Bayesian change-point analysis in linear regression model with scale mixtures of normal distributions

In this thesis, we consider Bayesian inference on the detection of variance change-point models with scale mixtures of normal (for short SMN) distributions. This class of distributions is symmetric and thick-tailed and includes as special cases: Gaussian, Student-t, contaminated normal, and slash distributions. The proposed models provide greater flexibility to analyze a lot of practical data, which often show heavy-tail and may not satisfy the normal assumption. As to the Bayesian analysis, we specify some prior distributions for the unknown parameters in the variance change-point models with the SMN distributions. Due to the complexity of the joint posterior distribution, we propose an efficient Gibbs-type with Metropolis- Hastings sampling algorithm for posterior Bayesian inference. Thereafter, following the idea of [1], we consider the problems of the single and multiple change-point detections. The performance of the proposed procedures is illustrated and analyzed by simulation studies. A real application to the closing price data of U.S. stock market has been analyzed for illustrative purposes.

Descriptive Statistics and Linear Regression

This morning Dr. Battle will introduce descriptive statistics and linear regression and how to apply these concepts in mathematical modeling. You will also learn how to use a spreadsheet to help with statistical analysis and to create graphs.

On Graphically Checking Goodness-of-fit of Binary Logistic Regression Models

OBJECTIVES: This paper is concerned with checking goodness-of-fit of binary logistic regression models. For the practitioners of data analysis, the broad classes of procedures for checking goodness-of-fit available in the literature are described. The challenges of model checking in the context of binary logistic regression are reviewed. As a viable solution, a simple graphical procedure for checking goodness-of-fit is proposed. METHODS: The graphical procedure proposed relies on pieces of information available from any logistic analysis; the focus is on combining and presenting these in an informative way. RESULTS: The information gained using this approach is presented with three examples. In the discussion, the proposed method is put into context and compared with other graphical procedures for checking goodness-of-fit of binary logistic models available in the literature. CONCLUSION: A simple graphical method can significantly improve the understanding of any logistic regression analysis and help to prevent faulty conclusions.

A Combinatorial Approach to the Variable Selection in Multiple Linear Regression: Analysis of Selwood et al Data set -A Case Study.

A combinatorial protocol (CP) is introduced here to interface it with the multiple linear regression (MLR) for variable selection. The efficiency of CP-MLR is primarily based on the restriction of entry of correlated variables to the model development stage. It has been used for the analysis of Selwood et al data set [16], and the obtained models are compared with those reported from GFA [8] and MUSEUM [9] approaches. For this data set CP-MLR could identify three highly independent models (27, 28 and 31) with Q2 value in the range of 0.632-0.518. Also, these models are divergent and unique. Even though, the present study does not share any models with GFA [8], and MUSEUM [9] results, there are several descriptors common to all these studies, including the present one. Also a simulation is carried out on the same data set to explain the model formation in CP-MLR. The results demonstrate that the proposed method should be able to offer solutions to data sets with 50 to 60 descriptors in reasonable time frame. By carefully selecting the inter-parameter correlation cutoff values in CP-MLR one can identify divergent models and handle data sets larger than the present one without involving excessive computer time.

Dual-energy X-ray absorptiometry for measuring total bone mineral content in the rat: study of accuracy and precision

Sequential studies of osteopenic bone disease in small animals require the availability of non-invasive, accurate and precise methods to assess bone mineral content (BMC) and bone mineral density (BMD). Dual-energy X-ray absorptiometry (DXA), which is currently used in humans for this purpose, can also be applied to small animals by means of adapted software. Precision and accuracy of DXA was evaluated in 10 rats weighing 50-265 g. The rats were anesthetized with a mixture of ketamine-xylazine administrated intraperitoneally. Each rat was scanned six times consecutively in the antero-posterior incidence after repositioning using the rat whole-body software for determination of whole-body BMC and BMD (Hologic QDR 1000, software version 5.52). Scan duration was 10-20 min depending on rat size. After the last measurement, rats were sacrificed and soft tissues were removed by dermestid beetles. Skeletons were then scanned in vitro (ultra high resolution software, version 4.47). Bones were subsequently ashed and dissolved in hydrochloric acid and total body calcium directly assayed by atomic absorption spectrophotometry (TBCa[chem]). Total body calcium was also calculated from the DXA whole-body in vivo measurement (TBCa[DXA]) and from the ultra high resolution measurement (TBCa[UH]) under the assumption that calcium accounts for 40.5% of the BMC expressed as hydroxyapatite. Precision error for whole-body BMC and BMD (mean +/- S.D.) was 1.3% and 1.5%, respectively. Simple regression analysis between TBCa[DXA] or TBCa[UH] and TBCa[chem] revealed tight correlations (n = 0.991 and 0.996, respectively), with slopes and intercepts which were significantly different from 1 and 0, respectively.(ABSTRACT TRUNCATED AT 250 WORDS)

Integration of Truncated Distributions in Exponential Family with Simulation Models of Logistics and Supply Chain Management

Truncated distributions of the exponential family have great influence in the simulation models. This paper discusses the truncated Weibull distribution specifically. The truncation of the distribution is achieved by the Maximum Likelihood Estimation method or combined with the expectation and variance expressions. After the fitting of distribution, the goodness-of-fit tests (the Chi-Square test and the Kolmogorov-Smirnov test) are executed to rule out the rejected hypotheses. Finally the distributions are integrated in various simulation models, e. g. shipment consolidation model, to compare the influence of truncated and original versions of Weibull distribution on the model.

Stochastic search for semiparametric linear regression models

This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar [Ann. Statist. 15(3) (1987) 1131–1154]. The idea is to generate a random finite subset of a parameter space which will automatically contain points which are very close to an unknown true parameter. The motivation for this procedure comes from recent work of Dümbgen et al. [Ann. Statist. 39(2) (2011) 702–730] on regression models with log-concave error distributions.

Tumor Regression Grading of Gastrointestinal Carcinomas after Neoadjuvant Treatment

Multimodal therapy concepts have been successfully implemented in the treatment of locally advanced gastrointestinal malignancies. The effects of neoadjuvant chemo- or radiochemotherapy such as scarry fibrosis or resorptive changes and inflammation can be determined by histopathological investigation of the subsequent resection specimen. Tumor regression grading (TRG) systems which aim to categorize the amount of regressive changes after cytotoxic treatment mostly refer onto the amount of therapy induced fibrosis in relation to residual tumor or the estimated percentage of residual tumor in relation to the previous tumor site. Commonly used TRGs for upper gastrointestinal carcinomas are the Mandard grading and the Becker grading system, e.g., and for rectal cancer the Dworak or the Rödel grading system, or other systems which follow similar definitions. Namely for gastro-esophageal carcinomas these TRGs provide important prognostic information since complete or subtotal tumor regression has shown to be associated with better patient's outcome. The prognostic value of TRG may even exceed those of currently used staging systems (e.g., TNM staging) for tumors treated by neoadjuvant therapy. There have been some limitations described regarding interobserver variability especially in borderline cases, which may be improved by standardization of work up of resection specimen and better training of histopathologic determination of regressive changes. It is highly recommended that TRG should be implemented in every histopathological report of neoadjuvant treated gastrointestinal carcinomas. The aim of this review is to disclose the relevance of histomorphological TRG to accomplish an optimal therapy for patients with gastrointestinal carcinomas.

Tumor regression grade of urothelial bladder cancer after neoadjuvant chemotherapy: a novel and successful strategy to predict survival.

Histopathologic tumor regression grades (TRGs) after neoadjuvant chemotherapy predict survival in different cancers. In bladder cancer, corresponding studies have not been conducted. Fifty-six patients with advanced invasive urothelial bladder cancer received neoadjuvant chemotherapy before cystectomy and lymphadenectomy. TRGs were defined as follows: TRG1: complete tumor regression; TRG2: >50% tumor regression; TRG3: 50% or less tumor regression. Separate TRGs were assigned for primary tumors and corresponding lymph nodes. The prognostic impact of these 2 TRGs, the highest (dominant) TRG per patient, and competing tumor features reflecting tumor regression (ypT/ypN stage, maximum diameter of the residual tumor) were determined. Tumor characteristics in initial transurethral resection of the bladder specimens were tested for response prediction. The frequency of TRGs 1, 2, and 3 in the primary tumors were n=16, n=19, and n=21; corresponding data from the lymph nodes were n=31, n=9, and n=16. Interobserver agreement in determination of the TRG was strong (κ=0.8). Univariately, all evaluated parameters were significantly (P≤0.001) related to overall survival; however, the segregation of the Kaplan-Meier curves was best for the dominant TRG. In multivariate analysis, only dominant TRG predicted overall survival independently (P=0.035). In transurethral resection specimens of the chemotherapy-naive bladder cancer, the only tumor feature with significant (P<0.03) predictive value for therapy response was a high proliferation rate. In conclusion, among all parameters reflecting tumor regression, the dominant TRG was the only independent risk factor. A favorable chemotherapy response is associated with a high proliferation rate in the initial chemotherapy-naive bladder cancer. This feature might help personalize neoadjuvant chemotherapy.

Comparison of partial least squares regression and principal component regression for pelvic shape prediction.

This paper studied two different regression techniques for pelvic shape prediction, i.e., the partial least square regression (PLSR) and the principal component regression (PCR). Three different predictors such as surface landmarks, morphological parameters, or surface models of neighboring structures were used in a cross-validation study to predict the pelvic shape. Results obtained from applying these two different regression techniques were compared to the population mean model. In almost all the prediction experiments, both regression techniques unanimously generated better results than the population mean model, while the difference on prediction accuracy between these two regression methods is not statistically significant (α=0.01).

3D volumetric intensity reconsturction from 2D x-ray images using partial least squares regression

Reconstruction of shape and intensity from 2D x-ray images has drawn more and more attentions. Previously introduced work suffers from the long computing time due to its iterative optimization characteristics and the requirement of generating digitally reconstructed radiographs within each iteration. In this paper, we propose a novel method which uses a patient-specific 3D surface model reconstructed from 2D x-ray images as a surrogate to get a patient-specific volumetric intensity reconstruction via partial least squares regression. No DRR generation is needed. The method was validated on 20 cadaveric proximal femurs by performing a leave-one-out study. Qualitative and quantitative results demonstrated the efficacy of the present method. Compared to the existing work, the present method has the advantage of much shorter computing time and can be applied to both DXA images as well as conventional x-ray images, which may hold the potentials to be applied to clinical routine task such as total hip arthroplasty (THA).