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.

In several large-scale replication projects, statistically non-significant results in both the original and the replication study have been interpreted as a \'replication success.\' Here, we discuss the logical problems with this approach: Non-significance in both studies does not ensure that the studies provide evidence for the absence of an effect and \'replication success\' can virtually always be achieved if the sample sizes are small enough. In addition, the relevant error rates are not controlled. We show how methods, such as equivalence testing and Bayes factors, can be used to adequately quantify the evidence for the absence of an effect and how they can be applied in the replication setting. Using data from the Reproducibility Project: Cancer Biology, the Experimental Philosophy Replicability Project, and the Reproducibility Project: Psychology we illustrate that many original and replication studies with \'null results\' are in fact inconclusive. We conclude that it is important to also replicate studies with statistically non-significant results, but that they should be designed, analyzed, and interpreted appropriately.

Bayesian statistics plays a pivotal role in advancing medical science by enabling healthcare companies, regulators, and stakeholders to assess the safety and efficacy of new treatments, interventions, and medical procedures. The Bayesian framework offers a unique advantage over the classical framework, especially when incorporating prior information into a new trial with quality external data, such as historical data or another source of co-data. In recent years, there has been a significant increase in regulatory submissions using Bayesian statistics due to its flexibility and ability to provide valuable insights for decision-making, addressing the modern complexity of clinical trials where frequentist trials are inadequate. For regulatory submissions, companies often need to consider the frequentist operating characteristics of the Bayesian analysis strategy, regardless of the design complexity. In particular, the focus is on the frequentist type I error rate and power for all realistic alternatives. This tutorial review aims to provide a comprehensive overview of the use of Bayesian statistics in sample size determination, control of type I error rate, multiplicity adjustments, external data borrowing, etc., in the regulatory environment of clinical trials. Fundamental concepts of Bayesian sample size determination and illustrative examples are provided to serve as a valuable resource for researchers, clinicians, and statisticians seeking to develop more complex and innovative designs.

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.

Measures of association play a central role in the social sciences to quantify the strength of a linear relationship between the variables of interest. In many applications researchers can translate scientific expectations to hypotheses with equality and/or order constraints on these measures of association. In this paper a Bayes factor test is proposed for testing multiple hypotheses with constraints on the measures of association between ordinal and/or continuous variables, possibly after correcting for certain covariates. This test can be used to obtain a direct answer to the research question how much evidence there is in the data for a social science theory relative to competing theories. The stand-alone software package \'BCT\' allows users to apply the methodology in an easy manner. The methodology will also be available in the R package \'BFpack\'. An empirical application from leisure studies about the associations between life, leisure and relationship satisfaction and an application about the differences about egalitarian justice beliefs across countries are used to illustrate the methodology.

Interval estimation is one of the most frequently used methods in statistical science, employed to provide a range of credible values a parameter is located in after taking into account the uncertainty in the data. However, while this interpretation only holds for Bayesian interval estimates, these suffer from two problems. First, Bayesian interval estimates can include values which have not been corroborated by observing the data. Second, Bayesian interval estimates and hypothesis tests can yield contradictory conclusions. In this paper a new theory for Bayesian hypothesis testing and interval estimation is presented. A new interval estimate is proposed, the Bayesian evidence interval, which is inspired by the Pereira-Stern theory of the full Bayesian significance test (FBST). It is shown that the evidence interval is a generalization of existing Bayesian interval estimates, that it solves the problems of standard Bayesian interval estimates and that it unifies Bayesian hypothesis testing and parameter estimation. The Bayesian evidence value is introduced, which quantifies the evidence for the (interval) null and alternative hypothesis. Based on the evidence interval and the evidence value, the (full) Bayesian evidence test (FBET) is proposed as a new, model-independent Bayesian hypothesis test. Additionally, a decision rule for hypothesis testing is derived which shows the relationship to a widely used decision rule based on the region of practical equivalence and Bayesian highest posterior density intervals and to the e-value in the FBST. In summary, the proposed method is universally applicable, computationally efficient, and while the evidence interval can be seen as an extension of existing Bayesian interval estimates, the FBET is a generalization of the FBST and contains it as a special case. Together, the theory developed provides a unification of Bayesian hypothesis testing and interval estimation and is made available in the R package fbst.

Mediation analysis is widely used to study whether the effect of an independent variable on an outcome is transmitted through a mediator. Bayesian methods have become increasingly popular for mediation analysis. However, limited research has been done on formal Bayesian hypothesis testing of mediation. Although hypothesis testing using Bayes factor for a single path is readily available, how to integrate the Bayes factors of two paths (from input to mediator and from mediator to outcome) while incorporating prior beliefs on the two paths and/or mediation is under-studied. In the current study, we propose a general approach to Bayesian hypothesis testing of mediation. The proposed approach allows researchers to specify prior odds based on the substantive research context and can be used in mediation modeling with latent variables. The impact of prior odds specifications on Bayesian hypothesis test of mediation is demonstrated via both real and hypothetical data examples. Both R functions and a user-friendly R web app are provided for the implementation of the proposed approach. Our study can add to researchers\' toolbox of mediation analysis and raise researchers\' awareness of the importance of prior odds specifications in Bayesian hypothesis testing of mediation.

The restricted mean survival time (RMST) evaluates the expectation of survival time truncated by a prespecified time point, because the mean survival time in the presence of censoring is typically not estimable. The frequentist inference procedure for RMST has been widely advocated for comparison of two survival curves, while research from the Bayesian perspective is rather limited. For the RMST of both right- and interval-censored data, we propose Bayesian nonparametric estimation and inference procedures. By assigning a mixture of Dirichlet processes (MDP) prior to the distribution function, we can estimate the posterior distribution of RMST. We also explore another Bayesian nonparametric approach using the Dirichlet process mixture model and make comparisons with the frequentist nonparametric method. Simulation studies demonstrate that the Bayesian nonparametric RMST under diffuse MDP priors leads to robust estimation and under informative priors it can incorporate prior knowledge into the nonparametric estimator. Analysis of real trial examples demonstrates the flexibility and interpretability of the Bayesian nonparametric RMST for both right- and interval-censored data.

Purpose: Segmentation of the vessel tree from retinal fundus images can be used to track changes in the retina and be an important first step in a diagnosis. Manual segmentation is a time-consuming process that is prone to error; effective and reliable automation can alleviate these problems but one of the difficulties is uneven image background, which may affect segmentation performance. Approach: We present a patch-based deep learning framework, based on a modified U-Net architecture, that automatically segments the retinal blood vessels from fundus images. In particular, we evaluate how various pre-processing techniques, images with either no processing, N4 bias field correction, contrast limited adaptive histogram equalization (CLAHE), or a combination of N4 and CLAHE, can compensate for uneven image background and impact final segmentation performance. Results: We achieved competitive results on three publicly available datasets as a benchmark for our comparisons of pre-processing techniques. In addition, we introduce Bayesian statistical testing, which indicates little practical difference ( Pr > 0.99 ) between pre-processing methods apart from the sensitivity metric. In terms of sensitivity and pre-processing, the combination of N4 correction and CLAHE performs better in comparison to unprocessed and N4 pre-processing ( Pr > 0.87 ); but compared to CLAHE alone, the differences are not significant ( Pr ≈ 0.38 to 0.88). Conclusions: We conclude that deep learning is an effective method for retinal vessel segmentation and that CLAHE pre-processing has the greatest positive impact on segmentation performance, with N4 correction helping only in images with extremely inhomogeneous background illumination.

Hypothesis testing is an essential statistical method in experimental psychology and the cognitive sciences. The problems of traditional null hypothesis significance testing (NHST) have been discussed widely, and among the proposed solutions to the replication problems caused by the inappropriate use of significance tests and p-values is a shift toward Bayesian data analysis. However, Bayesian hypothesis testing is concerned with various posterior indices for significance and the size of an effect. This complicates Bayesian hypothesis testing in practice, as the availability of multiple Bayesian alternatives to the traditional p-value causes confusion which one to select and why. In this paper, various Bayesian posterior indices which have been proposed in the literature are compared and their benefits and limitations are discussed. The comparison shows that conceptually not all proposed Bayesian alternatives to NHST and p-values are beneficial, and the usefulness of some indices strongly depends on the study design and research goal. However, the comparison also reveals that there exist at least two candidates among the available Bayesian posterior indices which have appealing theoretical properties and are widely underused in the cognitive sciences.