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.

Liraglutide once a day versus exenatide twice a day for type 2 diabetes: a 26-week randomised, parallel-group, multinational, open-label trial (LEAD-6)

BACKGROUND: Unlike most antihyperglycaemic drugs, glucagon-like peptide-1 (GLP-1) receptor agonists have a glucose-dependent action and promote weight loss. We compared the efficacy and safety of liraglutide, a human GLP-1 analogue, with exenatide, an exendin-based GLP-1 receptor agonist. METHODS: Adults with inadequately controlled type 2 diabetes on maximally tolerated doses of metformin, sulphonylurea, or both, were stratified by previous oral antidiabetic therapy and randomly assigned to receive additional liraglutide 1.8 mg once a day (n=233) or exenatide 10 microg twice a day (n=231) in a 26-week open-label, parallel-group, multinational (15 countries) study. The primary outcome was change in glycosylated haemoglobin (HbA(1c)). Efficacy analyses were by intention to treat. The trial is registered with ClinicalTrials.gov, number NCT00518882. FINDINGS: Mean baseline HbA(1c) for the study population was 8.2%. Liraglutide reduced mean HbA(1c) significantly more than did exenatide (-1.12% [SE 0.08] vs -0.79% [0.08]; estimated treatment difference -0.33; 95% CI -0.47 to -0.18; p<0.0001) and more patients achieved a HbA(1c) value of less than 7% (54%vs 43%, respectively; odds ratio 2.02; 95% CI 1.31 to 3.11; p=0.0015). Liraglutide reduced mean fasting plasma glucose more than did exenatide (-1.61 mmol/L [SE 0.20] vs -0.60 mmol/L [0.20]; estimated treatment difference -1.01 mmol/L; 95% CI -1.37 to -0.65; p<0.0001) but postprandial glucose control was less effective after breakfast and dinner. Both drugs promoted similar weight losses (liraglutide -3.24 kg vs exenatide -2.87 kg). Both drugs were well tolerated, but nausea was less persistent (estimated treatment rate ratio 0.448, p<0.0001) and minor hypoglycaemia less frequent with liraglutide than with exenatide (1.93 vs 2.60 events per patient per year; rate ratio 0.55; 95% CI 0.34 to 0.88; p=0.0131; 25.5%vs 33.6% had minor hypoglycaemia). Two patients taking both exenatide and a sulphonylurea had a major hypoglycaemic episode. INTERPRETATION: Liraglutide once a day provided significantly greater improvements in glycaemic control than did exenatide twice a day, and was generally better tolerated. The results suggest that liraglutide might be a treatment option for type 2 diabetes, especially when weight loss and risk of hypoglycaemia are major considerations.

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.

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.

Adjudication-related processes are underreported and lack standardization in clinical trials of venous thromboembolism: a systematic review

OBJECTIVES Although the use of an adjudication committee (AC) for outcomes is recommended in randomized controlled trials, there are limited data on the process of adjudication. We therefore aimed to assess whether the reporting of the adjudication process in venous thromboembolism (VTE) trials meets existing quality standards and which characteristics of trials influence the use of an AC. STUDY DESIGN AND SETTING We systematically searched MEDLINE and the Cochrane Library from January 1, 2003, to June 1, 2012, for randomized controlled trials on VTE. We abstracted information about characteristics and quality of trials and reporting of adjudication processes. We used stepwise backward logistic regression model to identify trial characteristics independently associated with the use of an AC. RESULTS We included 161 trials. Of these, 68.9% (111 of 161) reported the use of an AC. Overall, 99.1% (110 of 111) of trials with an AC used independent or blinded ACs, 14.4% (16 of 111) reported how the adjudication decision was reached within the AC, and 4.5% (5 of 111) reported on whether the reliability of adjudication was assessed. In multivariate analyses, multicenter trials [odds ratio (OR), 8.6; 95% confidence interval (CI): 2.7, 27.8], use of a data safety-monitoring board (OR, 3.7; 95% CI: 1.2, 11.6), and VTE as the primary outcome (OR, 5.7; 95% CI: 1.7, 19.4) were associated with the use of an AC. Trials without random allocation concealment (OR, 0.3; 95% CI: 0.1, 0.8) and open-label trials (OR, 0.3; 95% CI: 0.1, 1.0) were less likely to report an AC. CONCLUSION Recommended processes of adjudication are underreported and lack standardization in VTE-related clinical trials. The use of an AC varies substantially by trial characteristics.

Lameness and foot lesions in Swiss dairy cows: II. Risk factors.

The objective of this study was to evaluate risk factors associated with foot lesions and lameness in Swiss dairy cows. Potential risk factors were recorded by means of examination of 1'449 Swiss cows and the management systems of 78 farms during routine claw-trimming, and during personal interviews with the associated farmers. Statistical analysis of animal-based and herd level risk factors were performed using multivariate logistic regression models. The risk of being lame was increased in cows affected by digital dermatitis complex, heel-horn erosion, interdigital hyperplasia, Rusterholz' sole ulcer, deep laceration, double sole and severe hemorrhages. Cleanliness, BCS, affection with other foot lesions, breed, importance of claw health to the farmer, frequency of routine claw-trimming, producing according to the guidelines of the welfare label program RAUS, and silage feeding were shown to be associated with the occurrence of some of the evaluated foot lesions and lameness. The identified risk factors may help to improve management and the situation of lameness and claw health in dairy cows in Switzerland and other alpine areas with similar housing and pasturing systems.