Bayesian generalized linear models for meta-analysis of diagnostic tests

With the recognition of the importance of evidence-based medicine, there is an emerging need for methods to systematically synthesize available data. Specifically, methods to provide accurate estimates of test characteristics for diagnostic tests are needed to help physicians make better clinical decisions. To provide more flexible approaches for meta-analysis of diagnostic tests, we developed three Bayesian generalized linear models. Two of these models, a bivariate normal and a binomial model, analyzed pairs of sensitivity and specificity values while incorporating the correlation between these two outcome variables. Noninformative independent uniform priors were used for the variance of sensitivity, specificity and correlation. We also applied an inverse Wishart prior to check the sensitivity of the results. The third model was a multinomial model where the test results were modeled as multinomial random variables. All three models can include specific imaging techniques as covariates in order to compare performance. Vague normal priors were assigned to the coefficients of the covariates. The computations were carried out using the 'Bayesian inference using Gibbs sampling' implementation of Markov chain Monte Carlo techniques. We investigated the properties of the three proposed models through extensive simulation studies. We also applied these models to a previously published meta-analysis dataset on cervical cancer as well as to an unpublished melanoma dataset. In general, our findings show that the point estimates of sensitivity and specificity were consistent among Bayesian and frequentist bivariate normal and binomial models. However, in the simulation studies, the estimates of the correlation coefficient from Bayesian bivariate models are not as good as those obtained from frequentist estimation regardless of which prior distribution was used for the covariance matrix. The Bayesian multinomial model consistently underestimated the sensitivity and specificity regardless of the sample size and correlation coefficient. In conclusion, the Bayesian bivariate binomial model provides the most flexible framework for future applications because of its following strengths: (1) it facilitates direct comparison between different tests; (2) it captures the variability in both sensitivity and specificity simultaneously as well as the intercorrelation between the two; and (3) it can be directly applied to sparse data without ad hoc correction. ^

DISTRIBUTION FUNCTIONS, MEAN SQUARED ERRORS, AND CONFIDENCE LIMITS FOR RIDGE REGRESSION ESTIMATORS

A large number of ridge regression estimators have been proposed and used with little knowledge of their true distributions. Because of this lack of knowledge, these estimators cannot be used to test hypotheses or to form confidence intervals.^ This paper presents a basic technique for deriving the exact distribution functions for a class of generalized ridge estimators. The technique is applied to five prominent generalized ridge estimators. Graphs of the resulting distribution functions are presented. The actual behavior of these estimators is found to be considerably different than the behavior which is generally assumed for ridge estimators.^ This paper also uses the derived distributions to examine the mean squared error properties of the estimators. A technique for developing confidence intervals based on the generalized ridge estimators is also presented. ^

Spatial distribution of orofacial cleft birth defects and uranium-radium concentrations in tap water in Atascosa, Bee, Brooks, Calhoun, Duval, Goliad, Hidalgo, Jim Hogg, Jim Wells, Karnes, Kleberg, Live Oak, McMullen, Nueces, San Patricio, Refugio, Starr, Victoria, Webb, and Zavala Counties, Texas

Background Past and recent evidence shows that radionuclides in drinking water may be a public health concern. Developmental thresholds for birth defects with respect to chronic low level domestic radiation exposures, such as through drinking water, have not been definitely recognized, and there is a strong need to address this deficiency in information. In this study we examined the geographic distribution of orofacial cleft birth defects in and around uranium mining district Counties in South Texas (Atascosa, Bee, Brooks, Calhoun, Duval, Goliad, Hidalgo, Jim Hogg, Jim Wells, Karnes, Kleberg, Live Oak, McMullen, Nueces, San Patricio, Refugio, Starr, Victoria, Webb, and Zavala), from 1999 to 2007. The probable association of cleft birth defect rates by ZIP codes classified according to uranium and radium concentrations in drinking water supplies was evaluated. Similar associations between orofacial cleft birth defects and radium/radon in drinking water were reported earlier by Cech and co-investigators in another of the Gulf Coast region (Harris County, Texas).50, 55 Since substantial uranium mining activity existed and still exists in South Texas, contamination of drinking water sources with radiation and its relation to birth defects is a ground for concern. ^ Methods Residential addresses of orofacial cleft birth defect cases, as well as live births within the twenty Counties during 1999-2007 were geocoded and mapped. Prevalence rates were calculated by ZIP codes and were mapped accordingly. Locations of drinking water supplies were also geocoded and mapped. ZIP codes were stratified as having high combined uranium (≥30μg/L) vs. low combined uranium (<30μg/L). Likewise, ZIP codes having the uranium isotope, Ra-226 in drinking water, were also stratified as having elevated radium (≥3 pCi/L) vs. low radium (<3 pCi/L). A linear regression was performed using STATA® generalized linear model (GLM) program to evaluate the probable association between cleft birth defect rates by ZIP codes and concentration of uranium and radium via domestic water supply. These rates were further adjusted for potentially confounding variables such as maternal age, education, occupation, and ethnicity. ^ Results This study showed higher rates of cleft births in ZIP codes classified as having high combined uranium versus ZIP codes having low combined uranium. The model was further improved by adding radium stratified as explained above. Adjustment for maternal age and ethnicity did not substantially affect the statistical significance of uranium or radium concentrations in household water supplies. ^ Conclusion Although this study lacks individual exposure levels, the findings suggest a significant association between elevated uranium and radium concentrations in tap water and high orofacial birth defect rates by ZIP codes. Future case-control studies that can measure individual exposure levels and adjust for contending risk factors could result in a better understanding of the exposure-disease association.^

Distribution of Pliocene diatom faunas in the Northwest Pacific

High-resolution quantitative diatom data are tabulated for the early part of the late Pliocene ( 3.25 to 2.08 Ma ) at DSDP Site 580 in the northwestern Pacific. Sample spacing averages 11 k.y. between 3.1 and 2.8 Ma, but increases to 14 to 19 k.y. prior to 3.1 Ma and after 2.8 Ma. Q-mode factor analysis of the middle Pliocene assemblage reveals four factors which explain 92.4% of the total variance of the 47 samples studied between 3.25 and 2.55 Ma. Three of the factors are closely related to modern subarctic, transitional, and subtropical elements, while the fourth factor, which is dominated by Coscinodiscus marginatus and the extinct Pliocene species Neodenticula kamtschatica, appears to correspond to a middle Pliocene precursor of the subarctic water mass. Knowledge of the modern and generalized Pliocene paleoclimatic relationships of various diatom taxa is used to generate a paleoclimate curve ("Twt") based on the ratio of warm-water (subtropical) to cold-water diatoms with warm-water transitional taxa (Thalassionema nitzschioides, Thalassiosira oestrupii, and Coscinodiscus radiatus) factored into the equation at an intermediate (0.5) value. The "Twt" ratios at more southerly DSDP Sites 579 and 578 are consistently higher (warmer) than those at Site 580 throughout the Pliocene, suggesting the validity of the ratio as a paleoclimatic index. Diatom paleoclimatic data reveal a middle Pliocene (3.1 to 3.0 Ma) warm interval at Site 580 during which paleotemperatures may have exceeded maximum Holocene values by 3 °- 5.5 °C at least three times. This middle Pliocene warm interval is also recognized by planktic foraminifers in the North Atlantic, and it appears to correspond with generalized depleted oxygen isotope values suggesting polar warming. The diatom "Twt" curve for Site 580 compares fairly well with radiolarian and silicoflagellate paleoclimatic curves for Site 580, planktic foraminiferal sea-surface temperature estimates for the North Atlantic, and benthic oxygen isotope curves for late Pliocene, although higher resolution studies on paired samples are required to test the correspondence of these various paleoclimatic indices.

Response of Catch-Per-Unit-Effort to Spatial and Environmental Factors: an Exploratory Data Analysis Using Generalized Additive Models

Understanding spatial distributions and how environmental conditions influence catch-per-unit-effort (CPUE) is important for increased fishing efficiency and sustainable fisheries management. This study investigated the relationship between CPUE, spatial factors, temperature, and depth using generalized additive models. Combinations of factors, and not one single factor, were frequently included in the best model. Parameters which best described CPUE varied by geographic region. The amount of variance, or deviance, explained by the best models ranged from a low of 29% (halibut, Charlotte region) to a high of 94% (sablefish, Charlotte region). Depth, latitude, and longitude influenced most species in several regions. On the broad geographic scale, depth was associated with CPUE for every species, except dogfish. Latitude and longitude influenced most species, except halibut (Areas 4 A/D), sablefish, and cod. Temperature was important for describing distributions of halibut in Alaska, arrowtooth flounder in British Columbia, dogfish, Alaska skate, and Aleutian skate. The species-habitat relationships revealed in this study can be used to create improved fishing and management strategies.

New Orleans, Louisiana, Water Distribution System, 1902 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Map of the city of New Orleans : showing proposed water distribution system, [by] Sewerage and Water Board New Orleans, LA.; Geo. G. Earl, genl. sup't. It was published by the Sewerage and Water Board New Orleans in 1902. Scale [ca. 1:50,900]. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Louisiana State Plane Coordinate System, South NAD83 (in Feet) (Fipszone 1702). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, or other information associated with the principal map. This map shows water distribution features such as existing and proposed water mains (with sizes), suction pipes, and water purification station sites. Also shows other features such as roads, canals, levees, drainage, cemeteries, Parish boundaries, and more. Shaded to show built-up and unbuilt areas for construction. This layer is part of a selection of digitally scanned and georeferenced historic maps from The Harvard Map Collection as part of the Imaging the Urban Environment project. Maps selected for this project represent major urban areas and cities of the world, at various time periods. These maps typically portray both natural and manmade features at a large scale. The selection represents a range of regions, originators, ground condition dates, scales, and purposes.

Ensemble prediction distribution maps of macroalgae for current conditions and four climate change scenarios and high resultion bathymetry for Potter Cove, WAP, Antarctica

Species distribution models (SDM) predict species occurrence based on statistical relationships with environmental conditions. The R-package biomod2 which includes 10 different SDM techniques and 10 different evaluation methods was used in this study. Macroalgae are the main biomass producers in Potter Cove, King George Island (Isla 25 de Mayo), Antarctica, and they are sensitive to climate change factors such as suspended particulate matter (SPM). Macroalgae presence and absence data were used to test SDMs suitability and, simultaneously, to assess the environmental response of macroalgae as well as to model four scenarios of distribution shifts by varying SPM conditions due to climate change. According to the averaged evaluation scores of Relative Operating Characteristics (ROC) and True scale statistics (TSS) by models, those methods based on a multitude of decision trees such as Random Forest and Classification Tree Analysis, reached the highest predictive power followed by generalized boosted models (GBM) and maximum-entropy approaches (Maxent). The final ensemble model used 135 of 200 calculated models (TSS > 0.7) and identified hard substrate and SPM as the most influencing parameters followed by distance to glacier, total organic carbon (TOC), bathymetry and slope. The climate change scenarios show an invasive reaction of the macroalgae in case of less SPM and a retreat of the macroalgae in case of higher assumed SPM values.

Determining Spatial Distribution and Physical Properties of the Vashon Advance Outwash near Mountlake Terrace, Washington

This study is aimed at determining the spatial distribution, physical properties, and groundwater conditions of the Vashon advance outwash (Qva) in the Mountlake Terrace, WA area. The Qva is correlative with the Esperance Sand, as defined at its type section; however, local variations in the Qva are not well-characterized (Mullineaux, 1965). While the Qva is a dense glacial unit with low compressibility and high frictional shear strength (Gurtowski and Boirum, 1989), the strength of this unit can be reduced when it becomes saturated (Tubbs, 1974). This can lead to caving or flowing in excavations, and on a larger scale, can lead to slope failures and mass-wasting when intersected by steep slopes. By studying the Qva, we can better predict how it will behave under certain conditions, which will be beneficial to geologists, hydrogeologists, engineers, and environmental scientists during site assessments and early phases of project planning. In this study, I use data from 27 geotechnical borings from previous field investigations and C-Tech Corporation’s EnterVol software to create three-dimensional models of the subsurface geology in the study area. These models made it possible to visualize the spatial distribution of the Qva in relation to other geologic units. I also conducted a comparative study between data from the borings and generalized published data on the spatial distribution, relative density, soil classification, grain-size distribution, moisture content, groundwater conditions, and aquifer properties of the Qva. I found that the elevation of the top of the Qva ranges from 247 to 477 ft. I found that the Qva is thickest where the modern topography is high, and is thinnest where the topography is low. The thickness of the Qva ranges from absent to 242 ft. Along the northern, east-west trending transect, the Qva thins to the east as it rises above a ridge composed of Pre- Vashon glacial deposits. Along the southern, east-west trending transect, the Qva pinches out against a ridge composed of pre-Vashon interglacial deposits. Two plausible explanations for this ridge are paleotopography and active faulting associated with the Southern Whidbey Fault Zone. Further investigations should be done using geophysical methods and the modeling methods described in this study to determine the nature of this ridge. The relative density of the Qva in the study area ranges from loose to very dense, with the loose end of the spectrum probably relating to heave in saturated sands. I found subtle correlations between density and depth. Volumetric analysis of the soil groups listed in the boring logs indicate that the Qva in the study area is composed of approximately 9.5% gravel, 89.3% sand, and 1.2% silt and clay. The natural moisture content ranges from 3.0 to 35.4% in select samples from the Qva. The moisture content appears to increase with depth and fines content. The water table in the study area ranges in elevation from 231.9 to 458 ft, based on observations and measurements recorded in the boring logs. The results from rising-head and falling-head slug tests done at a single well in the study area indicate that the geometric mean of hydraulic conductivity is 15.93 ft/d (5.62 x 10-03 cm/s), the storativity is 3.28x10-03, and the estimated transmissivity is 738.58 ft2/d in the vicinity of this observation well. At this location, there was 1.73 ft of seasonal variation in groundwater elevation between August 2014 and March 2015.

Mollusca Non-Grata: The influence of top-down control and residence time on the abundance, distribution, and behavior of non-native marine snails in Washington State

Thesis (Ph.D.)--University of Washington, 2016-06

Changes in body water distribution during treatment with inhaled steroid in pre-school children

Primary objective: The study aimed to examine the changes in water distribution in the soft tissue during systemic steroid activity. Research design: A three-way cross-over, randomized, placebo-controlled, double-blind trial was used, including 4 weeks of fluticasone propionate pMDI 200 mug b.i.d. delivered via Babyhaler(R), budesonide pressurized metered dose inhaler (pMDI) 200 mug b.i.d. delivered via Nebuchamber(R) and placebo. Spacers were primed before use. In total, 40 children aged 1-3 years, with mild intermittent asthma were included. Twenty-five of the children completed all three treatments. At the end of each treatment period body impedance and skin ultrasonography were measured. Methods and procedures: We measured changes in water content of the soft tissues by two methods. Skin ultrasonography was used to detect small changes in dermal water content, and bioelectrical impedance was used to assess body water content and distribution. Main outcomes and results: We found an increase in skin density of the shin from fluticasone as measured by ultrasonography (p = 0.01). There was a tendency for a consistent elevation of impedance parameters from active treatments compared to placebo although overall this effect was not statistically significant (0.1< p <0.2). However, sub-analyses indicated a significant effect on whole-body and leg impedance from budesonide treatment (p <0.05). Conclusion: Decreased growth during inhaled steroid treatment seems to partly reflect generalized changes in body water.

A new method for identification of protein (sub)families in a set of proteins based on hydropathy distribution in proteins

Structural similarity among proteins is reflected in the distribution of hydropathicity along the amino acids in the protein sequence. Similarities in the hydropathy distributions are obvious for homologous proteins within a protein family. They also were observed for proteins with related structures, even when sequence similarities were undetectable. Here we present a novel method that employs the hydropathy distribution in proteins for identification of (sub)families in a set of (homologous) proteins. We represent proteins as points in a generalized hydropathy space, represented by vectors of specifically defined features. The features are derived from hydropathy of the individual amino acids. Projection of this space onto principal axes reveals groups of proteins with related hydropathy distributions. The groups identified correspond well to families of structurally and functionally related proteins. We found that this method accurately identifies protein families in a set of proteins, or subfamilies in a set of homologous proteins. Our results show that protein families can be identified by the analysis of hydropathy distribution, without the need for sequence alignment. (C) 2005 Wiley-Liss, Inc.

Designs for generalized linear models with several variables and model uncertainty

Standard factorial designs sometimes may be inadequate for experiments that aim to estimate a generalized linear model, for example, for describing a binary response in terms of several variables. A method is proposed for finding exact designs for such experiments that uses a criterion allowing for uncertainty in the link function, the linear predictor, or the model parameters, together with a design search. Designs are assessed and compared by simulation of the distribution of efficiencies relative to locally optimal designs over a space of possible models. Exact designs are investigated for two applications, and their advantages over factorial and central composite designs are demonstrated.

An upper bound on the Bayesian error bars for generalized linear regression

In the Bayesian framework, predictions for a regression problem are expressed in terms of a distribution of output values. The mode of this distribution corresponds to the most probable output, while the uncertainty associated with the predictions can conveniently be expressed in terms of error bars. In this paper we consider the evaluation of error bars in the context of the class of generalized linear regression models. We provide insights into the dependence of the error bars on the location of the data points and we derive an upper bound on the true error bars in terms of the contributions from individual data points which are themselves easily evaluated.

Study of Queuing Systems with a Generalized Departure Process

This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.

Trimmed Likelihood Estimation of the Parameters of the Generalized Extreme Value Distributions: a Monte-Carlo Study

2000 Mathematics Subject Classification: Primary 62F35; Secondary 62P99