Discrete Approximation of a Mixture Distribution via Restricted Divergence

Using the bayesmeta R package for Bayesian random-effects meta-regression

BACKGROUND

Random-effects meta-analysis within a hierarchical normal modeling framework is commonly implemented in a wide range of evidence synthesis applications. More general problems may even be tackled when considering meta-regression approaches that in addition allow for the inclusion of study-level covariables.

METHODS

We describe the Bayesian meta-regression implementation provided in the bayesmetaR package including the choice of priors, and we illustrate its practical use.

RESULTS

A wide range of example applications are given, such as binary and continuous covariables, subgroup analysis, indirect comparisons, and model selection. Example R code is provided.

CONCLUSIONS

The bayesmeta package provides a flexible implementation. Due to the avoidance of MCMC methods, computations are fast and reproducible, facilitating quick sensitivity checks or large-scale simulation studies.

Risk factors for prolonged air leak after pulmonary surgery: A systematic review and meta-analysis

This study aimed to comprehensively identify risk factors for the occurrence of prolonged air leak (PAL) in patients undergoing pulmonary surgery. Studies were retrieved from 3 databases, including PubMed, Web of Science, and EmBase up to 13 May 2020. We performed meta-analysis using Bayesian random effect models through divergence restricting conditional tessellation (DIRECT) algorithm. The effect size was expressed as odds ratio (OR) or mean difference (MD), each with 95% credible interval (CrI). The evidence quality was evaluated. Subgroup analyses and sensitivity analyses were conducted. Thirty-nine studies with 89006 patients were finally included. Pooled PAL incidence was 15%. Of 30 risk factors, 22 were significantly associated with increased PAL incidence. Five risk factors were ultimately selected with high evidence quality: smoking history (OR 1.84, 95%CrI 1.45 to 2.31, P<0.001), preoperative steroid use (OR 1.51, 95%CrI 0.87 to 2.65, P = 0.031), lower ratio of forced expiratory volume in 1 s and forced vital capacity (OR 1.99, 95%CrI 1.22 to 3.33, P = 0.005), non-fissureless technique (OR 2.14, 95%CrI 1.31 to 3.66, P = 0.003), and pathological TNM stage III/IV (OR 1.50, 95%CrI 1.07 to 2.12, P = 0.003). Regarding the negative impact of PAL on the personal cost and postoperative recovery, the verification of previous proposed factors and investigation of recently discovered ones both implied directions for risk stratification and the establishment of an applicable prediction model.

Does transcutaneous auricular vagus nerve stimulation affect vagally mediated heart rate variability? A living and interactive Bayesian meta-analysis

Non-invasive brain stimulation techniques, such as transcutaneous auricular vagus nerve stimulation (taVNS), have considerable potential for clinical use. Beneficial effects of taVNS have been demonstrated on symptoms in patients with mental or neurological disorders as well as transdiagnostic dimensions, including mood and motivation. However, since taVNS research is still an emerging field, the underlying neurophysiological processes are not yet fully understood, and the replicability of findings on biomarkers of taVNS effects has been questioned. The objective of this analysis was to synthesize the current evidence concerning the effects of taVNS on vagally mediated heart rate variability (vmHRV), a candidate biomarker that has, so far, received most attention in the field. We performed a living Bayesian random effects meta-analysis. To keep the synthesis of evidence transparent and up to date as new studies are being published, we developed a Shiny web app that regularly incorporates new results and enables users to modify study selection criteria to evaluate the robustness of the inference across potential confounds. Our analysis focuses on 16 single-blind studies comparing taVNS versus sham in healthy participants. The meta-analysis provides strong evidence for the null hypothesis (g = 0.014, CI_shortest = [-0.103, 0.132], BF₀₁ = 24.678), indicating that acute taVNS does not alter vmHRV compared to sham. To conclude, there is no support for the hypothesis that vmHRV is a robust biomarker for acute taVNS. By increasing transparency and timeliness, the concept of living meta-analyses can lead to transformational benefits in emerging fields such as non-invasive brain stimulation.

On weakly informative prior distributions for the heterogeneity parameter in Bayesian random-effects meta-analysis

The normal-normal hierarchical model (NNHM) constitutes a simple and widely used framework for meta-analysis. In the common case of only few studies contributing to the meta-analysis, standard approaches to inference tend to perform poorly, and Bayesian meta-analysis has been suggested as a potential solution. The Bayesian approach, however, requires the sensible specification of prior distributions. While noninformative priors are commonly used for the overall mean effect, the use of weakly informative priors has been suggested for the heterogeneity parameter, in particular in the setting of (very) few studies. To date, however, a consensus on how to generally specify a weakly informative heterogeneity prior is lacking. Here we investigate the problem more closely and provide some guidance on prior specification.

Bayesian Approaches for Confirmatory Trials in Rare Diseases: Opportunities and Challenges

The aim of this narrative review is to introduce the reader to Bayesian methods that, in our opinion, appear to be the most important in the context of rare diseases. A disease is defined as rare depending on the prevalence of the affected patients in the considered population, for example, about 1 in 1500 people in U.S.; about 1 in 2500 people in Japan; and fewer than 1 in 2000 people in Europe. There are between 6000 and 8000 rare diseases and the main issue in drug development is linked to the challenge of achieving robust evidence from clinical trials in small populations. A better use of all available information can help the development process and Bayesian statistics can provide a solid framework at the design stage, during the conduct of the trial, and at the analysis stage. The focus of this manuscript is to provide a review of Bayesian methods for sample size computation or reassessment during phase II or phase III trial, for response adaptive randomization and of for meta-analysis in rare disease. Challenges regarding prior distribution choice, computational burden and dissemination are also discussed.

Interval estimation of the overall treatment effect in random-effects meta-analyses: Recommendations from a simulation study comparing frequentist, Bayesian, and bootstrap methods

There exists a variety of interval estimators for the overall treatment effect in a random-effects meta-analysis. A recent literature review summarizing existing methods suggested that in most situations, the Hartung-Knapp/Sidik-Jonkman (HKSJ) method was preferable. However, a quantitative comparison of those methods in a common simulation study is still lacking. Thus, we conduct such a simulation study for continuous and binary outcomes, focusing on the medical field for application. Based on the literature review and some new theoretical considerations, a practicable number of interval estimators is selected for this comparison: the classical normal-approximation interval using the DerSimonian-Laird heterogeneity estimator, the HKSJ interval using either the Paule-Mandel or the Sidik-Jonkman heterogeneity estimator, the Skovgaard higher-order profile likelihood interval, a parametric bootstrap interval, and a Bayesian interval using different priors. We evaluate the performance measures (coverage and interval length) at specific points in the parameter space, that is, not averaging over a prior distribution. In this sense, our study is conducted from a frequentist point of view. We confirm the main finding of the literature review, the general recommendation of the HKSJ method (here with the Sidik-Jonkman heterogeneity estimator). For meta-analyses including only two studies, the high length of the HKSJ interval limits its practical usage. In this case, the Bayesian interval using a weakly informative prior for the heterogeneity may help. Our recommendations are illustrated using a real-world meta-analysis dealing with the efficacy of an intramyocardial bone marrow stem cell transplantation during coronary artery bypass grafting.

Nutritional interventions for the management of frailty in older adults: systematic review and meta-analysis of randomized clinical trials

CONTEXT

Although nutrition is considered an important intervention for the management of frailty, the actual effectiveness of interventions addressing nutrition in frail older people remains unclear.

OBJECTIVE

The aim for this systematic review was to appraise the evidence regarding the effectiveness of nutritional interventions for the management of frailty in older adults.

DATA EXTRACTION

We followed the Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines. The MEDLINE, Embase, Cumulative Index to Nursing and Allied Health Literature, Cochrane Central Register of Controlled Trials, Web of Science, and Latin American and Caribbean Health Sciences Literature databases were searched from January 2001 to November 2019. Two independent reviewers extracted relevant data. From 2370 initial records, 19 publications presenting data from 17 studies (1564 individuals; follow-up: 7-96 weeks) were included.

DATA ANALYSIS

None of the Bayesian random-effects meta-analyses comparing nutritional supplements with placebo regarding mortality, body mass index, weight, frailty status, muscle strength, gait speed, body composition, and cognitive function showed statistically significant differences. The same applies to a single meta-analysis comparing nutritional education with general health advice regarding muscle strength.

CONCLUSION

Our results suggest, mostly with low to very low degrees of certainty, that nutritional supplements or nutritional education delivered in isolation may not be effective for the management of frailty in older people.

REVIEW REGISTRATION NUMBER

CRD42018111510 (PROSPERO).

An alternative approach to frequentist meta-analysis: A demonstration of Bayesian meta-analysis in adolescent development research

INTRODUCTION

Past decades have seen a surge of applied and methodological research on meta-analysis. One methodological advancement that has gained significant traction is a Bayesian approach to meta-analysis.

METHODS

We present a non-technical introduction to Bayesian meta-analysis. This introduction re-analyzes data from a meta-analysis concerning the impact of media literacy interventions on attitudes and intentions related to risky health behaviors using a Bayesian approach. One data relate media literacy interventions to media literacy skills, and another relates media literacy interventions to attitudes and behavioral intentions towards risky health behaviors. In these examples we focus on how to conduct unconditional models via graphical and quantitative results. Further, we demonstrate how to conduct subgroup analyses using risk behavior type (drinking, sexual, or smoking).

RESULTS

We demonstrated how several meta-analytical quantities could be computed and interpreted in a Bayesian framework. This was done both graphically (plot of the marginal posterior distributions) and quantitatively (e.g., central tendency measures, highest posterior density intervals). Results also showed how analyzing effect sizes at the risk-behavior level could affect several interpretations.

CONCLUSIONS

We emphasize that in no way are Bayesian methods "superior" to frequentist methods, nor that frequentist methods should be abandoned. Instead, the two approaches should be viewed as familial, each with advantages and disadvantages, but strive at a common purpose. We hope for increased use of Bayesian meta-analyses, and Bayesian methodology at large, in adolescence research. Last, all R code is provided for readers to use as a foundation for their own research.

Dor versus Toupet fundoplication after Laparoscopic Heller Myotomy: Systematic review and Bayesian meta-analysis of randomized controlled trials

Laparoscopic Heller Myotomy (LHM) with partial fundoplication has become the treatment of choice for esophageal achalasia. However, the choice of the partial fundoplication is debated. The aim of this study was to compare outcomes for Dor and Toupet fundoplication after LHM. A systematic search of randomized controlled trials comparing Dor and Toupet fundoplication was performed using PubMed, EMBASE and Web of Science. Three studies met the inclusion criteria. Overall, 174 patients were included in the analysis. The postoperative abnormal acid reflux [pooled Risk Ratio 0.98 (95% HPD 0.54-1.80)] and dysphagia [pooled Risk Ratio 1.03 (95% HPD 0.51-2.05)] were similar comparing Dor and Toupet fundoplication. The % total time pH ≤ 4 [estimated pooled mean difference -0.08 (95% HPD -1.04-0.90)] and DeMeester score [estimated pooled mean difference 0.51 (95% HPD -0.90-1.94)] were comparable. Additionally, the operative time [estimated pooled mean difference 0.02 (95% HPD -0.53-0.52)] and iatrogenic esophageal perforation [pooled Risk Ratio 1.05 (95% HPD 0.52-2.10)] were similar in the two groups. Dor and Toupet fundoplication after laparoscopic Heller myotomy seem comparable in term of postoperative abnormal acid exposure and dysphagia. The choice of the partial fundoplication should be left to surgeon experience and tailored on each patient.

On estimands and the analysis of adverse events in the presence of varying follow-up times within the benefit assessment of therapies

The analysis of adverse events (AEs) is a key component in the assessment of a drug's safety profile. Inappropriate analysis methods may result in misleading conclusions about a therapy's safety and consequently its benefit-risk ratio. The statistical analysis of AEs is complicated by the fact that the follow-up times can vary between the patients included in a clinical trial. This paper takes as its focus the analysis of AE data in the presence of varying follow-up times within the benefit assessment of therapeutic interventions. Instead of approaching this issue directly and solely from an analysis point of view, we first discuss what should be estimated in the context of safety data, leading to the concept of estimands. Although the current discussion on estimands is mainly related to efficacy evaluation, the concept is applicable to safety endpoints as well. Within the framework of estimands, we present statistical methods for analysing AEs with the focus being on the time to the occurrence of the first AE of a specific type. We give recommendations which estimators should be used for the estimands described. Furthermore, we state practical implications of the analysis of AEs in clinical trials and give an overview of examples across different indications. We also provide a review of current practices of health technology assessment (HTA) agencies with respect to the evaluation of safety data. Finally, we describe problems with meta-analyses of AE data and sketch possible solutions.

Recent advances in methodology for clinical trials in small populations: the InSPiRe project

Where there are a limited number of patients, such as in a rare disease, clinical trials in these small populations present several challenges, including statistical issues. This led to an EU FP7 call for proposals in 2013. One of the three projects funded was the Innovative Methodology for Small Populations Research (InSPiRe) project. This paper summarizes the main results of the project, which was completed in 2017.The InSPiRe project has led to development of novel statistical methodology for clinical trials in small populations in four areas. We have explored new decision-making methods for small population clinical trials using a Bayesian decision-theoretic framework to compare costs with potential benefits, developed approaches for targeted treatment trials, enabling simultaneous identification of subgroups and confirmation of treatment effect for these patients, worked on early phase clinical trial design and on extrapolation from adult to pediatric studies, developing methods to enable use of pharmacokinetics and pharmacodynamics data, and also developed improved robust meta-analysis methods for a small number of trials to support the planning, analysis and interpretation of a trial as well as enabling extrapolation between patient groups. In addition to scientific publications, we have contributed to regulatory guidance and produced free software in order to facilitate implementation of the novel methods.

Model averaging for robust extrapolation in evidence synthesis

Extrapolation from a source to a target, eg, from adults to children, is a promising approach to utilize external information when data are sparse. In the context of meta-analyses, one is commonly faced with a small number of studies, whereas potentially relevant additional information may also be available. Here, we describe a simple extrapolation strategy using heavy-tailed mixture priors for effect estimation in meta-analysis, which effectively results in a model-averaging technique. The described method is robust in the sense that a potential prior-data conflict, ie, a discrepancy between source and target data, is explicitly anticipated. The aim of this paper is to develop a solution for this particular application to showcase the ease of implementation by providing R code, and to demonstrate the robustness of the general approach in simulations.

Methods for evidence synthesis in the case of very few studies

In systematic reviews, meta-analyses are routinely applied to summarize the results of the relevant studies for a specific research question. If one can assume that in all studies the same true effect is estimated, the application of a meta-analysis with common effect (commonly referred to as fixed-effect meta-analysis) is adequate. If between-study heterogeneity is expected to be present, the method of choice is a meta-analysis with random effects. The widely used DerSimonian and Laird method for meta-analyses with random effects has been criticized due to its unfavorable statistical properties, especially in the case of very few studies. A working group of the Cochrane Collaboration recommended the use of the Knapp-Hartung method for meta-analyses with random effects. However, as heterogeneity cannot be reliably estimated if only very few studies are available, the Knapp-Hartung method, while correctly accounting for the corresponding uncertainty, has very low power. Our aim is to summarize possible methods to perform meaningful evidence syntheses in the situation with only very few (ie, 2-4) studies. Some general recommendations are provided on which method should be used when. Our recommendations are based on the existing literature on methods for meta-analysis with very few studies and consensus of the authors. The recommendations are illustrated by 2 examples coming from dossier assessments of the Institute for Quality and Efficiency in Health Care.

How to use prior knowledge and still give new data a chance?

A common challenge for the development of drugs in rare diseases and special populations, eg, paediatrics, is the small numbers of patients that can be recruited into clinical trials. Extrapolation can be used to support development and licensing in paediatrics through the structured integration of available data in adults and prospectively generated data in paediatrics to derive conclusions that support licensing decisions in the target paediatric population. In this context, Bayesian analyses have been proposed to obtain formal proof of efficacy of a new drug or therapeutic principle by using additional information (data, opinion, or expectation), expressed through a prior distribution. However, little is said about the impact of the prior assumptions on the evaluation of outcome and prespecified strategies for decision‐making as required in the regulatory context.

On the basis of examples, we explore the use of data‐based Bayesian meta‐analytic–predictive methods and compare these approaches with common frequentist and Bayesian meta‐analysis models. Noninformative efficacy prior distributions usually do not change the conclusions irrespective of the chosen analysis method. However, if heterogeneity is considered, conclusions are highly dependent on the heterogeneity prior. When using informative efficacy priors based on previous study data in combination with heterogeneity priors, these may completely determine conclusions irrespective of the data generated in the target population. Thus, it is important to understand the impact of the prior assumptions and ensure that prospective trial data in the target population have an appropriate chance, to change prior belief to avoid trivial and potentially erroneous conclusions.