In recent years, statistical analyses, algorithms, and modeling of big data have been constrained due to computational complexity. Further, the added complexity of relationships among response and explanatory variables, such as higher-order interaction effects, make identifying predictors using standard statistical techniques difficult. These difficulties are only exacerbated in the case of small sample sizes in some studies. Recent analyses have targeted the identification of interaction effects in big data, but the development of methods to identify higher-order interaction effects has been limited by computational concerns. One recently studied method is the Feasible Solutions Algorithm (FSA), a fast, flexible method that aims to find a set of statistically optimal models via a stochastic search algorithm. Although FSA has shown promise, its current limits include that the user must choose the number of times to run the algorithm. Here, statistical guidance is provided for this number iterations by deriving a lower bound on the probability of obtaining the statistically optimal model in a number of iterations of FSA. Moreover, logistic regression is severely limited when two predictors can perfectly separate the two outcomes. In the case of small sample sizes, this occurs quite often by chance, especially in the case of a large number of predictors. Bhattacharyya distance is proposed as an alternative method to address this limitation. However, little is known about the theoretical properties or distribution of B-distance. Thus, properties and the distribution of this distance measure are derived here. A hypothesis test and confidence interval are developed and tested on both simulated and real data.

Organizations around the world have attempted to implement the concepts of the Toyota Production System (TPS), commonly referred to as Lean, with limited sustainable success. The central principles of TPS, continuous improvement and respect for people, are grounded in the Japanese values of Monozukuri and Hitozukuri. Monozukuri deals with creating or making a product, while Hitozukuri conveys the idea of developing people through learning. In order for organizations to adopt these values they must have a system that engages employees at all levels in applying problem solving to improve their work. This research uses organizational assessments obtained from a variety of organizations implementing the lean approach using the Monozukuri and Hitozukuri values, referred to as the True Lean System (TLS). This research uses an inductive research approach to identify and analyze factors that impact the use of problem solving within organizations implementing a TLS. First, the qualitative assessment data is studied using textual analysis to identify themes impacting TLS. This analysis identified three topics as the highest weighted themes: number of problem solving methods, standardization, and employee roles. This qualitative data is then transformed using an integrated design model to systematically code the information into quantitative numerical data. Finally, this data was analyzed statistically by logistic regression to identify the factors impacting the use of problem solving within these organizations. The results from the logistic regression suggest that the most successful problem solving organizations have established standards for work and training employees; as well as, a single problem solving method that all employees use when identifying and implementing continuous improvement ideas. Which leads to the conclusion, in order for an organization to sustain the concepts of TPS, there must be a focus on defining clear standardized work, training, and the implementation of a single problem solving method.

The purpose of this research is to investigate the performance of some ridge regression estimators for the logistic regression model in the presence of moderate to high correlation among the explanatory variables. As a performance criterion, we use the mean square error (MSE), the mean absolute percentage error (MAPE), the magnitude of bias, and the percentage of times the ridge regression estimator produces a higher MSE than the maximum likelihood estimator. A Monto Carlo simulation study has been executed to compare the performance of the ridge regression estimators under different experimental conditions. The degree of correlation, sample size, number of independent variables, and log odds ratio has been varied in the design of experiment. Simulation results show that under certain conditions, the ridge regression estimators outperform the maximum likelihood estimator. Moreover, an empirical data analysis supports the main findings of this study. This thesis proposed and recommended some good ridge regression estimators of the logistic regression model for the practitioners in the field of health, physical and social sciences.

Occupational and environmental epidemiological studies often involve ordinal data, including antibody titer data, indicators of health perceptions, and certain psychometrics. Ideally, such data should be analyzed using approaches that exploit the ordinal nature of the scale, while making a minimum of assumptions. In this work, we first review and illustrate the analytical technique of ordinal logistic regression called the "proportional odds model". This model, which is based on a constrained ordinal model, is considered the most popular ordinal model. We use hypothetical data to illustrate a situation where the proportional odds model holds exactly, and we demonstrate through derivations and simulations how using this model has better statistical power than simple logistic regression. The section concludes with an example illustrating the use of the model in avian and swine influenza research. In the middle section of this work, we show how the proportional model assumption can be relaxed to a less restrictive model called the "trend odds model". We demonstrate how this model is related to latent logistic, normal, and exponential distributions. In particular, scale changes in these potential latent distributions are found to be consistent with the trend odds assumption, with the logistic and exponential distributions having odds that increase in a linear or nearly linear fashion. Actual data of antibody titer against avian and swine influenza among occupationally- exposed participants and non-exposed controls illustrate the fit and interpretation of the proportional odds model and the trend odds model. Finally, we show how to perform a multivariable analysis in which some of the variables meet the proportional model assumption and some meet the trend odds assumption. Likert-scaled data pertaining to violence among middle school students illustrate the fit and interpretation of the multivariable proportional-trend odds model. In conclusion, the proportional odds model provides superior power compared to models that employ arbitrary dichotomization of ordinal data. In addition, the added complexity of the trend odds model provides improved power over the proportional odds model when there are moderate to severe departures from proportionality. The increase in power is of great public health relevance in a time of increasingly scarce resources for occupational and environmental health research. The trend odds model indicates and tests the presence of a trend in odds, providing a new dimension to risk factors and disease etiology analyses. In addition to applications demonstrated in this work, other research areas in occupational and environmental health can benefit from the use of these methods. For example, worker fatigue is often self-reported using ordinal scales, and traumatic brain injury recovery is measured using recovery scores such as the Glasgow Outcome Scale (GOS).

When the delicate hormonal balance in early pregnancy is disrupted, the consequences can be significant. We have a poor understanding of the "cross-talk" in the fetal/placental/ovarian axis that occurs throughout pregnancy and is essential for normal fetal development. This lack of knowledge challenges our ability to recognize disruptions in this axis that may be a signal for future disease. As a result, our ability to apply preventive measures against adverse obstetric outcomes, such as preterm birth (PTB), are quite limited. Attempts to predict PTB using biomarkers of feto-placental health have been largely unsuccessful, but no one has considered the inclusion of ovarian biomarkers in these models. Anti-Mullerian hormone (AMH) is a biomarker of ovarian activity that has recently been found to decline in early pregnancy at a time that corresponds to the involution of the corpus luteum (CL). The signal for CL involution is believed to originate from the placenta; therefore, the AMH levels in pregnancy may reflect the degree of ovarian up or down-regulation based on feto-placental needs. As the major function of the CL in pregnancy is the production of progesterone, which acts as an anti-inflammatory agent in the placental bed, changes in CL-derived progesterone could result in higher or lower degrees of placental inflammation. Therefore, monitoring the changes in AMH levels may provide insight into the inflammatory state of the placenta which could then be used as a signal for possible adverse obstetric outcomes resulting from a pro-inflammatory state, such as PTB. The first aim of this project was to test the hypothesis of an association between AMH levels in early pregnancy and PTB risk. When the differences in AMH levels between the 1st and 2nd trimesters of pregnancy were stratified by the level of maternal serum alpha-fetoprotein (MSAFP) and controlled for maternal weight gain between trimesters, small or absent decreases in AMH levels were associated with a higher probability of preterm birth. However, when AMH was modeled alone, no significant associations were found. The need for changes in multiple biomarkers in the fetal/placental/ovarian axis suggests that a change is only significant if it can impact multiple axis points. Therefore, models that included two biomarkers from different part of the axis would find stronger associations than two biomarkers from a single point (e.g. two feto-placental biomarkers), and monitoring these changes may help identify women at risk for PTB. The strategy of the second aim was to determine if the changes in AMH levels in early pregnancy could be used to predict time to delivery. Again, only when the risks of AMH and MSAFP were combined was a significant, dose-dependent relationship found with time to delivery. In women with an MSAFP of >1 multiple of the median (MoM), smaller declines and/or elevations in AMH levels were significantly associated with shorter times to delivery. In fact, 19% of women in the highest risk group delivered prior to 32 weeks gestation compared to 7% in the lowest risk group, and all infants who delivered prior to 24 weeks gestation were in the highest risk category. Thus, the amount of change in the AMH level when MSAFP is elevated may reflect the level of disruption in the fetal/placental/ovarian axis, which can then be used to predict time to delivery. Finally, the third aim of this study was to determine if AMH levels were associated with a pro-inflammatory placental state other than PTB. The degree of placental inflammation is known to vary by fetal gender, with male placentas having higher levels of inflammation compared to female placentas. When AMH levels were compared between women with male vs. female fetuses in early pregnancy, 1st trimester AMH levels were found to be lower when carrying a male fetus. Further, sexually-dimorphic patterns in AMH levels were seen between genders when stratified by birth outcome (term vs. preterm delivery). The stronger ovarian response seen in women with female fetuses suggests a better survival function and may account for the discrepancies between PTB rates in males and females. This also strengthens our hypothesis that the dynamic changes in AMH levels reflect the degree of placental inflammation and the need for CL-derived progesterone. This project demonstrates that the changes in AMH levels may be representative of the cross-talk occurring in the fetal/placental/ovarian axis in early pregnancy. Further, changes in AMH levels may be an indication of the amount of inflammation in the placenta and the physiologic need for higher levels of progesterone to control this inflammatory state when considered along with MSAFP. Therefore, the consideration of AMH levels as a biomarker of ovarian activity along with biomarkers of feto-placental health may provide clinically useful information about the development of future diseases such as preterm birth.

[pt] Este trabalho visa analisar os modelos atuais de avaliação de risco de crédito aplicados a empresas não-financeiras e desenvolver um modelo estatístico com o emprego da ferramenta LOGIT - Regressão Logística com base nos clientes jurídicos de uma empresa do ramo industrial. Este modelo tem como objetivo principal determinar a probabilidade de um cliente ser considerado como adimplente ou inadimplente. Com esta ferramenta o analista de crédito pode definir até que ponto se torna interessante para a empresa efetuar uma venda a prazo para o cliente. / [en] This dissertation has the objective of analyzing the current models of credit risk in non financial companies and to develop a statistical model with Logistic Regression. The main purpose of this model is to determine the probability of a client (business company) being considered a good or bad risk. This model will allow the credit analyst to measure the credit risk involved with credit sales.

1997年爆發的亞洲金融危機起因之一為金融機構信用過度擴充，隨著企業紛紛倒閉，金融機構的逾放比迅速攀升，因此，提高放款的質與量，便成了目前各金融機構經營的首重目標。為降低逾放比率、提高放款量、爭取放款時效、減少審核時間，使用自動化的審核制度是有必要的，而客觀科學化的評分方法更能使徵信資料得到迅速的整理與分析，以利放款決策的有效釐定。 本研究以國內某金融機構為研究對象，採用Logistic Regression Model為信用評等模式，針對其目前所使用之個人擔保放款的信用評分表表列變數和表外變數，深入探討並從中找出影響授信成敗之顯著變數，建立最適之信用評等模式。

Project (M.S.)--Brigham Young University. Dept. of Statistics, 2006. / Includes bibliographical references (p. 66-67).

The rate of overweight in children is increasing at an alarming rate. The IOM (2005) estimated 9 million children over the age of six in the United States are obese. Between 1980 and 2002 the CDC (2002) estimated the rate of childhood obesity has doubled for adolescents ages 12 to 19 years (7% to 16%), and tripled for those children ages six to 11 years (5% to 16%). The health consequences of being overweight are severe and lead to decreased longevity and quality of life. The purpose of this study was to determine which factors (diet, physical activity, stress, sleep, gender, ethnicity, parental obesity, self-perception, and SES) have predictive value in the development of overweight in children in grades six through eight. The epidemiological framework, Web of Causation was used to guide this study. This model originally described by MacMahon, Pugh, and Ispen (1960) allows for the investigation of multiple causative and associated factors including lifestyle, environment, psychosocial factors, health care availability, nutrition, and physical activity. A cross-sectional predictive study was completed with 75 parent and child participants from a parochial school in south Florida. A univariate analysis of all potential predictors identified in the literature using a significance of p < .25 was performed. The dependent factor was the child's BMI greater than 85% for age and gender. Fourteen factors were included in the final forward stepwise logistic regression analysis. Instruments included family demographics, the parent and student Middle School Physical Activity and Nutrition Survey (MSPAN), the Perceived Stress Scale (PSS) and Harter's Self-Perception Scale for Children (SPSC). The sample demographics were Hispanic (60%), Caucasian (25%), and Multiethnic (8%), and other (7%). The final logistics regression model found that father's obesity (OR 5.99; p= 0.001) and Self-perception of Physical Appearance (OR 0.43; p=0.038) were predictive factors of overweight in this sample of children. The findings of this study supported that family dynamics play a part in the development of this chronic disease. Future research should be directed at defining factors that place children at risk for overweight in order to develop meaningful interventions to curb this pandemic.

Influenza is a public health problem that causes serious illness and deaths all over the world. Vaccination has been shown to be the most effective mean to prevent infection. The primary component of influenza vaccine is the weakened strains. Vaccination triggers the immune system to develop antibodies against those strains whose viral surface glycoprotein hemagglutinin (HA) is similar to that of vaccine strains. However, influenza vaccine must be updated annually since the antigenic structure of HA is constantly mutation. Hemagglutination inhibition (HI) assay is a laboratory procedure frequently applied to evaluate the antigenic relationships of the influenza viruses. It enables the World Health Organization (WHO) to recommend appropriate updates on strains that will most likely be protective against the circulating influenza strains. However, HI assay is labour intensive and time-consuming since it requires several controls for standardization. We use two machine-learning methods, i.e. Artificial Neural Network (ANN) and Logistic Regression, and a Mixed-Integer Optimization Model to predict antigenic variety. The ANN generalizes the input data to patterns inherent in the data, and then uses these patterns to make predictions. The logistic regression model identifies and selects the amino acid positions, which contribute most significantly to antigenic difference. The output of the logistic regression model will be used to predict the antigenic variants based on the predicted probability. The Mixed-Integer Optimization Model is formulated to find hyperplanes that enable binary classification. The performances of our models are evaluated by cross validation.