Prior convictions

Beyond 'statistical significance': A nontechnical primer of Bayesian statistics and Bayes factors for health researchers

RATIONALE

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.

AIM

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.

IMPLICATIONS

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.

Pragmatic randomized controlled trials: strengthening the concept through a robust international collaborative network: PRIME-9-Pragmatic Research and Innovation through Multinational Experimentation

In an era focused on value-based healthcare, the quality of healthcare and resource allocation should be underpinned by empirical evidence. Pragmatic clinical trials (pRCTs) are essential in this endeavor, providing randomized controlled trial (RCT) insights that encapsulate real-world effects of interventions. The rising popularity of pRCTs can be attributed to their ability to mirror real-world practices, accommodate larger sample sizes, and provide cost advantages over traditional RCTs. By harmonizing efficacy with effectiveness, pRCTs assist decision-makers in prioritizing interventions that have a substantial public health impact and align with the tenets of value-based health care. An international network for pRCT provides several advantages, including larger and diverse patient populations, access to a broader range of healthcare settings, sharing knowledge and expertise, and overcoming ethical and regulatory barriers. The hypothesis and study design of pRCT answers the decision-maker's questions. pRCT compares clinically relevant alternative interventions, recruits participants from diverse practice settings, and collects data on various health outcomes. They are scarce because the medical products industry typically does not fund pRCT. Prioritizing these studies by expanding the infrastructure to conduct clinical research within the healthcare delivery system and increasing public and private funding for these studies will be necessary to facilitate pRCTs. These changes require more clinical and health policy decision-makers in clinical research priority setting, infrastructure development, and funding. This paper presents a comprehensive overview of pRCTs, emphasizing their importance in evidence-based medicine and the advantages of an international collaborative network for their execution. It details the development of PRIME-9, an international initiative across nine countries to advance pRCTs, and explores various statistical approaches for these trials. The paper underscores the need to overcome current challenges, such as funding limitations and infrastructural constraints, to leverage the full potential of pRCTs in optimizing healthcare quality and resource utilization.

Bayesian methods: a potential path forward for sepsis trials

BACKGROUND

Given the success of recent platform trials for COVID-19, Bayesian statistical methods have become an option for complex, heterogenous syndromes like sepsis. However, study design will require careful consideration of how statistical power varies using Bayesian methods across different choices for how historical data are incorporated through a prior distribution and how the analysis is ultimately conducted. Our objective with the current analysis is to assess how different uses of historical data through a prior distribution, and type of analysis influence results of a proposed trial that will be analyzed using Bayesian statistical methods.

METHODS

We conducted a simulation study incorporating historical data from a published multicenter, randomized clinical trial in the US and Canada of polymyxin B hemadsorption for treatment of endotoxemic septic shock. Historical data come from a 179-patient subgroup of the previous trial of adult critically ill patients with septic shock, multiple organ failure and an endotoxin activity of 0.60-0.89. The trial intervention consisted of two polymyxin B hemoadsorption treatments (2 h each) completed within 24 h of enrollment.

RESULTS

In our simulations for a new trial of 150 patients, a range of hypothetical results were observed. Across a range of baseline risks and treatment effects and four ways of including historical data, we demonstrate an increase in power with the use of clinically defensible incorporation of historical data. In one possible trial result, for example, with an observed reduction in risk of mortality from 44 to 37%, the probability of benefit is 96% with a fixed weight of 75% on prior data and 90% with a commensurate (adaptive-weighting) prior; the same data give an 80% probability of benefit if historical data are ignored.

CONCLUSIONS

Using Bayesian methods and a biologically justifiable use of historical data in a prior distribution yields a study design with higher power than a conventional design that ignores relevant historical data. Bayesian methods may be a viable option for trials in critical care medicine where beneficial treatments have been elusive.

Bayesian analysis of the Substrate Ablation vs. Antiarrhythmic Drug Therapy for Symptomatic Ventricular Tachycardia trial

BACKGROUND AND AIMS

Bayesian analyses can provide additional insights into the results of clinical trials, aiding in the decision-making process. We analysed the Substrate Ablation vs. Antiarrhythmic Drug Therapy for Symptomatic Ventricular Tachycardia (SURVIVE-VT) trial using Bayesian survival models.

METHODS AND RESULTS

The SURVIVE-VT trial randomized patients with ischaemic cardiomyopathy and monomorphic ventricular tachycardia (VT) to catheter ablation or antiarrhythmic drugs (AAD) as a first-line strategy. The primary outcome was a composite of cardiovascular death, appropriate implantable cardioverter-defibrillator shocks, unplanned heart failure hospitalizations, or severe treatment-related complications. We used informative, skeptical, and non-informative priors with different probabilities of large effects to compute the posterior distributions using Markov Chain Monte Carlo methods. We calculated the probabilities of hazard ratios (HR) being <1, <0.9, and <0.75, as well as 2-year survival estimates. Of the 144 randomized patients, 71 underwent catheter ablation and 73 received AAD. Regardless of the prior, catheter ablation had a >98% probability of reducing the primary outcome (HR < 1) and a >96% probability of achieving a reduction of >10% (HR < 0.9). The probability of a >25% (HR < 0.75) reduction of treatment-related complications was >90%. Catheter ablation had a high probability (>93%) of reducing incessant/slow undetected VT/electric storm, unplanned hospitalizations for ventricular arrhythmias, and overall cardiovascular admissions > 25%, with absolute differences of 15.2%, 21.2%, and 20.2%, respectively.

CONCLUSION

In patients with ischaemic cardiomyopathy and VT, catheter ablation as a first-line therapy resulted in a high probability of reducing several clinical outcomes compared to AAD. Our study highlights the value of Bayesian analysis in clinical trials and its potential for guiding treatment decisions.

TRIAL REGISTRATION

ClinicalTrials.gov identifier: NCT03734562.

Modern Statistical Methods for the Surgeon Scientist: The Clash of Frequentist versus Bayesian Paradigms

The practice of evidence-based medicine is the result of a multitude of research and trials aimed toward improving health-care outcomes. An understanding of the associated data remains paramount toward optimizing patient outcomes. Medical statistics commonly revolve around frequentist concepts that are convoluted and nonintuitive for nonstatisticians. Within this article, we will discuss frequentist statistics, their limitations, as well as introduce Bayesian statistics as an alternative approach for data interpretation. By doing so, we intend to highlight the importance of correct statistical interpretations through clinically relevant examples while providing a deeper understanding of the underlying philosophies of frequentist and Bayesian statistics.

Blood Pressure-Lowering Effect of Fimasartan Versus Comparators: A Cross-Inference With a Systematic Review and Meta-Analysis Through a Quality Management System

PURPOSE

Fimasartan, one of the newest angiotensin receptor blockers (ARBs) available worldwide, has been investigated extensively since its initial development. Our study group conducted a systematic review and meta-analysis of randomized controlled trials (RCTs) evaluating fimasartan and comparators for their blood pressure (BP)-lowering effect. Moreover, we employed a cross-inference (frequentist and Bayesian inference) system, which has never been used in the medical field, to confirm the results of our study. In addition, a quality management system was integrated throughout the study for data quality.

METHODS

PubMed, EMBASE, the Cochrane Central Register of Controlled Trials, ClinicalKey, and ClinicalTrial.gov were searched for RCT studies from March 1998 to March 2022. In each study, the mean differences (MD^s) and 95% CIs were identified for reductions in clinic sitting systolic and diastolic BP (SiSBP/SiDBP) or 24-hour mean systolic BP and diastolic BP by ambulatory BP monitoring (ASBP/ADBP) from baseline between the fimasartan and comparator groups, followed by meta-analysis. A subsequent meta-analysis was performed with frequentist and Bayesian inference as a tool in the cross-checking system.

FINDINGS

Eleven RCTs with a total of 2459 subjects were included in the study. The clinic SiSBP/SiDBP-lowering effect of fimasartan was significantly greater relative to those of comparators (MD for clinic SiSBP, -2.58 mm Hg [95% CI, -4.35 to -0.81; P = 0.004]; MD for clinic SiDBP, -2.13 mm Hg [95% CI, -2.96 to -1.30; P = 0.00001]). The ASBP/ADBP-lowering effect of fimasartan was also significantly greater relative to those of comparators (MD for ASBP, -3.58 mm Hg [95% CI, -5.74 to -1.43; P = 0.001]; MD for ADBP, -1.99 mm Hg [95% CI, -3.34 to -0.63; P = 0.004]).

IMPLICATIONS

Fimasartan seems to be more effective in lowering BP than its comparators, including other ARBs. Although there is a limited amount of data and a minuscule number of study subjects available, the results of cross-inference (frequentist + Bayesian) were fairly consistent with the meta-analysis results through our quality management system.

Use of Bayesian Statistics to Reanalyze Data From the Pragmatic Randomized Optimal Platelet and Plasma Ratios Trial

IMPORTANCE

Frequentist statistical approaches are the most common strategies for clinical trial design; however, bayesian trial design may provide a more optimal study technique for trauma-related studies.

OBJECTIVE

To describe the outcomes of bayesian statistical approaches using data from the Pragmatic Randomized Optimal Platelet and Plasma Ratios (PROPPR) Trial.

DESIGN, SETTING, AND PARTICIPANTS

This quality improvement study performed a post hoc bayesian analysis of the PROPPR Trial using multiple hierarchical models to assess the association of resuscitation strategy with mortality. The PROPPR Trial took place at 12 US level I trauma centers from August 2012 to December 2013. A total of 680 severely injured trauma patients who were anticipated to require large volume transfusions were included in the study. Data analysis for this quality improvement study was conducted from December 2021 and June 2022.

INTERVENTIONS

In the PROPPR Trial, patients were randomized to receive a balanced transfusion (equal portions of plasma, platelets, and red blood cells [1:1:1]) vs a red blood cell-heavy strategy (1:1:2) during their initial resuscitation.

MAIN OUTCOMES AND MEASURES

Primary outcomes from the PROPPR trial included 24-hour and 30-day all-cause mortality using frequentist statistical methods. Bayesian methods were used to define the posterior probabilities associated with the resuscitation strategies at each of the original primary end points.

RESULTS

Overall, 680 patients (546 [80.3%] male; median [IQR] age, 34 [24-51] years, 330 [48.5%] with penetrating injury; median [IQR] Injury Severity Score, 26 [17-41]; 591 [87.0%] with severe hemorrhage) were included in the original PROPPR Trial. Between the groups, no significant differences in mortality were originally detected at 24 hours (12.7% vs 17.0%; adjusted risk ratio [RR], 0.75 [95% CI, 0.52-1.08]; P = .12) or 30 days (22.4% vs 26.1%; adjusted RR, 0.86 [95% CI, 0.65-1.12]; P = .26). Using bayesian approaches, a 1:1:1 resuscitation was found to have a 93% (Bayes factor, 13.7; RR, 0.75 [95% credible interval, 0.45-1.11]) and 87% (Bayes factor, 6.56; RR, 0.82 [95% credible interval, 0.57-1.16]) probability of being superior to a 1:1:2 resuscitation with regards to 24-hour and 30-day mortality, respectively.

CONCLUSIONS AND RELEVANCE

In this quality improvement study, a post hoc bayesian analysis of the PROPPR Trial found evidence in support of mortality reduction with a balanced resuscitation strategy for patients in hemorrhagic shock. Bayesian statistical methods offer probability-based results capable of direct comparison between various interventions and should be considered for future studies assessing trauma-related outcomes.

Antidiabetic effect of gemigliptin: a systematic review and meta-analysis of randomized controlled trials with Bayesian inference through a quality management system

Gemigliptin is one of the latest dipeptidyl peptidase-4 inhibitors developed by LG Life Sciences. Since the early 2000s, several randomized controlled trials (RCTs) of gemigliptin have been conducted. However, no study has directly compared its antidiabetic effects through a systematic review and meta-analysis. Therefore, in this study, we performed a systematic review and meta-analysis on RCTs. In particular, a subsequent meta-analysis was performed using Bayesian inference, and an updated quality management system model was integrated throughout our study. The mean differences and 95% confidence intervals for glycated hemoglobin (HbA1c), fasting plasma glucose (FPG), homeostatic model assessment beta cell function (HOMA-β), and low-density lipoprotein (LDL) were evaluated for the efficacy outcomes of gemigliptin as compared to those of placebo and other oral antidiabetic drugs (OADs). In conclusion, we found that gemigliptin was superior to placebo and comparable to other OADs in terms of the effect on HbA1c, FPG, HOMA-β, and LDL. Further, gemigliptin was more effective than other OADs in HbA1c and HOMA-β in Bayesian inference analysis and statistically significant to other OADs in HbA1c and HOMA-β in sensitivity analysis excluding metformin. However, to confirm the results, more studies need to be analysed and the minimum clinically important difference must be applied.

Telemedicine for Children With Medical Complexity: A Randomized Clinical Trial

BACKGROUND

Telemedicine is widely used but has uncertain value. We assessed telemedicine to further improve outcomes and reduce costs of comprehensive care (CC) for medically complex children.

METHODS

We conducted a single-center randomized clinical trial comparing telemedicine with CC relative to CC alone for medically complex children in reducing care days outside the home (clinic, emergency department, or hospital; primary outcome), rate of children developing serious illnesses (causing death, ICU admission, or hospital stay >7 days), and health system costs. We used intent-to-treat Bayesian analyses with neutral prior assuming no benefit. All participants received CC, which included 24/7 phone access to primary care providers (PCPs), low patient-to-PCP ratio, and hospital consultation from PCPs. The telemedicine group also received remote audiovisual communication with the PCPs.

RESULTS

Between August 22, 2018, and March 23, 2020, we randomly assigned 422 medically complex children (209 to CC with telemedicine and 213 to CC alone) before meeting predefined stopping rules. The probability of a reduction with CC with telemedicine versus CC alone was 99% for care days outside the home (12.94 vs 16.94 per child-year; Bayesian rate ratio, 0.80 [95% credible interval, 0.66-0.98]), 95% for rate of children with a serious illness (0.29 vs 0.62 per child-year; rate ratio, 0.68 [0.43-1.07]) and 91% for mean total health system costs (US$33 718 vs US$41 281 per child-year; Bayesian cost ratio, 0.85 [0.67-1.08]).

CONCLUSION

The addition of telemedicine to CC likely reduced care days outside the home, serious illnesses, other adverse outcomes, and health care costs for medically complex children.

Efficacy and Tolerability of Evogliptin in Patients with Type 2 Diabetes Mellitus: A Systematic Review and Meta-analysis with Bayesian Inference Through a Quality-management System

PURPOSE

Evogliptin is one of the latest dipeptidyl peptidase-4 (DPP-4) inhibitor, and a number of clinical trials have been performed following its development, including several randomized controlled trials (RCTs) performed to evaluate its efficacy and tolerability. In our study, we performed a systematic review and meta-analysis of its efficacy and tolerability by collecting RCTs and confirmed the results with Bayesian inference. Moreover, an updated quality-management system was integrated into the study process of systematic review.

METHODS

PubMed, EMBASE, the Cochrane Central Register of Controlled Trials, and ClinicalTrials.gov were searched for literature published between May 1990 and November 2020. We selected 6 homogeneous RCTs in 1017 subjects for efficacy and 1070 subjects for tolerability analysis. Regarding the efficacy profile, the mean differences from baseline (95% CIs) in hemoglobin (Hb) A_1c and fasting plasma glucose (FPG) were generated as end points and derived from each study. Regarding the tolerability profile, risk ratios of adverse events (AEs), serious AEs, adverse drug reactions, and hypoglycemia were generated from baseline to outcome measurements as derived from each study. A subsequent meta-analysis was performed with Bayesian inference.

FINDINGS

For HbA_1c and FPG, the results suggested a statistically significant improvement with evogliptin versus placebo (HbA_1c, -0.44 [95% CI, -0.54 to -0.34; P < 0.00001] and posterior median, -0.38 [95% CI, -0.51 to -0.24]; FPG, -0.61 [95% CI, -0.90 to -0.31; P < 0.0001] and posterior median, -0.48 [95% CI, -0.90 to -0.16]), but no statistically significant difference with evogliptin versus other DPP-4 inhibitors (HbA_1c, -0.01 [95% CI, -0.14 to 0.12] and posterior median, -0.06 [95% CI, -0.25 to 0.12]; FPG, 0.17 [95% CI, -0.10 to 0.44] and posterior median, 0.27 [95% CI, -0.12 to 0.65]). In terms of tolerability, the overall prevalence of adverse events, including hypoglycemia, was similar between evogliptin and other DPP-4 inhibitors and placebo.

IMPLICATIONS

Evogliptin appears more efficacious in terms of changes in HbA_1c and FPG compared with placebo, with an efficacy comparable to those of other DPP-4 inhibitors, although with the limited data studied and the minuscule sample sizes, the predictions of posterior medians, mean differences, and risk ratios of HbA_1c, FPG, and AEs by Bayesian inference were consistent with our findings through our quality-management system.

Powering Bias and Clinically Important Treatment Effects in Randomized Trials of Critical Illness

OBJECTIVES

Recurring issues in clinical trial design may bias results toward the null, yielding findings inconclusive for treatment effects. This study evaluated for powering bias among high-impact critical care trials and the associated risk of masking clinically important treatment effects.

DESIGN, SETTING, AND PATIENTS

Secondary analysis of multicenter randomized trials of critically ill adults in which mortality was the main endpoint. Trials were eligible for inclusion if published between 2008 and 2018 in leading journals. Analyses evaluated for accuracy of estimated control group mortality, adaptive sample size strategy, plausibility of predicted treatment effect, and results relative to the minimal clinically important difference. The main outcome was the mortality risk difference at the study-specific follow-up interval.

INTERVENTIONS

None.

MEASUREMENTS AND MAIN RESULTS

Of 101 included trials, 12 met statistical significance for their main endpoint, five for increased intervention-associated mortality. Most trials (77.3%) overestimated control group mortality in power calculations (observed minus predicted difference, -6.7% ± 9.8%; p < 0.01). Due to this misestimation of control group mortality, in 14 trials, the intervention would have had to prevent at least half of all deaths to achieve the hypothesized treatment effect. Seven trials prespecified adaptive sample size strategies that might have mitigated this issue. The observed risk difference for mortality fell within 5% of predicted in 20 trials, of which 16 did not reach statistical significance. Half of trials (47.0%) were powered for an absolute risk reduction greater than or equal to 10%, but this effect size was observed in only three trials with a statistically significant treatment benefit. Most trials (67.3%) could not exclude clinically important treatment benefit or harm.

CONCLUSIONS

The design of most high-impact critical care trials biased results toward the null by overestimating control group mortality and powering for unrealistic treatment effects. Clinically important treatment effects often cannot be excluded.

Bayesian Analyses of Cardiovascular Trials-Bringing Added Value to the Table

The limitations of traditional statistical analyses of randomised clinical trials that follow the frequentist inference paradigm have been increasingly noted. This article discusses the Bayesian approach to statistical inference in randomised clinical trials, demonstrating its functioning, utility, and limitations through an examination of current cardiovascular examples. A simplified overview of the mechanics of Bayesian inference and a glossary of the Bayesian terminology is first provided. The duality of the Bayesian approach, providing both an evidential calculus based on the likelihood ratio and a belief calculus that incorporates our prior beliefs with the current data, is presented. Specific cardiovascular trials are reanalysed with Bayesian methods. It is claimed that the Bayesian approach, by providing an enhanced ability to appreciate and model uncertainty, leads to an enriched understanding of the strength and quantification of the evidence, of the distinction between statistical and clinical significance, of the within- and between-trial variability, of subgroup analyses, of the utility of informative priors, and of our ability to synthesise and update our knowledge base. Ultimately, it is argued that the Bayesian approach is more intuitive and transparent, permits enhanced data analysis and interpretation, and may lead to improved decision making not only by trialists but also by practicing clinicians, guideline writers, and even expert regulatory advisory consultants.

Common methodological issues and suggested solutions in bone research

Bone research is a dynamic area of scientific investigation that usually encompasses multidisciplines. Virtually all basic cellular research, clinical research and epidemiologic research rely on statistical concepts and methodology for inference. This paper discusses common issues and suggested solutions concerning the application of statistical thinking in bone research, particularly in clinical and epidemiological investigations. The issues are sample size estimation, biases and confounders, analysis of longitudinal data, categorization of continuous data, selection of significant variables, over-fitting, P-values, false positive finding, confidence interval, and Bayesian inference. It is hoped that by adopting the suggested measures the scientific quality of bone research can improve.

Clinical trials in critical care: can a Bayesian approach enhance clinical and scientific decision making?

Recent Bayesian reanalyses of prominent trials in critical illness have generated controversy by contradicting the initial conclusions based on conventional frequentist analyses. Many clinicians might be sceptical that Bayesian analysis, a philosophical and statistical approach that combines prior beliefs with data to generate probabilities, provides more useful information about clinical trials than the frequentist approach. In this Personal View, we introduce clinicians to the rationale, process, and interpretation of Bayesian analysis through a systematic review and reanalysis of interventional trials in critical illness. In the majority of cases, Bayesian and frequentist analyses agreed. In the remainder, Bayesian analysis identified interventions where benefit was probable despite the absence of statistical significance, where interpretation depended substantially on choice of prior distribution, and where benefit was improbable despite statistical significance. Bayesian analysis in critical care medicine can help to distinguish harm from uncertainty and establish the probability of clinically important benefit for clinicians, policy makers, and patients.

P-values and significance: The null hypothesis that they are not related is correct

False signals and therapeutic optimism have led medicine down many a wrong pathway. Apart from the unnecessary costs of care and redundant research expenditure and efforts this has caused, therapies which were eventually discontinued may have come at a staggering cost of lives lost. Still most statistical information in the medical literature is presented with its p-values and little else. The use of p<0.05 was proposed as an arbitrary threshold for defining a statistically significant difference. Strong signals manifest even with the use of small sample sizes and are highly replicable. However, weak signals, which are increasingly the focus of modern research, may be obscured by the presence of other powerful variables in the dataset are more likely to decay in subsequent studies due to multiple causes. It is time to set higher standards for evidence in medical research. Data that should always be presented in conjunction with the p-value are the Confidence Intervals, which illustrate the uncertainty inherent to the results, and the Fragility Index, which reflects result robustness. Multiple RCTs should be the standard for implementing change. Ideally these studies should consistently demonstrate p-values <0.005, study and control groups with well separated 95% CIs and high fragility indices.

Bayesian Analysis: A Practical Approach to Interpret Clinical Trials and Create Clinical Practice Guidelines

Bayesian analysis is firmly grounded in the science of probability and has been increasingly supplementing or replacing traditional approaches based on P values. In this review, we present gradually more complex examples, along with programming code and data sets, to show how Bayesian analysis takes evidence from randomized clinical trials to update what is already known about specific treatments in cardiovascular medicine. In the example of revascularization choices for diabetic patients who have multivessel coronary artery disease, we combine the results of the FREEDOM trial (Future Revascularization Evaluation in Patients with Diabetes Mellitus: Optimal Management of Multivessel Disease) with prior probability distributions to show how strongly we should believe in the new Class I recommendation ("should be done") for a preference of bypass surgery over percutaneous coronary intervention. In the debate about the duration of dual antiplatelet therapy after drug-eluting stent implantation, we avoid a common pitfall in traditional meta-analysis and create a network of randomized clinical trials to compare outcomes after specific treatment durations. Although we find no credible increase in mortality, we affirm the tradeoff between increased bleeding and reduced myocardial infarctions with prolonged dual antiplatelet therapy, findings that support the new Class IIb recommendation ("may be considered") to extend dual antiplatelet therapy after drug-eluting stent implantation. In the decision between culprit artery-only and multivessel percutaneous coronary intervention in patients with ST-segment elevation myocardial infarction, we use hierarchical meta-analysis to analyze evidence from observational studies and randomized clinical trials and find that the probability of all-cause mortality at longest follow-up is similar after both strategies, a finding that challenges the older ban against noninfarct-artery intervention during primary percutaneous coronary intervention. These examples illustrate how Bayesian analysis integrates new trial information with existing knowledge to reduce uncertainty and change attitudes about treatments in cardiovascular medicine.

Using previous trial results to inform hypothesis testing of new interventions

Results of industry-sponsored Phase III trials registered at clinicaltrials.gov include a rich amount of information on the efficacy of medical interventions. We propose that these results can be used to inform hypothesis testing of a new intervention through the Bayes principle. The posterior probability of positive efficacy offers an accessible interpretation of the uncertainty of efficacy and a convenient metric for global false-positive control.

Creating falseness-How to establish statistical evidence of the untrue

Null hypothesis significance testing is the typical statistical approach in search of the truthfulness of hypotheses. This method does not formally consider the prior credence in the hypothesis, which affects the chances of reaching correct conclusions. When scientifically implausible or empirically weakly supported hypotheses are tested, there is an increased risk that a positive finding in a test in fact is false positive. This article argues that when scientifically weakly supported hypotheses are tested repeatedly-such as when studying the clinical effects of homeopathy-the accumulation of false positive study findings will risk providing false evidence also in systematic reviews and meta-analyses. False positive findings are detrimental to science and society, as once published, they accumulate persistent untrue evidence, which risks giving rise to nonpurposive research programmes, policy changes, and promotion of ineffective treatments. The problems with false positive findings are discussed, and advice is given on how to minimize the problem. The standard of evidence of a hypothesis should depend not only on the results of statistical analyses but also on its a priori support. Positive findings from studies investigating hypotheses with poor theoretical and empirical foundations should be viewed as tentative until the results are replicated and/or the hypothesis gains more empirical evidence supporting it as likely to be true.

Updating Evidence for Using Hypothermia in Pediatric Severe Traumatic Brain Injury: Conventional and Bayesian Meta-Analytic Perspectives

OBJECTIVE

To evaluate clinical trials of hypothermia management on outcome in pediatric patients with severe traumatic brain injury using conventional and Bayesian meta-analyses.

DATA SOURCES

Screening of PubMed and other databases to identify randomized controlled trials of hypothermia for pediatric severe traumatic brain injury published before September 2016.

STUDY SELECTION

Four investigators assessed and reviewed randomized controlled trial data.

DATA EXTRACTION

Details of trial design, patient number, Glasgow Coma Scale score, hypothermia and control normothermia therapy, and outcome of mortality were collated.

DATA SYNTHESIS

In conventional meta-analysis, random-effects models were expressed as odds ratio (odds ratio with 95% credible-interval). Bayesian outcome probabilities were calculated as probability of odds ratio greater than or equal to 1. In seven randomized controlled trials (n = 472, patients 0-17 yr old), there was no difference in mortality (hypothermia vs normothermia) with pooled estimate 1.42 (credible-interval, 0.77-2.61; p = 0.26). Duration of hypothermia (24, 48, or 72 hr) did not show difference in mortality. (Similar results were found using poor outcome.) Bayesian analyses of randomized controlled trials ordered by time of study completed recruitment showed, after the seventh trial, chance of relative risk reduction of death by greater than 20% is 1-in-3. An optimistic belief (0.90 probability that relative risk reduction of death > 20% hypothermia vs normothermia) gives a chance of relative risk reduction of death by greater than 20% of 1-in-2.

CONCLUSIONS

Conventional meta-analysis shows the null hypothesis-no difference between hypothermia versus normothermia on mortality and poor outcome-cannot be rejected. However, Bayesian meta-analysis shows chance of relative risk reduction of death greater than 20% with hypothermia versus normothermia is 1-in-3, which may be further altered by one's optimistic or skeptical belief about a patient.

Alternative designs for clinical trials in rare diseases

Evidence-based medicine requires strong scientific evidence upon which to base treatment. In rare diseases, study populations are often small, and thus this evidence is difficult to accrue. Investigators, though, should be creative and develop a flexible toolkit of methods to deal with the problems inherent in the study of rare disease. This narrative review presents alternative clinical trial designs for studying treatments of rare diseases, including cross-over and n-of-1 trials, randomized placebo-phase design, enriched enrollment, randomized withdrawal design, and classes of adaptive designs. Examples of applications of these designs are presented along with their advantages and disadvantages. Additional analytical considerations such as Bayesian analysis, internal pilots, and use of biomarkers as surrogate outcomes are further discussed. A framework for selecting appropriate clinical trial design is proposed to guide investigators in the process of selecting alternative designs for rare diseases. © 2016 Wiley Periodicals, Inc.

The Risk of Atrial Fibrillation With Ivabradine Treatment: A Meta-analysis With Trial Sequential Analysis of More Than 40000 Patients

Recent trials reported that risk of atrial fibrillation (AF) is increased in patients using ivabradine compared with controls. We performed this meta-analysis to investigate the risk of AF association with ivabradine treatment on the basis of data obtained from randomized controlled trials (RCTs). We searched PubMed, EMBASE, Scopus, and the Cochrane Library for RCTs that comprised >100 patients. The incidence of AF was assessed. We obtained data from European Medicines Agency (EMA) scientific reports for the RCTs in which the incidence of AF was not reported. We used trial sequential analysis (TSA) to provide information on when we had reached firm evidence of new AF based on a 15% relative risk increase (RRI) in ivabradine treatment. Three RCTs and 1 EMA overall oral safety set (OOSS) pooled analysis (included 5 RCTs) were included in the meta-analysis (N = 40 437). The incidence of AF was 5.34% in patients using ivabradine and 4.56% in placebo. There was significantly higher incidence of AF (24% RRI) in the ivabradine group when compared with placebo before (RR: 1.24, 95% confidence interval: 1.08-1.42, P = 0.003, I 1980 = 53%) and after excluding OOSS (RR: 1.24, 95% confidence interval: 1.06-1.44, P = 0.008). In the TSA, the cumulative z-curve crossed both the traditional boundary (P = 0.05) and the trial sequential monitoring boundary, indicating firm evidence for ≥15% increase in ivabradine treatment when compared with placebo. Study results indicate that AF is more common in the ivabradine group (24% RRI) than in controls.

Chelation therapy to treat atherosclerosis, particularly in diabetes: is it time to reconsider?

INTRODUCTION

Case reports and case series have suggested a possible beneficial effect of chelation therapy in patients with atherosclerotic disease. Small randomized trials conducted in patients with angina or peripheral artery disease, however, were not sufficiently powered to provide conclusive evidence on clinical outcomes.

AREAS COVERED

The Trial to Assess Chelation Therapy (TACT) was the first randomized trial adequately powered to detect the effects of chelation therapy on clinical endpoints. We discuss results and future research. Expert commentary: Chelation reduced adverse cardiovascular events in a post myocardial infarction (MI) population. Patients with diabetes demonstrated even greater benefit, with a number needed to treat of 6.5 patients to prevent a cardiac event over 5 years, with a 41% relative reduction in risk of a cardiac event (p = 0.0002). These results led to the revision of the ACC/AHA guideline recommendations for chelation therapy, changing its classification from class III to class IIb. TACT2, a replicative trial, will assess the effects of chelation therapy on cardiovascular outcomes in diabetic patients with a prior myocardial infarction. We are seeking participating sites for TACT2.

New Pathways for Evaluating Potential Acute Stroke Therapies

Pharmacological therapy for acute ischemic stroke remains limited to one successful, approved treatment: tissue plasminogen activator within 3 h of stroke onset. Many neuroprotective drugs and a few other thrombolytics were evaluated in clinical trials, but none demonstrated unequivocal success and were approved by regulatory agencies. The development paradigm for such therapies needs to provide convincing evidence of efficacy and safety to obtain approval by the Food and Drug Administration (FDA). The FDA modernization act of 1997 stated that such evidence could be derived from one large phase III trial with a clinical endpoint and supportive evidence. Drugs being developed for acute ischemic stroke can potentially be approved under this act by coupling a major phase III trial with supportive evidence provided by a phase IIB trial demonstrating an effect on a relevant biomarker such as magnetic resonance imaging or computed tomography assessment of ischemic lesion growth. Statistical approaches have been developed to optimize the design of such an imaging-based phase IIB study, for example approaches that modify randomization probabilities to assign larger proportions of patients to the ‘winning’ strategy (i.e. ‘pick the winner’ strategies) with an interim assessment to reduce the sample size requirement. Demonstrating a treatment effect on a relevant imaging-based biomarker should provide supportive evidence for a new drug application, if a subsequent phase III trial with a clinical outcome demonstrates a significant treatment effect.

Duration of Dual Antiplatelet Therapy: A Systematic Review for the 2016 ACC/AHA Guideline Focused Update on Duration of Dual Antiplatelet Therapy in Patients With Coronary Artery Disease: A Report of the American College of Cardiology/American Heart Association Task Force on Clinical Practice Guidelines

BACKGROUND

The optimal duration of dual antiplatelet therapy (DAPT) after implantation of newer-generation drug-eluting stents (DES) remains uncertain. Similarly, questions remain about the role of DAPT in long-term therapy of stable post-myocardial infarction (MI) patients.

AIM

Our objective was to compare the incidence of death, major hemorrhage, MI, stent thrombosis, and major adverse cardiac events in patients randomized to prolonged or short-course DAPT after implantation of newer-generation DES and in secondary prevention after MI.

METHODS

We used traditional frequentist statistical and Bayesian approaches to address the following questions: Q1) What is the minimum duration of DAPT required after DES implantation? Q2) What is the clinical benefit of prolonging DAPT up to 18 to 48 months? Q3) What is the clinical effect of DAPT in stable patients who are >1 year past an MI?

RESULTS

We reviewed evidence from 11 randomized controlled trials (RCTs) that enrolled 33 051 patients who received predominantly newer-generation DES to answer: A1) Use of DAPT for 12 months, as compared with use for 3 to 6 months, resulted in no significant differences in incidence of death (odds ratio [OR]: 1.17; 95% confidence interval [CI]: 0.85 to 1.63), major hemorrhage (OR: 1.65; 95% CI: 0.97 to 2.82), MI (OR: 0.87; 95% CI: 0.65 to 1.18), or stent thrombosis (OR: 0.87; 95% CI: 0.49 to 1.55). Bayesian models confirmed the primary analysis. A2) Use of DAPT for 18 to 48 months, compared with use for 6 to 12 months, was associated with no difference in incidence of all-cause death (OR: 1.14; 95% CI: 0.92 to 1.42) but was associated with increased major hemorrhage (OR: 1.58; 95% CI: 1.20 to 2.09), decreased MI (OR: 0.67; 95% CI: 0.47 to 0.95), and decreased stent thrombosis (OR: 0.45; 95% CI: 0.24 to 0.74). A risk-benefit analysis found 3 fewer stent thromboses (95% CI: 2 to 5) and 6 fewer MIs (95% CI: 2 to 11) but 5 more major bleeds (95% CI: 3 to 9) per 1000 patients treated with prolonged DAPT per year. Post hoc analyses provided weak evidence of increased mortality with prolonged DAPT. We reviewed evidence from 1 RCT of 21 162 patients and a post hoc analysis of 1 RCT of 15 603 patients to answer: A3): Use of DAPT >1 year after MI reduced the composite risk of cardiovascular death, MI, or stroke (hazard ratio: 0.84; 95% CI: 0.74 to 0.95) but increased major bleeding (hazard ratio: 2.32; 95% CI: 1.68 to 3.21). A meta-analysis and a post hoc analysis of an RCT in patients with stable cardiovascular disease produced similar findings.

CONCLUSIONS

The primary analysis provides moderately strong evidence that prolonged DAPT after implantation of newer-generation DES entails a tradeoff between reductions in stent thrombosis and MI and increases in major hemorrhage. Secondary analyses provide weak evidence of increased mortality with prolonged DAPT after DES implantation. In patients whose coronary thrombotic risk was defined by a prior MI rather than by DES implantation, the primary analysis provides moderately strong evidence of reduced cardiovascular events at the expense of increased bleeding.

Dietary Intervention for Overweight and Obese Adults: Comparison of Low-Carbohydrate and Low-Fat Diets. A Meta-Analysis

BACKGROUND

Reduced calorie, low fat diet is currently recommended diet for overweight and obese adults. Prior data suggest that low carbohydrate diets may also be a viable option for those who are overweight and obese.

PURPOSE

Compare the effects of low carbohydrate versus low fats diet on weight and atherosclerotic cardiovascular disease risk in overweight and obese patients.

DATA SOURCES

Systematic literature review via PubMed (1966-2014).

STUDY SELECTION

Randomized controlled trials with ≥8 weeks follow up, comparing low carbohydrate (≤120gm carbohydrates/day) and low fat diet (≤30% energy from fat/day).

DATA EXTRACTION

Data were extracted and prepared for analysis using double data entry. Prior to identification of candidate publications, the outcomes of change in weight and metabolic factors were selected as defined by Cochrane Collaboration. Assessment of the effects of diets on predicted risk of atherosclerotic cardiovascular disease risk was added during the data collection phase.

DATA SYNTHESIS

1797 patients were included from 17 trials with <1 year follow up in 12. Compared with low fat diet, low carbohydrate was associated with significantly greater reduction in weight (Δ = -2.0 kg, 95% CI: -3.1, -0.9) and significantly lower predicted risk of atherosclerotic cardiovascular disease events (p<0.03). Frequentist and Bayesian results were concordant. The probability of greater weight loss associated with low carbohydrate was >99% while the reduction in predicted risk favoring low carbohydrate was >98%.

LIMITATIONS

Lack of patient-level data and heterogeneity in dropout rates and outcomes reported.

CONCLUSIONS

This trial-level meta-analysis of randomized controlled trials comparing LoCHO diets with LoFAT diets in strictly adherent populations demonstrates that each diet was associated with significant weight loss and reduction in predicted risk of ASCVD events. However, LoCHO diet was associated with modest but significantly greater improvements in weight loss and predicted ASCVD risk in studies from 8 weeks to 24 months in duration. These results suggest that future evaluations of dietary guidelines should consider low carbohydrate diets as effective and safe intervention for weight management in the overweight and obese, although long-term effects require further investigation.

Bayesian methodology for the design and interpretation of clinical trials in critical care medicine: a primer for clinicians

OBJECTIVES

To review Bayesian methodology and its utility to clinical decision making and research in the critical care field.

DATA SOURCE AND STUDY SELECTION

Clinical, epidemiological, and biostatistical studies on Bayesian methods in PubMed and Embase from their inception to December 2013.

DATA SYNTHESIS

Bayesian methods have been extensively used by a wide range of scientific fields, including astronomy, engineering, chemistry, genetics, physics, geology, paleontology, climatology, cryptography, linguistics, ecology, and computational sciences. The application of medical knowledge in clinical research is analogous to the application of medical knowledge in clinical practice. Bedside physicians have to make most diagnostic and treatment decisions on critically ill patients every day without clear-cut evidence-based medicine (more subjective than objective evidence). Similarly, clinical researchers have to make most decisions about trial design with limited available data. Bayesian methodology allows both subjective and objective aspects of knowledge to be formally measured and transparently incorporated into the design, execution, and interpretation of clinical trials. In addition, various degrees of knowledge and several hypotheses can be tested at the same time in a single clinical trial without the risk of multiplicity. Notably, the Bayesian technology is naturally suited for the interpretation of clinical trial findings for the individualized care of critically ill patients and for the optimization of public health policies.

CONCLUSIONS

We propose that the application of the versatile Bayesian methodology in conjunction with the conventional statistical methods is not only ripe for actual use in critical care clinical research but it is also a necessary step to maximize the performance of clinical trials and its translation to the practice of critical care medicine.

Bayesian data analysis in observational comparative effectiveness research: rationale and examples

Many comparative effectiveness research and patient-centered outcomes research studies will need to be observational for one or both of two reasons: first, randomized trials are expensive and time-consuming; and second, only observational studies can answer some research questions. It is generally recognized that there is a need to increase the scientific validity and efficiency of observational studies. Bayesian methods for the design and analysis of observational studies are scientifically valid and offer many advantages over frequentist methods, including, importantly, the ability to conduct comparative effectiveness research/patient-centered outcomes research more efficiently. Bayesian data analysis is being introduced into outcomes studies that we are conducting. Our purpose here is to describe our view of some of the advantages of Bayesian methods for observational studies and to illustrate both realized and potential advantages by describing studies we are conducting in which various Bayesian methods have been or could be implemented.

Comparative efficacy and tolerability of anti-epileptic drugs for refractory focal epilepsy: systematic review and network meta-analysis reveals the need for long term comparator trials

AIMS

To evaluate the comparative efficacy (50% reduction in seizure frequency) and tolerability (premature withdrawal due to adverse events) of anti-epileptic drugs (AEDs) for refractory epilepsy.

METHODS

We searched Cochrane Central Register of Controlled Trials (Cochrane Library 2009, issue 2) including Epilepsy Group's specialized register, MEDLINE (1950 to March 2009), EMBASE (1980 to March 2009), and Current Contents Connect (1998 to March 2009) to conduct a systematic review of published studies, developed a treatment network and undertook a network meta-analysis.

RESULTS

Forty-three eligible trials with 6346 patients and 12 interventions, including placebo, contributed to the analysis. Only three direct drug comparator trials were identified, the remaining 40 trials being placebo-controlled. Conventional random-effects meta-analysis indicated all drugs were superior in efficacy to placebo (overall odds ratio (OR] 3.78, 95% CI 3.14, 4.55) but did not permit firm distinction between drugs on the basis of the efficacy or tolerability. A Bayesian network meta-analysis prioritized oxcarbazepine, topiramate and pregabalin on the basis of short term efficacy. However, sodium valproate, levetiracetam, gabapentin and vigabatrin were prioritized on the basis of short-term efficacy and tolerability, with the caveat that vigabatrin is recognized as being associated with serious visual disturbance with chronic use.

CONCLUSION

Of the wide range of AEDs licensed for the treatment of refractory epilepsy, sodium valproate, levetiracetam and gabapentin demonstrated the best balance of efficacy and tolerability. Until regulators mandate greater use of active comparator trials with longer term follow-up, network meta-analysis provides the only available means to quantify these clinically important parameters.

Monitoring in clinical trials: benefit or bias?

Monitoring ongoing clinical trials for early signs of effectiveness is an option for improving cost-effectiveness of trials that is becoming increasingly common. Alongside the obvious advantages made possible by monitoring, however, there are some downsides. In particular, there is growing concern in the medical community that trials stopped early for benefit tend to overestimate treatment effect. In this paper, I examine this problem from the point of view of statistical methodology, starting from the observation that the overestimation is caused by the statistical method adopted. Consequently, I argue that some modifications can and should be made to the present statistical framework in order not to miss the advantages the possibility of monitoring can grant.

Clinical trial design for endovascular ischemic stroke intervention

BACKGROUND

Randomized, double-blinded, placebo-controlled trials have significant impact on clinical practice. The ultimate goal of a clinical trial of therapy for acute ischemic stroke (AIS) is to compare 2 interventions. Challenges may include interventional therapy standardization, enrollment rate, patient selection, biases, data and safety monitoring, reporting, and financial and logistical support.

METHOD

Selected randomized and single-arm prospective AIS trial designs. Clinical trial elements and their challenges are reviewed. Innovative designs and proposed recommendations to overcome some of the specific challenges and limitations are discussed.

RESULTS

AIS therapy trials have specific challenges related to ethical issues, enrollment rate, outcome measures, limited time to treatment, efficacy, safety, and limited or variable operator experience with complex technology in a delicate end organ. Proposed suggestions for improving trial design include the following: incorporation of a lead-in phase; careful patient and outcome measure selection; historical, concurrent, or hybrid controls; open data access; and a Bayesian approach. An open data paradigm may facilitate creation of computerized prediction models for future trials (minimizing cost by decreasing sample size or providing futility analyses and directing resources to other trials). Collaborative, consortium, and network infrastructures may allow more effective and efficient study completion. Self-learning, self-correcting trials with intrinsic flexibility to adapt may help future clinical trial design in AIS.

CONCLUSION

The randomized clinical trial design in AIS endovascular therapy is challenging. Lead-in phases, careful patient selection, use of innovative outcome measures, control groups, and newer clinical trial design may enhance conduct of future trials, their validity, and their results.

From hot hands to declining effects: the risks of small numbers

About 25 years ago, a group of researchers demonstrated that there is no such thing as the "hot hand" in professional basketball. When a player hits 5 or 7 shots in a row (or misses 10 in a row), what's at work is random variation, nothing more. However, random causes do not stop players, coaches, fans, and media from talking about and acting on "hot hands," telling stories and making choices that ultimately are based on randomness. The same phenomenon is true in medicine. Some clinical trials with small numbers of events yielded positive findings, which in turn led clinicians, academics, and government officials to talk, telling stories and sometimes making choices that were later shown to be based on randomness. I provide some cardiovascular examples, such as the use of angiotensin receptor blockers for chronic heart failure, nesiritide for acute heart failure, and cytochrome P-450 (CYP) 2C19 genotyping for the acute coronary syndromes. I also review the more general "decline effect," by which drugs appear to yield a lower effect size over time. The decline effect is due at least in part to over interpretation of small studies, which are more likely to be noticed because of publication bias. As funders of research, we at the National Heart, Lung, and Blood Institute seek to support projects that will yield robust, credible evidence that will affect practice and policy in the right way. We must be alert to the risks of small numbers.

Significance testing as perverse probabilistic reasoning

Truth claims in the medical literature rely heavily on statistical significance testing. Unfortunately, most physicians misunderstand the underlying probabilistic logic of significance tests and consequently often misinterpret their results. This near-universal misunderstanding is highlighted by means of a simple quiz which we administered to 246 physicians at two major academic hospitals, on which the proportion of incorrect responses exceeded 90%. A solid understanding of the fundamental concepts of probability theory is becoming essential to the rational interpretation of medical information. This essay provides a technically sound review of these concepts that is accessible to a medical audience. We also briefly review the debate in the cognitive sciences regarding physicians' aptitude for probabilistic inference.

What the Tortoise said to Achilles

Practitioners and investigators often view clinical trials from very different perspectives-the former in terms of individuals and the latter in terms of groups. The following whimsical dialogue highlights the philosophical foundations of these contrasting perspectives and illustrates their potential impact on patient care and public policy. The title alludes to a piece by Lewis Carroll regarding Zeno's paradox, purportedly proving that the fleet-footed Achilles cannot outrun the plodding Tortoise in a foot race.

Effect of Supersaturated Oxygen Delivery on Infarct Size After Percutaneous Coronary Intervention in Acute Myocardial Infarction

Background— Myocardial salvage is often suboptimal after percutaneous coronary intervention in ST-segment elevation myocardial infarction. Posthoc subgroup analysis from a previous trial (AMIHOT I) suggested that intracoronary delivery of supersaturated oxygen (SSO 2 ) may reduce infarct size in patients with large ST-segment elevation myocardial infarction treated early.

Methods and Results— A prospective, multicenter trial was performed in which 301 patients with anterior ST-segment elevation myocardial infarction undergoing percutaneous coronary intervention within 6 hours of symptom onset were randomized to a 90-minute intracoronary SSO 2 infusion in the left anterior descending artery infarct territory (n=222) or control (n=79). The primary efficacy measure was infarct size in the intention-to-treat population (powered for superiority), and the primary safety measure was composite major adverse cardiovascular events at 30 days in the intention-to-treat and per-protocol populations (powered for noninferiority), with Bayesian hierarchical modeling used to allow partial pooling of evidence from AMIHOT I. Among 281 randomized patients with tc-99m-sestamibi single-photon emission computed tomography data in AMIHOT II, median (interquartile range) infarct size was 26.5% (8.5%, 44%) with control compared with 20% (6%, 37%) after SSO 2 . The pooled adjusted infarct size was 25% (7%, 42%) with control compared with 18.5% (3.5%, 34.5%) after SSO 2 ( P Wilcoxon =0.02; Bayesian posterior probability of superiority, 96.9%). The Bayesian pooled 30-day mean (�SE) rates of major adverse cardiovascular events were 5.0�1.4% for control and 5.9�1.4% for SSO 2 by intention-to-treat, and 5.1�1.5% for control and 4.7�1.5% for SSO 2 by per-protocol analysis (posterior probability of noninferiority, 99.5% and 99.9%, respectively).

Conclusions— Among patients with anterior ST-segment elevation myocardial infarction undergoing percutaneous coronary intervention within 6 hours of symptom onset, infusion of SSO 2 into the left anterior descending artery infarct territory results in a significant reduction in infarct size with noninferior rates of major adverse cardiovascular events at 30 days.

Clinical Trial Registration— clinicaltrials.gov Identifier: NCT00175058

Bayesian statistical inference enhances the interpretation of contemporary randomized controlled trials

OBJECTIVE

Randomized trials generally use "frequentist" statistics based on P-values and 95% confidence intervals. Frequentist methods have limitations that might be overcome, in part, by Bayesian inference. To illustrate these advantages, we re-analyzed randomized trials published in four general medical journals during 2004.

STUDY DESIGN AND SETTING

We used Medline to identify randomized superiority trials with two parallel arms, individual-level randomization and dichotomous or time-to-event primary outcomes. Studies with P<0.05 in favor of the intervention were deemed "positive"; otherwise, they were "negative." We used several prior distributions and exact conjugate analyses to calculate Bayesian posterior probabilities for clinically relevant effects.

RESULTS

Of 88 included studies, 39 were positive using a frequentist analysis. Although the Bayesian posterior probabilities of any benefit (relative risk or hazard ratio<1) were high in positive studies, these probabilities were lower and variable for larger benefits. The positive studies had only moderate probabilities for exceeding the effects that were assumed for calculating the sample size. By comparison, there were moderate probabilities of any benefit in negative studies.

CONCLUSION

Bayesian and frequentist analyses complement each other when interpreting the results of randomized trials. Future reports of randomized trials should include both.