2nd level modelling in fMRI analysis with a clinically depressed sample - Comparisons between classical and Bayesian methods

ObjectiveTo show how a simple Bayesian analysis method can be used to improve the evidence base in patient populations where recruitment and retention are challenging.MethodsA Bayesian conjugate analysis method was...

What to believe: Bayesian methods for data analysis

Statistical mediation analysis is used to investigate intermediate variables in the relation between independent and dependent variables. Causal interpretation of mediation analyses is challenging because randomization of subjects to levels of the independent variable does not rule out the possibility of unmeasured confounders of the mediator to outcome relation. Furthermore, commonly used frequentist methods for mediation analysis compute the probability of the data given the null hypothesis, which is not the probability of a hypothesis given the data as in Bayesian analysis. Under certain assumptions, applying the potential outcomes framework to mediation analysis allows for the computation of causal effects, and statistical mediation in the Bayesian framework gives indirect effects probabilistic interpretations. This tutorial combines causal inference and Bayesian methods for mediation analysis so the indirect and direct effects have both causal and probabilistic interpretations. Steps in Bayesian causal mediation analysis are shown in the application to an empirical example.

We developed and tested the Bayesian multiple comparison correction method for Bayesian voxelwise second-level fMRI analysis with R. The performance of the developed method was tested with simulation and real image datasets. First, we compared false alarm and hit rates, which were used as proxies for selectivity and sensitivity, respectively, between Bayesian and classical inference methods. For the comparison, we created simulated images, added noise to the created images, and analyzed the noise-added images while applying Bayesian and classical multiple comparison correction methods. Second, we analyzed five real image datasets to examine how our Bayesian method worked in realistic settings. When the performance assessment was conducted, the Bayesian correction method demonstrated good sensitivity (hit rate ≥ 75%) and acceptable selectivity (false alarm rate < 10%) when N ≥ 8. Furthermore, the Bayesian correction method showed better sensitivity compared with the classical correction method while maintaining the aforementioned acceptable selectivity.

SummaryBackgroundZika virus (ZIKV) infection during pregnancy is associated with an increased risk of congenital malformations. The prevalence of short and long-term consequences, however, remains uncertain due to heterogeneity across studies. Individual Participant Data Meta-Analysis (IPD-MA) offers an alternative approach to provide more precise and generalisable estimates through data harmonisation across studies, allowing for standardised definitions and exploration of heterogeneity. This project was undertaken to estimate absolute and relative risks of adverse outcomes for individuals with ZIKV infection during pregnancy.MethodsIPD-MA studies and their datasets were identified through a systematic search conducted in 2018 with the following criteria: observational longitudinal or surveillance-based studies investigating ZIKV during pregnancy or at birth, measured fetal, infant, or child outcomes, and included at least 10 participants. Here we used IPD data shared by March 2022 from 18 studies from international health organisations and research networks, comprising 24 unique datasets, in 11 countries. Datasets were harmonised with standardised definitions, using variables related to pregnant individuals, methods used for ZIKV diagnoses, fetal characteristics and outcomes, and pooled for analysis. Frequentist and Bayesian regression methods were applied to estimate outcome prevalence and evaluate the association between maternal ZIKV infection and fetal loss, microcephaly and congenital zika syndrome as primary outcomes.FindingsData including 9568 pregnant individuals and 9608 newborns, were harmonised. The risk of severe primary microcephaly was significantly higher in ZIKV-positive pregnancies (1.5%, CI 0.8%–2.7%) compared to ZIKV-negative ones (0.3%, CI 0.1%–1.0%), with a relative risk of 4.5 (CI 1.5–13.3) in the one-stage meta-analysis. While some risk estimates were consistent between Bayesian and Frequentist methods, estimates for other outcomes varied, underscoring the influence of both the analytical approach and the definition of ZIKV on the associations.InterpretationOur findings align with previously published meta-analyses and indicate an added burden to adverse pregnancy outcomes with higher prevalence compared to pre-epidemic population-based average values. Future research should focus on additional outcomes with clear definitions of maternal infection. Women of reproductive age should be informed about the risks of Zika infection during pregnancy to support reproductive planning.FundingThis project was supported by the 10.13039/100010269Wellcome Trust grant number 206532/Z/17/Z, the 10.13039/100004423WHOHealth Emergencies Programme Global Arbovirus Initiative, and the 10.13039/100004423WHO Department of Sexual and Reproductive Health and Research, including the Human Reproduction Special Programme (HRP).

An introduction to using Bayesian linear regression with clinical data

This paper provides a conceptual overview of Classical/Frequentist and Bayesian statistical inference, focusing on their philosophical foundations and relevance to social work research. While most social workers are trained in Frequentist methods which highlight null hypothesis significance testing, Bayesian inference offers a different framework that assigns probabilities to hypotheses and emphasizes degrees of belief given observed data. The paper explains key differences between the two approaches, explores the role of the Metropolis Algorithm in Bayesian inference, and shows how this algorithm can approximate posterior distributions and credible intervals. The discussion aims to encourage social work researchers to broaden their methodological toolkit by considering Bayesian approaches, especially when addressing substantive applied questions.

With the emergence of Biobanks alongside large-scale genome-wide association studies (GWAS) we will soon be in the enviable situation of obtaining precise estimates of population allele frequencies for SNPs which make up the panels in standard genotyping arrays, such as those produced from Illumina and Affymetrix. For disease association studies it is well known that for rare diseases with known population minor allele frequencies (pMAFs) a case-only design is most powerful. That is, for a fixed budget the optimal procedure is to genotype only cases (affecteds). In such tests experimenters look for a divergence from allele distribution in cases from that of the known population pMAF; in order to test the null hypothesis of no association between the disease status and the allele frequency. However, what has not been previously characterized is the utility of controls (known unaffecteds) when available. In this study we consider frequentist and Bayesian statistical methods for testing for SNP genotype association when population MAFs are known and when both cases and controls are available. We demonstrate that for rare diseases the most powerful frequentist design is, somewhat counterintuitively, to actively discard the controls even though they contain information on the association. In contrast we develop a Bayesian test which uses all available information (cases and controls) and appears to exhibit uniformaly greater power than all frequentist methods we considered.

Abstract. In Italy, rainfall is the primary trigger of landslides that frequently cause fatalities and large economic damage. Using a variety of information sources, we have compiled a catalogue listing 753 rainfall events that have resulted in landslides in Italy. For each event in the catalogue, the exact or approximate location of the landslide and the time or period of initiation of the slope failure is known, together with information on the rainfall duration D, and the rainfall mean intensity I, that have resulted in the slope failure. The catalogue represents the single largest collection of information on rainfall-induced landslides in Italy, and was exploited to determine the minimum rainfall conditions necessary for landslide occurrence in Italy, and in the Abruzzo Region, central Italy. For the purpose, new national rainfall thresholds for Italy and new regional rainfall thresholds for the Abruzzo Region were established, using two independent statistical methods, including a Bayesian inference method and a new Frequentist approach. The two methods proved complementary, with the Bayesian method more suited to analyze small data sets, and the Frequentist method performing better when applied to large data sets. The new regional thresholds for the Abruzzo Region are lower than the new national thresholds for Italy, and lower than the regional thresholds proposed in the literature for the Piedmont and Lombardy Regions in northern Italy, and for the Campania Region in southern Italy. This is important, because it shows that landslides in Italy can be triggered by less severe rainfall conditions than previously recognized. The Frequentist method experimented in this work allows for the definition of multiple minimum rainfall thresholds, each based on a different exceedance probability level. This makes the thresholds suited for the design of probabilistic schemes for the prediction of rainfall-induced landslides. A scheme based on four probabilistic thresholds is proposed. The four thresholds separate five fields, each characterized by different rainfall intensity-duration conditions, and corresponding different probability of possible landslide occurrence. The scheme can be implemented in landslide warning systems that operate on rainfall thresholds, and on precipitation measurements or forecasts.

Results from randomized control trials (RCTs) may not be representative when individuals refuse to be randomized or are excluded for having a preference for which treatment they receive. If trial designs do not allow for participant treatment preferences, trials can suffer in accrual, adherence, retention, and external validity of results. Thus, there is interest surrounding clinical trial designs that incorporate participant treatment preferences. We propose a Partially Randomized, Patient Preference, Sequential, Multiple Assignment, Randomized Trial (PRPP-SMART) which combines a Partially Randomized, Patient Preference (PRPP) design with a Sequential, Multiple Assignment, Randomized Trial (SMART) design. This novel PRPP-SMART design is a multi-stage clinical trial design where, at each stage, participants either receive their preferred treatment, or if they do not have a preferred treatment, they are randomized. This paper focuses on the clinical trial design for PRPP-SMARTs and the development of Bayesian and frequentist weighted and replicated regression models (WRRMs) to analyze data from such trials. We propose a two-stage PRPP-SMART with binary end of stage outcomes and estimate the embedded dynamic treatment regimes (DTRs). Our WRRMs use data from both randomized and non-randomized participants for efficient estimation of the DTR effects. We compare our method to a more traditional PRPP analysis which only considers participants randomized to treatment. Our Bayesian and frequentist methods produce more efficient DTR estimates with negligible bias despite the inclusion of non-randomized participants in the analysis. The proposed PRPP-SMART design and analytic method is a promising approach to incorporate participant treatment preferences into clinical trial design.

Bayesian approaches have been demonstrated as effective methods for reliability analysis of complex systems with small-amount data, which integrate prior information and sample data using Bayes’ theorem. However, there is an assumption that precise prior probability distributions are available for unknown parameters, yet these prior distributions are sometimes unavailable in practical engineering. A possible way to avoiding this assumption is to generalize Bayesian reliability analysis approach by using imprecise probability theory. In this paper, we adopt a set of imprecise Dirichlet distributions as priors to quantify uncertainty of unknown parameters and extend traditional Bayesian reliability analysis approach by introducing an imprecise Dirichlet model (IDM). When the prior information is rare, the result of imprecise Bayesian analysis method is too rough to support engineering decision-making, so we proposed an optimization model to reduce the imprecision of the new method. Spindles are crucial for machine tools and reliability data related to spindles of new-developed machine tools are often rare. We can then use the imprecise Bayesian reliability analysis method to assess its reliability. In this paper, we mainly investigate the reliability assessment of a motorized spindle to illustrate the effectiveness of the proposed method.

Bayesian methods are an important set of tools for performing meta-analyses. They avoid some potentially unrealistic assumptions that are required by conventional frequentist methods. More importantly, meta-analysts can incorporate prior information from many sources, including experts’ opinions and prior meta-analyses. Nevertheless, Bayesian methods are used less frequently than conventional frequentist methods, primarily because of the need for nontrivial statistical coding, while frequentist approaches can be implemented via many user-friendly software packages. This article aims at providing a practical review of implementations for Bayesian meta-analyses with various prior distributions. We present Bayesian methods for meta-analyses with the focus on odds ratio for binary outcomes. We summarize various commonly used prior distribution choices for the between-studies heterogeneity variance, a critical parameter in meta-analyses. They include the inverse-gamma, uniform, and half-normal distributions, as well as evidence-based informative log-normal priors. Five real-world examples are presented to illustrate their performance. We provide all of the statistical code for future use by practitioners. Under certain circumstances, Bayesian methods can produce markedly different results from those by frequentist methods, including a change in decision on statistical significance. When data information is limited, the choice of priors may have a large impact on meta-analytic results, in which case sensitivity analyses are recommended. Moreover, the algorithm for implementing Bayesian analyses may not converge for extremely sparse data; caution is needed in interpreting respective results. As such, convergence should be routinely examined. When select statistical assumptions that are made by conventional frequentist methods are violated, Bayesian methods provide a reliable alternative to perform a meta-analysis.

This paper presents a Bayesian statistical analysis method for updating earthquake ground motion versus damage relationships in the form of fragility curves and for estimating confidence bounds on these fragility curves. As building damage data from past earthquakes become increasingly available, these data need to be combined with analytical fragility curves to arrive at more robust fragility curves. The Bayesian method provides a technique for updating these relationships. The parameters of analytical fragility curves are used to estimate the prior distributions of damage in the Bayesian analysis. In an earlier paper, Singhal and Kiremidjian presented a general methodology for the development of analytical motion-damage relationships in terms of seismic fragility curves and damage probability matrices. Data on building damage are used to estimate the likelihood functions. The Bayesian method for fragility analysis is illustrated by using the damage data on reinforced concrete (RC) frame buildings from the January 17, 1994 Northridge, Calif. earthquake. The uncertainties in the fragility curves are represented by confidence bounds around the median fragility curves.

Chapter 4 - Bayesian nonparametric methods for financial and macroeconomic time series analysis

In this paper, we propose a practical method to estimate the milling head reliability based on the accelerated degradation test and Bayesian lifetime analysis method. By carefully analyzing the failure mechanism of the milling head, we adopt the accelerated degradation test to identify and parameterize the failure law of this component. The equivalent lifetime for the Bayesian lifetime analysis is also derived from the accelerated degradation data. Finally, the estimation is carried out based on the parametric failure law and the equivalent lifetime using the Bayesian Weibull lifetime analysis method. The reliability estimation of the milling head can be improved by the combination of the failure mechanical based accelerated degradation test and the Bayesian field lifetime data analysis. The proposed method is a practical and cost-effective reliability estimation method for highly reliable and expensive mechanical component with a pre-defined failure mechanism.