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.^

Analysis of life expectancy using linear and nonlinear models

Life expectancy has consistently increased over the last 150 years due to improvements in nutrition, medicine, and public health. Several studies found that in many developed countries, life expectancy continued to rise following a nearly linear trend, which was contrary to a common belief that the rate of improvement in life expectancy would decelerate and was fit with an S-shaped curve. Using samples of countries that exhibited a wide range of economic development levels, we explored the change in life expectancy over time by employing both nonlinear and linear models. We then observed if there were any significant differences in estimates between linear models, assuming an auto-correlated error structure. When data did not have a sigmoidal shape, nonlinear growth models sometimes failed to provide meaningful parameter estimates. The existence of an inflection point and asymptotes in the growth models made them inflexible with life expectancy data. In linear models, there was no significant difference in the life expectancy growth rate and future estimates between ordinary least squares (OLS) and generalized least squares (GLS). However, the generalized least squares model was more robust because the data involved time-series variables and residuals were positively correlated. ^

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).

Pollen record and calculated holocene vegetation and climate dynamics from Sihailongwan Maar Lake, NE China

High-resolution palynological analysis on annually laminated sediments of Sihailongwan Maar Lake (SHL) provides new insights into the Holocene vegetation and climate dynamics of NE China. The robust chronology of the presented record is based on varve counting and AMS radiocarbon dates from terrestrial plant macro-remains. In addition to the qualitative interpretation of the pollen data, we provide quantitative reconstructions of vegetation and climate based on the method of biomization and weighted averaging partial least squares regression (WA-PLS) technique, respectively. Power spectra were computed to investigate the frequency domain distribution of proxy signals and potential natural periodicities. Pollen assemblages, pollen-derived biome scores and climate variables as well as the cyclicity pattern indicate that NE China experienced significant changes in temperature and moisture conditions during the Holocene. Within the earliest phase of the Holocene, a large-scale reorganization of vegetation occurred, reflecting the reconstructed shift towards higher temperatures and precipitation values and the initial Holocene strengthening and northward expansion of the East Asian summer monsoon (EASM). Afterwards, summer temperatures remain at a high level, whereas the reconstructed precipitation shows an increasing trend until approximately 4000 cal. yr BP. Since 3500 cal. yr BP, temperature and precipitation values decline, indicating moderate cooling and weakening of the EASM. A distinct periodicity of 550-600 years and evidence of a Mid-Holocene transition from a temperature-triggered to a predominantly moisture-triggered climate regime are derived from the power spectra analysis. The results obtained from SHL are largely consistent with other palaeoenvironmental records from NE China, substantiating the regional nature of the reconstructed vegetation and climate patterns. However, the reconstructed climate changes contrast with the moisture evolution recorded in S China and the mid-latitude (semi-)arid regions of N China. Whereas a clear insolation-related trend of monsoon intensity over the Holocene is lacking from the SHL record, variations in the coupled atmosphere-Pacific Ocean system can largely explain the reconstructed changes in NE China.

Paleomagnetic of lower Cretaceous sediments from the Argo and Gascoyne Abyssal Plain

Lower Cretaceous sediments were sampled for magnetostratigraphy at three sites. ODP Site 765 and DSDP Site 261, in the Argo Abyssal Plain, consist primarily of brownish-red to gray claystone having hematite and magnetite carriers of characteristic magnetization. ODP Site 766, in the Gascoyne Abyssal Plain, consists mainly of dark greenish-gray volcaniclastic turbidites with magnetite as the carrier of characteristic magnetization. Progressive thermal demagnetization (Sites 765 and 261) or alternating field demagnetization (Site 766) yielded well-defined polarity zones and a set of reliable paleolatitudes. Magnetic polarity chrons were assigned to polarity zones using biostratigraphic correlations. Late Aptian chron M"-1"r, a brief reversed-polarity chron younger than MOr, is a narrow, 40-cm feature delimited in Hole 765C. Early Aptian reversed-polarity chron MOr is also present in Hole 765C. Polarity chrons Mir through M3r were observed in the Barremian of all three sites. Valanginian and Hauterivian polarity chrons can be tentatively assigned to polarity zones only in Hole 766A. The paleolatitude of this region remained at 35° to 37°S from the Berriasian through the Aptian. During this interval, there was approximately 16° of clockwise rotation, with the oriented sample suites of Site 765 displaying a Berriasian declination of 307° to an Aptian declination of 323°. These results are consistent with the interpolated Early Cretaceous apparent polar wander for Australia, but indicate that this region was approximately 5? farther north than predicted.

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.