atm, anhydrous, olivine and plagioclase coexist near the liquidus, whereas orthopyroxene and then clinopyroxene appear with decreasing temperature. Crystallization of 50 wt% produces a residual liquid that is rich in FeO* (10.8 wt%) and poor in Al2O3 (13.6 wt%). At 2 kbar, H2O-saturated, the liquidus phases are olivine and chromian spinel, with high-Ca clinopyroxene appearing after ~10% crystallization. Plagioclase saturation is suppressed until ~20% crystallization has occurred. The residual liquid from 35 wt% crystallization is rich in AI2O3 (17.4 wt%), and poor in MgO (4.82 wt%); it contains moderate FeO* (8.2 wt%), and resembles the low-MgO andesites recovered from Hole 839B. On the basis of these experiments we conclude that the primitive lavas recovered from Hole 839B have experienced crystallization along the Ol + Cpx saturation boundary, under hydrous conditions (an ankaramitic liquid line of descent), and variable amounts of olivine and chromian spinel accumulation. The low-MgO andesites from Hole 839B are the products of hydrous fractional crystallization, at crustal pressures, of a parent magma similar to basaltic andesite Sample 135-839B-15R-2, 63-67 cm.

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Ocean warming and ocean acidification, both consequences of anthropogenic production of CO2, will combine to influence the physiological performance of many species in the marine environment. In this study, we used an integrative approach to forecast the impact of future ocean conditions on larval purple sea urchins (Strongylocentrotus purpuratus) from the northeast Pacific Ocean. In laboratory experiments that simulated ocean warming and ocean acidification, we examined larval development, skeletal growth, metabolism and patterns of gene expression using an orthogonal comparison of two temperature (13°C and 18°C) and pCO2 (400 and 1100 µatm) conditions. Simultaneous exposure to increased temperature and pCO2 significantly reduced larval metabolism and triggered a widespread downregulation of histone encoding genes. pCO2 but not temperature impaired skeletal growth and reduced the expression of a major spicule matrix protein, suggesting that skeletal growth will not be further inhibited by ocean warming. Importantly, shifts in skeletal growth were not associated with developmental delay. Collectively, our results indicate that global change variables will have additive effects that exceed thresholds for optimized physiological performance in this keystone marine species.

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Anthropogenically-modulated reductions in pH, termed ocean acidification, could pose a major threat to the physiological performance, stocks, and biodiversity of calcifiers and may devalue their ecosystem services. Recent debate has focussed on the need to develop approaches to arrest the potential negative impacts of ocean acidification on ecosystems dominated by calcareous organisms. In this study, we demonstrate the role of a discrete (i.e. diffusion) boundary layer (DBL), formed at the surface of some calcifying species under slow flows, in buffering them from the corrosive effects of low pH seawater. The coralline macroalga Arthrocardia corymbosa was grown in a multifactorial experiment with two mean pH levels (8.05 'ambient' and 7.65 a worst case 'ocean acidification' scenario projected for 2100), each with two levels of seawater flow (fast and slow, i.e. DBL thin or thick). Coralline algae grown under slow flows with thick DBLs (i.e., unstirred with regular replenishment of seawater to their surface) maintained net growth and calcification at pH 7.65 whereas those in higher flows with thin DBLs had net dissolution. Growth under ambient seawater pH (8.05) was not significantly different in thin and thick DBL treatments. No other measured diagnostic (recruit sizes and numbers, photosynthetic metrics, %C, %N, %MgCO3) responded to the effects of reduced seawater pH. Thus, flow conditions that promote the formation of thick DBLs, may enhance the subsistence of calcifiers by creating localised hydrodynamic conditions where metabolic activity ameliorates the negative impacts of ocean acidification.

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Major and trace element compositions of basalts from the lower part of Hole 504B indicate their cogenetic nature. The cored sequence of interlayered pillow lavas and massive lava flows was produced by eruption of lavas, slightly variable in composition. Plagioclase and olivine crystallization in a shallow magma chamber, followed by small-scale fractionation at higher levels, is responsible for these variations. Except in highly fractured zones within the basement, there are systematic variations in the style and degree of rock alteration with depth. Trace element characteristics of altered rocks and secondary minerals indicate that progressive changes in sea water composition occurred as it reacted with basaltic crust.

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Sediment samples collected at DSDP Leg 96 Mississippi Fan Sites 615, 616, 620, 621, and 623, Orca Basin Site 618, and Pigmy Basin Site 619 were analyzed for 22 major, minor, and trace elements. This study was undertaken to document the downhole variability in inorganic geochemistry between sites. The mineralogy of the clays, including those from Sites 614, 617, and 622 on the fan, was determined by X-ray diffraction to define the principal clay minerals present at the sites, examine any downhole trends in clay mineralogy, and aid in the interpretation of the geochemical signature of the sediments. Clay mineral composition at all the sites is smectite:illite:chlorite:kaolinite in the approximate percentage ratio 50:20:20:10. Geochemical results indicate only slight variation between and within the sites, with the exception of a discrete unit of carbonates that occurs near the bottom of Site 615. Variation in the major, minor, and trace element composition can be explained by a change in the relative abundance of quartz, clay minerals, and carbonates.

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The aim of the present study was to evaluate the influence of different light quality, especially ultraviolet radiation (UVR), on the dynamics of volatile halogenated organic compounds (VHOCs) at the sea surface. Short term experiments were conducted with floating gas-tight mesocosms of different optical qualities. Six halocarbons (CH3I, CHCl3, CH2Br2, CH2ClI, CHBr3 and CH2I2), known to be produced by phytoplankton, together with a variety of biological and environmental variables were measured in the coastal southern Baltic Sea and in the Raunefjord (North Sea). These experiments showed that ambient levels of UVR have no significant influence on VHOC dynamics in the natural systems. We attribute it to the low radiation doses that phytoplankton cells receive in a normal turbulent surface mixed layer. The VHOC concentrations were influenced by their production and removal processes, but they were not correlated with biological or environmental parameters investigated. Diatoms were most likely the dominant biogenic source of VHOCs in the Baltic Sea experiment, whereas in the Raunefjord experiment macroalgae probably contributed strongly to the production of VHOCs. The variable stable carbon isotope signatures (d13C values) of bromoform (CHBr3) also indicate that different autotrophic organisms were responsible for CHBr3 production in the two coastal environments. In the Raunefjord, despite strong daily variations in CHBr3 concentration, the carbon isotopic ratio was fairly stable with a mean value of -26 per mil. During the declining spring phytoplankton bloom in the Baltic Sea, the d13C values of CHBr3 were enriched in 13C and showed noticeable diurnal changes (-12 per mil ± 4). These results show that isotope signature analysis is a useful tool to study both the origin and dynamics of VHOCs in natural systems.