Functional magnetic resonance imaging research employing regional homogeneity (ReHo) analysis has uncovered aberrant local brain connectivity in individuals with mild cognitive impairment (MCI) and Alzheimer\'s disease (AD) in comparison with healthy controls. However, the precise localization, extent, and possible overlap of these aberrations are still not fully understood. To bridge this gap, we applied a novel meta-analytic and Bayesian method (minimum Bayes Factor Activation Likelihood Estimation, mBF-ALE) for a systematic exploration of local functional connectivity alterations in MCI and AD brains. We extracted ReHo data via a standardized MEDLINE database search, which included 35 peer-reviewed experiments, 1,256 individuals with AD or MCI, 1,118 healthy controls, and 205 x-y-z coordinates of ReHo variation. We then separated the data into two distinct datasets: one for MCI and the other for AD. Two mBF-ALE analyses were conducted, thresholded at \"very strong evidence\" (mBF ≥ 150), with a minimum cluster size of 200 mm³. We also assessed the spatial consistency and sensitivity of our Bayesian results using the canonical version of the ALE algorithm. For MCI, we observed two clusters of ReHo decrease and one of ReHo increase. Decreased local connectivity was notable in the left precuneus (Brodmann area - BA 7) and left inferior temporal gyrus (BA 20), while increased connectivity was evident in the right parahippocampal gyrus (BA 36). The canonical ALE confirmed these locations, except for the inferior temporal gyrus. In AD, one cluster each of ReHo decrease and increase were found, with decreased connectivity in the right posterior cingulate cortex (BA 30 extending to BA 23) and increased connectivity in the left posterior cingulate cortex (BA 31). These locations were confirmed by the canonical ALE. The identification of these distinct functional connectivity patterns sheds new light on the complex pathophysiology of MCI and AD, offering promising directions for future neuroimaging-based interventions. Additionally, the use of a Bayesian framework for statistical thresholding enhances the robustness of neuroimaging meta-analyses, broadening its applicability to small datasets.

BACKGROUND: Renal cell carcinoma (RCC) remains a global health concern due to its poor survival rate. This study aimed to investigate the influence of medical determinants and socioeconomic status on survival outcomes of RCC patients. We analyzed the survival data of 41,563 RCC patients recorded under the Surveillance, Epidemiology, and End Results (SEER) program from 2012 to 2020.
METHODS: We employed a competing risk model, assuming lifetime of RCC patients under various risks follows Chen distribution. This model accounts for uncertainty related to survival time as well as causes of death, including missing cause of death. For model analysis, we utilized Bayesian inference and obtained the estimate of various key parameters such as cumulative incidence function (CIF) and cause-specific hazard. Additionally, we performed Bayesian hypothesis testing to assess the impact of multiple factors on the survival time of RCC patients.
RESULTS: Our findings revealed that the survival time of RCC patients is significantly influenced by gender, income, marital status, chemotherapy, tumor size, and laterality. However, we observed no significant effect of race and origin on patient\'s survival time. The CIF plots indicated a number of important distinctions in incidence of causes of death corresponding to factors income, marital status, race, chemotherapy, and tumor size.
CONCLUSIONS: The study highlights the impact of various medical and socioeconomic factors on survival time of RCC patients. Moreover, it also demonstrates the utility of competing risk model for survival analysis of RCC patients under Bayesian paradigm. This model provides a robust and flexible framework to deal with missing data, which can be particularly useful in real-life situations where patients information might be incomplete.

OBJECTIVE: To quantify the strength of statistical evidence of randomised controlled trials (RCTs) for novel cancer drugs approved by the Food and Drug Administration (FDA) in the last two decades.
METHODS: We used data on overall survival (OS), progression-free survival (PFS), and tumour response (TR) for novel cancer drugs approved for the first time by the FDA between January 2000 and December 2020. We assessed strength of statistical evidence by calculating Bayes Factors (BFs) for all available endpoints, and we pooled evidence using Bayesian fixed-effect meta-analysis for indications approved based on two RCTs. Strength of statistical evidence was compared between endpoints, approval pathways, lines of treatment, and types of cancer.
RESULTS: We analysed the available data from 82 RCTs corresponding to 68 indications supported by a single RCT and seven indications supported by two RCTs. Median strength of statistical evidence was ambiguous for OS (BF = 1.9; IQR 0.5-14.5), and strong for PFS (BF = 24,767.8; IQR 109.0-7.3*106) and TR (BF = 113.9; IQR 3.0-547,100). Overall, 44 indications (58.7%) were approved without clear statistical evidence for OS improvements and seven indications (9.3%) were approved without statistical evidence for improvements on any endpoint. Strength of statistical evidence was lower for accelerated approval compared to non-accelerated approval across all three endpoints. No meaningful differences were observed for line of treatment and cancer type.
CONCLUSIONS: This analysis is limited to statistical evidence. We did not consider non-statistical factors (e.g., risk of bias, quality of the evidence).
CONCLUSIONS: BFs offer novel insights into the strength of statistical evidence underlying cancer drug approvals. Most novel cancer drugs lack strong statistical evidence that they improve OS, and a few lack statistical evidence for efficacy altogether. These cases require a transparent and clear explanation. When evidence is ambiguous, additional post-marketing trials could reduce uncertainty.

BACKGROUND: Hypothesis testing is integral to health research and is commonly completed through frequentist statistics focused on computing p values. p Values have been long criticized for offering limited information about the relationship of variables and strength of evidence concerning the plausibility, presence and certainty of associations among variables. Bayesian statistics is a potential alternative for inference-making. Despite emerging discussion on Bayesian statistics across various disciplines, the uptake of Bayesian statistics in health research is still limited.
OBJECTIVE: To offer a primer on Bayesian statistics and Bayes factors for health researchers to gain preliminary knowledge of its use, application and interpretation in health research.
METHODS: Theoretical and empirical literature on Bayesian statistics and methods were used to develop this methodological primer.
CONCLUSIONS: Using Bayesian statistics in health research without a careful and complete understanding of its underlying philosophy and differences from frequentist testing, estimation and interpretation methods can result in similar ritualistic use as done for p values.
CONCLUSIONS: Health researchers should supplement frequentists statistics with Bayesian statistics when analysing research data. The overreliance on p values for clinical decisions making should be avoided. Bayes factors offer a more intuitive measure of assessing the strength of evidence for null and alternative hypothesis.

Network psychometrics uses graphical models to assess the network structure of psychological variables. An important task in their analysis is determining which variables are unrelated in the network, i.e., are independent given the rest of the network variables. This conditional independence structure is a gateway to understanding the causal structure underlying psychological processes. Thus, it is crucial to have an appropriate method for evaluating conditional independence and dependence hypotheses. Bayesian approaches to testing such hypotheses allow researchers to differentiate between absence of evidence and evidence of absence of connections (edges) between pairs of variables in a network. Three Bayesian approaches to assessing conditional independence have been proposed in the network psychometrics literature. We believe that their theoretical foundations are not widely known, and therefore we provide a conceptual review of the proposed methods and highlight their strengths and limitations through a simulation study. We also illustrate the methods using an empirical example with data on Dark Triad Personality. Finally, we provide recommendations on how to choose the optimal method and discuss the current gaps in the literature on this important topic.

This article considers a stable vector autoregressive (VAR) model and investigates return predictability in a Bayesian context. The bivariate VAR system comprises asset returns and a further prediction variable, such as the dividend-price ratio, and allows pinning down the question of return predictability to the value of one particular model parameter. We develop a new shrinkage type prior for this parameter and compare our Bayesian approach to ordinary least squares estimation and to the reduced-bias estimator proposed in Amihud and Hurvich (2004. \"Predictive Regressions: A Reduced-Bias Estimation Method.\" Journal of Financial and Quantitative Analysis 39: 813-41). A simulation study shows that the Bayesian approach dominates the reduced-bias estimator in terms of observed size (false positive) and power (false negative). We apply our methodology to a system comprising annual CRSP value-weighted returns running, respectively, from 1926 to 2004 and from 1953 to 2021, and the logarithmic dividend-price ratio. For the first sample, the Bayesian approach supports the hypothesis of no return predictability, while for the second data set weak evidence for predictability is observed. Then, instead of the dividend-price ratio, some prediction variables proposed in Welch and Goyal (2008. \"A Comprehensive Look at the Empirical Performance of Equity Premium Prediction.\" Review of Financial Studies 21: 1455-508) are used. Also with these prediction variables, only weak evidence for return predictability is supported by Bayesian testing. These results are corroborated with an out-of-sample forecasting analysis.

The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study\'s data is raised to the power of α, and then used as the prior distribution in the analysis of the replication data. Posterior distribution and Bayes factor hypothesis tests related to the power parameter α quantify the degree of compatibility between the original and replication study. Inferences for other parameters, such as effect sizes, dynamically borrow information from the original study. The degree of borrowing depends on the conflict between the two studies. The practical value of the approach is illustrated on data from three replication studies, and the connection to hierarchical modeling approaches explored. We generalize the known connection between normal power priors and normal hierarchical models for fixed parameters and show that normal power prior inferences with a beta prior on the power parameter α align with normal hierarchical model inferences using a generalized beta prior on the relative heterogeneity variance I2. The connection illustrates that power prior modeling is unnatural from the perspective of hierarchical modeling since it corresponds to specifying priors on a relative rather than an absolute heterogeneity scale.

Synthesizing results across multiple studies is a popular way to increase the robustness of scientific findings. The most well-known method for doing this is meta-analysis. However, because meta-analysis requires conceptually comparable effect sizes with the same statistical form, meta-analysis may not be possible when studies are highly diverse in terms of their research design, participant characteristics, or operationalization of key variables. In these situations, Bayesian evidence synthesis may constitute a flexible and feasible alternative, as this method combines studies at the hypothesis level rather than at the level of the effect size. This method therefore poses less constraints on the studies to be combined. In this study, we introduce Bayesian evidence synthesis and show through simulations when this method diverges from what would be expected in a meta-analysis to help researchers correctly interpret the synthesis results. As an empirical demonstration, we also apply Bayesian evidence synthesis to a published meta-analysis on statistical learning in people with and without developmental language disorder. We highlight the strengths and weaknesses of the proposed method and offer suggestions for future research.

In preparation to the launch of a pharmaceutical product, an estimate of its shelf life via stability testing is required by regulatory agencies. The ICH-Q1E guidance has been the worldwide reference to reach this objective, but in recent years several authors have criticized many of its aspects. To that end we discuss a complete Bayesian transcript of the ICH-Q1E, treating all the apparent shortcomings, while also addressing the presence of multiple batches using a linear mixed model (LMM) for proper shelf life prediction by explicitly modelling the batch-to-batch variability. This comprises a redefinition of the linear models proposed in the ICH-Q1E by suitable LMM counterparts, and a Bayesian analogue for model selection, which is more intuitive and remedies detrimental features of the ICH approach. In that context, a proper mathematical foundation of shelf life is provided that we use to investigate and mathematically compare the two available approaches to shelf life determination via shelf life distribution and batch distribution. The discussed method is then tested and evaluated using real data in comparison with the ICH-Q1E approach demonstrating their approximate equivalency for 6 batches. As a major objective, we extended the LMM with auxiliary fixed effects, here the concentration, which interconnect data sets allowing a prediction of shelf lives for concentrations lacking a sufficient number of batches. This establishes a novel approach to accelerate the speed to submission while retaining the patients\' safety. Both case studies underline the inherent superiority of LMMs within a Bayesian framework regarding predictability and interpretability, and we hope that the relevant authorities will accept this approach in the future.

The Non-Informative Nuisance Parameter Principle concerns the problem of how inferences about a parameter of interest should be made in the presence of nuisance parameters. The principle is examined in the context of the hypothesis testing problem. We prove that the mixed test obeys the principle for discrete sample spaces. We also show how adherence of the mixed test to the principle can make performance of the test much easier. These findings are illustrated with new solutions to well-known problems of testing hypotheses for count data.