On the Existence of Uniformly Most Powerful Bayesian Tests With Application to Non-Central Chi-Squared Tests.

Uniformly most powerful Bayesian tests (UMPBT's) are an objective class of Bayesian hypothesis tests that can be considered the Bayesian counterpart of classical uniformly most powerful tests. Because the rejection regions of UMPBT's can be matched to the rejection regions of classical uniformly most powerful tests (UMPTs), UMPBT's provide a mechanism for calibrating Bayesian evidence thresholds, Bayes factors, classical significance levels and p-values. The purpose of this article is to expand the application of UMPBT's outside the class of exponential family models. Specifically, we introduce sufficient conditions for the existence of UMPBT's and propose a unified approach for their derivation. An important application of our methodology is the extension of UMPBT's to testing whether the non-centrality parameter of a chi-squared distribution is zero. The resulting tests have broad applicability, providing default alternative hypotheses to compute Bayes factors in, for example, Pearson's chi-squared test for goodness-of-fit, tests of independence in contingency tables, and likelihood ratio, score and Wald tests.

Dual GIP and GLP-1 Receptor Agonist Tirzepatide Improves Beta-cell Function and Insulin Sensitivity in Type 2 Diabetes.

CONTEXT: Novel dual glucose-dependent insulinotropic polypeptide (GIP) and glucagon-like peptide-1 (GLP-1) receptor agonist (RA) tirzepatide demonstrated substantially greater glucose control and weight loss (WL) compared with selective GLP-1RA dulaglutide. OBJECTIVE: Explore mechanisms of glucose control by tirzepatide. DESIGN: Post hoc analyses of fasting biomarkers and multiple linear regression analysis. SETTING: Forty-seven sites in 4 countries. PATIENTS OR OTHER PARTICIPANTS: Three hundred and sixteen subjects with type 2 diabetes. INTERVENTIONS: Tirzepatide (1, 5, 10, 15 mg), dulaglutide (1.5 mg), placebo. MAIN OUTCOME MEASURES: Analyze biomarkers of beta-cell function and insulin resistance (IR) and evaluate WL contributions to IR improvements at 26 weeks. RESULTS: Homeostatic model assessment (HOMA) 2-B significantly increased with dulaglutide and tirzepatide 5, 10, and 15 mg compared with placebo (P ≤ .02). Proinsulin/insulin and proinsulin/C-peptide ratios significantly decreased with tirzepatide 10 and 15 mg compared with placebo and dulaglutide (P ≤ .007). Tirzepatide 10 and 15 mg significantly decreased fasting insulin (P ≤ .033) and tirzepatide 10 mg significantly decreased HOMA2-IR (P = .004) compared with placebo and dulaglutide. Markers of improved insulin sensitivity (IS) adiponectin, IGFBP-1, and IGFBP-2 significantly increased by 1 or more doses of tirzepatide (P < .05). To determine whether improvements in IR were directly attributable to WL, multiple linear regression analysis with potential confounding variables age, sex, metformin, triglycerides, and glycated hemoglobin A1c was conducted. WL significantly (P ≤ .028) explained only 13% and 21% of improvement in HOMA2-IR with tirzepatide 10 and 15 mg, respectively. CONCLUSIONS: Tirzepatide improved markers of IS and beta-cell function to a greater extent than dulaglutide. IS effects of tirzepatide were only partly attributable to WL, suggesting dual receptor agonism confers distinct mechanisms of glycemic control.

Effects of Novel Dual GIP and GLP-1 Receptor Agonist Tirzepatide on Biomarkers of Nonalcoholic Steatohepatitis in Patients With Type 2 Diabetes.

OBJECTIVE: To determine the effect of tirzepatide, a dual agonist of glucose-dependent insulinotropic polypeptide and glucagon-like peptide 1 receptors, on biomarkers of nonalcoholic steatohepatitis (NASH) and fibrosis in patients with type 2 diabetes mellitus (T2DM). RESEARCH DESIGN AND METHODS: Patients with T2DM received either once weekly tirzepatide (1, 5, 10, or 15 mg), dulaglutide (1.5 mg), or placebo for 26 weeks. Changes from baseline in alanine aminotransferase (ALT), aspartate aminotransferase (AST), keratin-18 (K-18), procollagen III (Pro-C3), and adiponectin were analyzed in a modified intention-to-treat population. RESULTS: Significant (P < 0.05) reductions from baseline in ALT (all groups), AST (all groups except tirzepatide 10 mg), K-18 (tirzepatide 5, 10, 15 mg), and Pro-C3 (tirzepatide 15 mg) were observed at 26 weeks. Decreases with tirzepatide were significant compared with placebo for K-18 (10 mg) and Pro-C3 (15 mg) and with dulaglutide for ALT (10, 15 mg). Adiponectin significantly increased from baseline with tirzepatide compared with placebo (10, 15 mg). CONCLUSIONS: In post hoc analyses, higher tirzepatide doses significantly decreased NASH-related biomarkers and increased adiponectin in patients with T2DM.

BAYESIAN VARIABLE SELECTION FOR SURVIVAL DATA USING INVERSE MOMENT PRIORS.

Efficient variable selection in high dimensional cancer genomic studies is critical for discovering genes associated with specific cancer types and for predicting response to treatment. Censored survival data is prevalent in such studies. In this article we introduce a Bayesian variable selection procedure that uses a mixture prior composed of a point mass at zero and an inverse moment prior in conjunction with the partial likelihood defined by the Cox proportional hazard model. The procedure is implemented in the R package BVSNLP, which supports parallel computing and uses a stochastic search method to explore the model space. Bayesian model averaging is used for prediction. The proposed algorithm provides better performance than other variable selection procedures in simulation studies, and appears to provide more consistent variable selection when applied to actual genomic datasets.

The dual glucose-dependent insulinotropic peptide and glucagon-like peptide-1 receptor agonist, tirzepatide, improves lipoprotein biomarkers associated with insulin resistance and cardiovascular risk in patients with type 2 diabetes.

AIM: To better understand the marked decrease in serum triglycerides observed with tirzepatide in patients with type 2 diabetes, additional lipoprotein-related biomarkers were measured post hoc in available samples from the same study. MATERIALS AND METHODS: Patients were randomized to receive once-weekly subcutaneous tirzepatide (1, 5, 10 or 15 mg), dulaglutide (1.5 mg) or placebo. Serum lipoprotein profile, apolipoprotein (apo) A-I, B and C-III and preheparin lipoprotein lipase (LPL) were measured at baseline and at 4, 12 and 26 weeks. Lipoprotein particle profile by nuclear magnetic resonance was assessed at baseline and 26 weeks. The lipoprotein insulin resistance (LPIR) score was calculated. RESULTS: At 26 weeks, tirzepatide dose-dependently decreased apoB and apoC-III levels, and increased serum preheparin LPL compared with placebo. Tirzepatide 10 and 15 mg decreased large triglyceride-rich lipoprotein particles (TRLP), small low-density lipoprotein particles (LDLP) and LPIR score compared with both placebo and dulaglutide. Treatment with dulaglutide also reduced apoB and apoC-III levels but had no effect on either serum LPL or large TRLP, small LDLP and LPIR score. The number of total LDLP was also decreased with tirzepatide 10 and 15 mg compared with placebo. A greater reduction in apoC-III with tirzepatide was observed in patients with high compared with normal baseline triglycerides. At 26 weeks, change in apoC-III, but not body weight, was the best predictor of changes in triglycerides with tirzepatide, explaining up to 22.9% of their variability. CONCLUSIONS: Tirzepatide treatment dose-dependently decreased levels of apoC-III and apoB and the number of large TRLP and small LDLP, suggesting a net improvement in atherogenic lipoprotein profile.

Bayesian variable selection for binary outcomes in high-dimensional genomic studies using non-local priors.

MOTIVATION: The advent of new genomic technologies has resulted in the production of massive data sets. Analyses of these data require new statistical and computational methods. In this article, we propose one such method that is useful in selecting explanatory variables for prediction of a binary response. Although this problem has recently been addressed using penalized likelihood methods, we adopt a Bayesian approach that utilizes a mixture of non-local prior densities and point masses on the binary regression coefficient vectors. RESULTS: The resulting method, which we call iMOMLogit, provides improved performance in identifying true models and reducing estimation and prediction error in a number of simulation studies. More importantly, its application to several genomic datasets produces predictions that have high accuracy using far fewer explanatory variables than competing methods. We also describe a novel approach for setting prior hyperparameters by examining the total variation distance between the prior distributions on the regression parameters and the distribution of the maximum likelihood estimator under the null distribution. Finally, we describe a computational algorithm that can be used to implement iMOMLogit in ultrahigh-dimensional settings ([Formula: see text]) and provide diagnostics to assess the probability that this algorithm has identified the highest posterior probability model. AVAILABILITY AND IMPLEMENTATION: Software to implement this method can be downloaded at: http://www.stat.tamu.edu/∼amir/code.html CONTACT: wwang7@mdanderson.org or vjohnson@stat.tamu.edu SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.