BEST SUBSET SELECTION FOR CATEGORICAL DATA

When choosing among models to describe categorical data, the necessity to consider interactions makes selection more difficult. With just four variables, considering all interactions, there are 166 different hierarchical models and many more non-hierarchical models. Two procedures have been developed for categorical data which will produce the "best" subset or subsets of each model size where size refers to the number of effects in the model. Both procedures are patterned after the Leaps and Bounds approach used by Furnival and Wilson for continuous data and do not generally require fitting all models. For hierarchical models, likelihood ratio statistics (G('2)) are computed using iterative proportional fitting and "best" is determined by comparing, among models with the same number of effects, the Pr((chi)(,k)('2) (GREATERTHEQ) G(,ij)('2)) where k is the degrees of freedom for ith model of size j. To fit non-hierarchical as well as hierarchical models, a weighted least squares procedure has been developed.^ The procedures are applied to published occupational data relating to the occurrence of byssinosis. These results are compared to previously published analyses of the same data. Also, the procedures are applied to published data on symptoms in psychiatric patients and again compared to previously published analyses.^ These procedures will make categorical data analysis more accessible to researchers who are not statisticians. The procedures should also encourage more complex exploratory analyses of epidemiologic data and contribute to the development of new hypotheses for study. ^

AN EMPIRICAL ESTIMATION OF MEDICAL AND NON-MEDICAL INPUTS IN THE PRODUCTION OF CARDIO-RESPIRATORY PHYSICAL HEALTH STATUS

The purpose of this study was to examine, in the context of an economic model of health production, the relationship between inputs (health influencing activities) and fitness.^ Primary data were collected from 204 employees of a large insurance company at the time of their enrollment in an industrially-based health promotion program. The inputs of production included medical care use, exercise, smoking, drinking, eating, coronary disease history, and obesity. The variables of age, gender and education known to affect the production process were also examined. Two estimates of fitness were used; self-report and a physiologic estimate based on exercise treadmill performance. Ordinary least squares and two-stage least squares regression analyses were used to estimate the fitness production functions.^ In the production of self-reported fitness status the coefficients for the exercise, smoking, eating, and drinking production inputs, and the control variable of gender were statistically significant and possessed theoretically correct signs. In the production of physiologic fitness exercise, smoking and gender were statistically significant. Exercise and gender were theoretically consistent while smoking was not. Results are compared with previous analyses of health production. ^

THE IMPROVEMENT REGION IN RIDGE REGRESSION

One of the difficulties in the practical application of ridge regression is that, for a given data set, it is unknown whether a selected ridge estimator has smaller squared error than the least squares estimator. The concept of the improvement region is defined, and a technique is developed which obtains approximate confidence intervals for the value of ridge k which produces the maximum reduction in mean squared error. Two simulation experiments were conducted to investigate how accurate these approximate confidence intervals might be. ^

Spatial analysis of cardiovascular disease mortality and air pollution in Harris County, Texas

The association between fine particulate matter air pollution (PM2.5) and cardiovascular disease (CVD) mortality was spatially analyzed for Harris County, Texas, at the census tract level. The objective was to assess how increased PM2.5 exposure related to CVD mortality in this area while controlling for race, income, education, and age. An estimated exposure raster was created for Harris County using Kriging to estimate the PM2.5 exposure at the census tract level. The PM2.5 exposure and the CVD mortality rates were analyzed in an Ordinary Least Squares (OLS) regression model and the residuals were subsequently assessed for spatial autocorrelation. Race, median household income, and age were all found to be significant (p<0.05) predictors in the model. This study found that for every one μg/m3 increase in PM2.5 exposure, holding age and education variables constant, an increase of 16.57 CVD deaths per 100,000 would be predicted for increased minimum exposure values and an increase of 14.47 CVD deaths per 100,000 would be predicted for increased maximum exposure values. This finding supports previous studies associating PM2.5 exposure with CVD mortality. This study further identified the areas of greatest PM2.5 exposure in Harris County as being the geographical locations of populations with the highest risk of CVD (i.e., predominantly older, low-income populations with a predominance of African Americans). The magnitude of the effect of PM2.5 exposure on CVD mortality rates in the study region indicates a need for further community-level studies in Harris County, and suggests that reducing excess PM2.5 exposure would reduce CVD mortality.^

Regression with autocorrelated data: A study of time trend of global infant mortality rate

The infant mortality rate (IMR) is considered to be one of the most important indices of a country's well-being. Countries around the world and other health organizations like the World Health Organization are dedicating their resources, knowledge and energy to reduce the infant mortality rates. The well-known Millennium Development Goal 4 (MDG 4), whose aim is to archive a two thirds reduction of the under-five mortality rate between 1990 and 2015, is an example of the commitment. ^ In this study our goal is to model the trends of IMR between the 1950s to 2010s for selected countries. We would like to know how the IMR is changing overtime and how it differs across countries. ^ IMR data collected over time forms a time series. The repeated observations of IMR time series are not statistically independent. So in modeling the trend of IMR, it is necessary to account for these correlations. We proposed to use the generalized least squares method in general linear models setting to deal with the variance-covariance structure in our model. In order to estimate the variance-covariance matrix, we referred to the time-series models, especially the autoregressive and moving average models. Furthermore, we will compared results from general linear model with correlation structure to that from ordinary least squares method without taking into account the correlation structure to check how significantly the estimates change.^

Design and Optimization of Four-dimensional Cone-beam Computed Tomography in Image-guided Radiation Therapy

The influence of respiratory motion on patient anatomy poses a challenge to accurate radiation therapy, especially in lung cancer treatment. Modern radiation therapy planning uses models of tumor respiratory motion to account for target motion in targeting. The tumor motion model can be verified on a per-treatment session basis with four-dimensional cone-beam computed tomography (4D-CBCT), which acquires an image set of the dynamic target throughout the respiratory cycle during the therapy session. 4D-CBCT is undersampled if the scan time is too short. However, short scan time is desirable in clinical practice to reduce patient setup time. This dissertation presents the design and optimization of 4D-CBCT to reduce the impact of undersampling artifacts with short scan times. This work measures the impact of undersampling artifacts on the accuracy of target motion measurement under different sampling conditions and for various object sizes and motions. The results provide a minimum scan time such that the target tracking error is less than a specified tolerance. This work also presents new image reconstruction algorithms for reducing undersampling artifacts in undersampled datasets by taking advantage of the assumption that the relevant motion of interest is contained within a volume-of-interest (VOI). It is shown that the VOI-based reconstruction provides more accurate image intensity than standard reconstruction. The VOI-based reconstruction produced 43% fewer least-squares error inside the VOI and 84% fewer error throughout the image in a study designed to simulate target motion. The VOI-based reconstruction approach can reduce acquisition time and improve image quality in 4D-CBCT.

Application of the general linear model to assess the effect of missing data on bone marrow mononuclear cell therapy with infusion timing and follow-up MRI

With most clinical trials, missing data presents a statistical problem in evaluating a treatment's efficacy. There are many methods commonly used to assess missing data; however, these methods leave room for bias to enter the study. This thesis was a secondary analysis on data taken from TIME, a phase 2 randomized clinical trial conducted to evaluate the safety and effect of the administration timing of bone marrow mononuclear cells (BMMNC) for subjects with acute myocardial infarction (AMI).^ We evaluated the effect of missing data by comparing the variance inflation factor (VIF) of the effect of therapy between all subjects and only subjects with complete data. Through the general linear model, an unbiased solution was made for the VIF of the treatment's efficacy using the weighted least squares method to incorporate missing data. Two groups were identified from the TIME data: 1) all subjects and 2) subjects with complete data (baseline and follow-up measurements). After the general solution was found for the VIF, it was migrated Excel 2010 to evaluate data from TIME. The resulting numerical value from the two groups was compared to assess the effect of missing data.^ The VIF values from the TIME study were considerably less in the group with missing data. By design, we varied the correlation factor in order to evaluate the VIFs of both groups. As the correlation factor increased, the VIF values increased at a faster rate in the group with only complete data. Furthermore, while varying the correlation factor, the number of subjects with missing data was also varied to see how missing data affects the VIF. When subjects with only baseline data was increased, we saw a significant rate increase in VIF values in the group with only complete data while the group with missing data saw a steady and consistent increase in the VIF. The same was seen when we varied the group with follow-up only data. This essentially showed that the VIFs steadily increased when missing data is not ignored. When missing data is ignored as with our comparison group, the VIF values sharply increase as correlation increases.^

Inorganic carbon and geochemistry measurements from landfast sea ice in Resolute Passage, Nunavut, Canada, as part of the Arctic-ICE project, May - June 2010

We conducted a six-week investigation of the sea ice inorganic carbon system during the winter-spring transition in the Canadian Arctic Archipelago. Samples for the determination of sea ice geochemistry were collected in conjunction with physical and biological parameters as part of the 2010 Arctic-ICE (Arctic - Ice-Covered Ecosystem in a Rapidly Changing Environment) program, a sea ice-based process study in Resolute Passage, Nunavut. The goal of Arctic-ICE was to determine the physical-biological processes controlling the timing of primary production in Arctic landfast sea ice and to better understand the influence of these processes on the drawdown and release of climatically active gases. The field study was conducted from 1 May to 21 June, 2010.

Current meter data from mooring stations in the English Channel (Table 1)

A new technique for the harmonic analysis of current observations is described. It consists in applying a linear band pass filter which separates the various species and removes the contribution of non-tidal effects at intertidal frequencies. The tidal constituents are then evaluated through the method of least squares. In spite of the narrowness of the filter, only three days of data are lost through the filtering procedure and the only requirement on the data is that the time interval between samples be an integer fraction of one day. This technique is illustrated through the analysis of a few French current observations from the English Channel within the framework of INOUT. The characteristics of the main tidal constituents are given.

Sedimentaology, pollen profile, and climate reconstruction on a sediment core from Trou Lake, Yukon, Canada

Beringian climate and environmental history are poorly characterized at its easternmost edge. Lake sediments from the northern Yukon Territory have recorded sedimentation, vegetation, summer temperature and precipitation changes since ~16 cal ka BP. Herb-dominated tundra persisted until ~14.7 cal ka BP with mean July air temperatures less than or equal to 5 °C colder and annual precipitation 50 to 120 mm lower than today. Temperatures rapidly increased during the Bølling/Allerød interstadial towards modern conditions, favoring establishment of Betula-Salix shrub tundra. Pollen-inferred temperature reconstructions recorded a pronounced Younger Dryas stadial in east Beringia with a temperature drop of ~1.5 °C (~2.5 to 3.0 °C below modern conditions) and low net precipitation (90 to 170 mm) but show little evidence of an early Holocene thermal maximum in the pollen record. Sustained low net precipitation and increased evaporation during early Holocene warming suggest a moisture-limited spread of vegetation and an obscured summer temperature maximum. Northern Yukon Holocene moisture availability increased in response to a retreating Laurentide Ice Sheet, postglacial sea level rise, and decreasing summer insolation that in turn led to establishment of Alnus-Betula shrub tundra from ~5 cal ka BP until present, and conversion of a continental climate into a coastal-maritime climate near the Beaufort Sea.

Regional geoid model for the area of the subglacial Lake Vostok

We present a regional geoid model for the area of Lake Vostok, Antarctica, from a combination of local airborne gravity, ice-surface and ice-thickness data and a lake bathymetry model. The topography data are used for residual terrain modelling (RTM) in a remove-compute-restore approach together with the GOCE satellite model GOCO03S. The disturbing potential at the Earth's surface, i.e. the quasigeoid, is predicted by least-squares collocation (LSC) and subsequently converted to geoid heights. Compared to GOCO03S our regional solution provides an additional short-wavelength signal of up to 1.48 m, or 0.56 m standard deviation, respectively. More details can be found in Schwabe et. al (2014).

Paleomagneitc of early Cretaceous sediments from the western Central Atlantic

Drilling at Sites 534 and 603 of the Deep Sea Drilling Project recovered thick sections of Berriasian through Aptian white limestones to dark gray marls, interbedded with claystone and clastic turbidites. Progressive thermal demagnetization removed a normal-polarity overprint carried by goethite and/or pyrrhotite. The resulting characteristic magnetization is carried predominantly by magnetite. Directions and reliability of characteristic magnetization of each sample were computed by using least squares line-fits of magnetization vectors. The corrected true mean inclinations of the sites suggest that the western North Atlantic underwent approximately 6° of steady southward motion between the Berriasian and Aptian stages. The patterns of magnetic polarity of the two sites, when plotted on stratigraphic columns of the pelagic sediments without turbidite beds, display a fairly consistent magnetostratigraphy through most of the Hauterivian-Barremian interval, using dinoflagellate and nannofossil events and facies changes in pelagic sediment as controls on the correlations. The composite magnetostratigraphy appears to include most of the features of the M-sequence block model of magnetic anomalies from Ml to Ml ON (Barremian-Hauterivian) and from M16 to M23 (Berriasian-Tithonian). The Valanginian magnetostratigraphy of the sites does not exhibit reversed polarity intervals corresponding to Ml 1 to M13 of the M-sequence model; this may be the result of poor magnetization, of a major unrecognized hiatus in the early to middle Valanginian in the western North Atlantic, or of an error in the standard block model. Based on these tentative polarity-zone correlations, the Hauterivian/Barremian boundary occurs in or near the reversed-polarity Chron M7 or M5, depending upon whether the dinoflagellate or nannofossil zonation, respectively, is used; the Valanginian/Hauterivian boundary, as defined by the dinoflagellate zonation, is near reversed-polarity Chron M10N.

Basalt density, basement age, and intrusive/extrusive relations from DSDP Legs 2 through 7, 9, and 14

Densities of layer 2 basalt recovered during the Deep Sea Drilling Project have been found to decrease steadily with age, a finding ascribed to progressive submarine weathering in the context of sea-floor spreading. The least-squares solution for 52 density measurements gives a rate of decrease in density of (Delta p)/(Delta t) = -0.0046 g per ccm m.y. = -16 percent per 100 m.y., which is in excellent agreement with earlier estimates based on observed chemical depletion rates of dredged oceanic basalt. Weathering of sea-floor basalt, should it penetrate to any considerable depth in layer 2, will decrease layer 2 seismic refraction velocities, act as a source of geothermal heat, and substantially influence the chemistry of sea water and the overlying column of sediment.

Iberian Margin 420 kyr geochemical and color variations record

Here we report 420 kyr long records of sediment geochemical and color variations from the southwestern Iberian Margin. We synchronized the Iberian Margin sediment record to Antarctic ice cores and speleothem records on millennial time scales and investigated the phase responses relative to orbital forcing of multiple proxy records available from these cores. Iberian Margin sediments contain strong precession power. Sediment "redness" (a* and 570-560 nm) and the ratio of long-chain alcohols to n-alkanes (C26OH/(C26OH + C29)) are highly coherent and in-phase with precession. Redder layers and more oxidizing conditions (low alcohol ratio) occur near precession minima (summer insolation maxima). We suggest these proxies respond rapidly to low-latitude insolation forcing by wind-driven processes (e.g., dust transport, upwelling, precipitation). Most Iberian Margin sediment parameters lag obliquity maxima by 7-8 ka, indicating a consistent linear response to insolation forcing at obliquity frequencies driven mainly by high-latitude processes. Although the lengths of the time series are short (420 ka) for detecting 100 kyr eccentricity cycles, the phase relationships support those obtained by Shackleton []. Antarctic temperature and the Iberian Margin alcohol ratios (C26OH/(C26OH + C29)) lead eccentricity maxima by 6 kyr, with lower ratios (increased oxygenation) occurring at eccentricity maxima. CO2, CH4, and Iberian SST are nearly in phase with eccentricity, and minimum ice volume (as inferred from Pacific d18Oseawater) lags eccentricity maxima by 10 kyr. The phase relationships derived in this study continue to support a potential role of the Earth's carbon cycle in contributing to the 100 kyr cycle.

Integrated Paleocene calcareous plankton magnetobiochronology of DSDP Hole 43-384 in the Northwest Atlantic Ocean

At Deep Sea Drilling Site 384 (J-Anomaly Ridge, Grand Banks Continental Rise, NW Atlantic Ocean) Paleocene nannofossil chalks and oozes (~70 m thick) are unconformably/disconformably underlain (~168 m; upper Maastrichtian) and overlain (~98.7 m; upper lower Eocene) by sediments of comparable lithologies. The chalks are more indurated in stratigraphically higher levels of the Paleocene reflecting increasing amounts of biosiliceous (radiolarians and diatoms) components. This site serves as an excellent location for an integrated calcareous and siliceous microfossil zonal stratigraphy and stable isotope stratigraphy. We report the results of a magnetostratigraphic study which, when incorporated with published magnetostratigraphic results, reveals an essentially complete magnetostratigraphic record spanning the interval from Magnetochron C31n (late Maastrichtian) to C25n (partim) (late Paleocene, Thanetian). Integrated magnetobiochronology and stable isotope stratigraphy support the interpretation of, and constrain the estimated duration of, a short hiatus (~0.9 my) within the younger part of Chron C29r (including the K/P boundary) and an ~6 my hiatus separating upper Paleocene (Magnetozone C25n) and upper lower Eocene (Magnetozone C22r) sediments. Some 30 planktonic foraminiferal datum levels [including the criteria used to denote the Paleocene planktonic foraminiferal (sub)tropical zonal scheme of Berggren and Miller, Micropaleontology 34 (4) (1988) 362-380 and Berggren et al., SEPM Spec. Publ. 54 (1995) 129-212, Geol. Soc. Am. Bull. 107 (11) (1995) 1272-1287], and nearly two dozen calcareous nannoplankton datum levels have been recognized and calibrated to the magnetochronology. Planktonic foraminiferal Subzones P4a and P4b of (upper Paleocene) Zone P4 are emended/redefined based on the discovery of a longer stratigraphic extension of Acarinina subsphaerica (into at last Magnetozone C25n). Stable isotope stratigraphies from benthic foraminifera and fine fraction (<38 µm) carbonate have been calibrated to the biochronology and magnetostratigraphy. A minimum in benthic foraminifer delta13C was reached near the Danian/Selandian boundary (within Chron C26r, planktonic foraminiferal Zone P3a and calcareous nannoplankton Zone NP4) and is followed by the rise to maximum delta13C values in the late Thanetian (near the base of C25n, in Zone P4c and NP9a, respectively) that can be used for global correlation in the Paleocene.