Bayesian meta-analysis: The role of the between-sample heterogeneity

Heterogeneity in meta-analysis: a comprehensive overview

In recent years, meta-analysis has evolved to a critically important field of Statistics, and has significant applications in Medicine and Health Sciences. In this work we briefly present existing methodologies to conduct meta-analysis along with any discussion and recent developments accompanying them. Undoubtedly, studies brought together in a systematic review will differ in one way or another. This yields a considerable amount of variability, any kind of which may be termed heterogeneity. To this end, reports of meta-analyses commonly present a statistical test of heterogeneity when attempting to establish whether the included studies are indeed similar in terms of the reported output or not. We intend to provide an overview of the topic, discuss the potential sources of heterogeneity commonly met in the literature and provide useful guidelines on how to address this issue and to detect heterogeneity. Moreover, we review the recent developments in the Bayesian approach along with the various graphical tools and statistical software that are currently available to the analyst. In addition, we discuss sensitivity analysis issues and other approaches of understanding the causes of heterogeneity. Finally, we explore heterogeneity in meta-analysis for time to event data in a nutshell, pointing out its unique characteristics.

Bayesian estimation and testing in random-effects meta-analysis of rare binary events allowing for flexible group variability

Rare binary events data arise frequently in medical research. Due to lack of statistical power in individual studies involving such data, meta-analysis has become an increasingly important tool for combining results from multiple independent studies. However, traditional meta-analysis methods often report severely biased estimates in such rare-event settings. Moreover, many rely on models assuming a pre-specified direction for variability between control and treatment groups for mathematical convenience, which may be violated in practice. Based on a flexible random-effects model that removes the assumption about the direction, we propose new Bayesian procedures for estimating and testing the overall treatment effect and inter-study heterogeneity. Our Markov chain Monte Carlo algorithm employs Pólya-Gamma augmentation so that all conditionals are known distributions, greatly facilitating computational efficiency. Our simulation shows that the proposed approach generally reports less biased and more stable estimates compared to existing methods. We further illustrate our approach using two real examples, one using rosiglitazone data from 56 studies and the other using stomach ulcers data from 41 studies.

Bayesian heterogeneity in a meta-analysis with two studies and binary data

The meta-analysis of two trials is valuable in many practical situations, such as studies of rare and/or orphan diseases focussed on a single intervention. In this context, additional concerns, like small sample size and/or heterogeneity in the results obtained, might make standard frequentist and Bayesian techniques inappropriate. In a meta-analysis, moreover, the presence of between-sample heterogeneity adds model uncertainty, which must be taken into consideration when drawing inferences. We suggest that the most appropriate way to measure this heterogeneity is by clustering the samples and then determining the posterior probability of the cluster models. The meta-inference is obtained as a mixture of all the meta-inferences for the cluster models, where the mixing distribution is the posterior model probability. We present a simple two-component form of Bayesian model averaging that is unaffected by characteristics such as small study size or zero-cell counts, and which is capable of incorporating uncertainties into the estimation process. Illustrative examples are given and analysed, using real sparse binomial data.

Bayesian Meta-Analysis for Binary Data and Prior Distribution on Models

In meta-analysis, the structure of the between-sample heterogeneity plays a crucial role in estimating the meta-parameter. A Bayesian meta-analysis for binary data has recently been proposed that measures this heterogeneity by clustering the samples and then determining the posterior probability of the cluster models through model selection. The meta-parameter is then estimated using Bayesian model averaging techniques. Although an objective Bayesian meta-analysis is proposed for each type of heterogeneity, we concentrate the attention of this paper on priors over the models. We consider four alternative priors which are motivated by reasonable but different assumptions. A frequentist validation with simulated data has been carried out to analyze the properties of each prior distribution for a set of different number of studies and sample sizes. The results show the importance of choosing an adequate model prior as the posterior probabilities for the models are very sensitive to it. The hierarchical Poisson prior and the hierarchical uniform prior show a good performance when the real model is the homogeneity, or when the sample sizes are high enough. However, the uniform prior can detect the true model when it is an intermediate model (neither homogeneity nor heterogeneity) even for small sample sizes and few studies. An illustrative example with real data is also given, showing the sensitivity of the estimation of the meta-parameter to the model prior.

Effects of Anti-Diabetic Drugs on Fracture Risk: A Systematic Review and Network Meta-Analysis

PURPOSE

Available data on the effects of anti-diabetic drugs on fracture risk are contradictory. Therefore, our study aimed to analyze all available data on the effects of anti-diabetic drugs on fracture risk in type 2 diabetes mellitus (T2DM) patients.

METHODS

Embase, Medline, ClinicalTrials.gov, and Cochrane CENTRAL were searched for relevant trials. All data analyses were performed with STATA (12.0) and R language (3.6.0). Risk ratio (RR) with its 95% confidence interval (CI) was calculated by combining data for the fracture effects of anti-diabetic drugs, including sodium-glucose co-transporter 2 (SGLT2) inhibitors, dipeptidyl peptidase-4 (DPP-4) inhibitors, glucagon-like peptide-1 (GLP-1) receptor agonists, meglitinides, α-glucosidase inhibitors, thiazolidinediones, biguanides, insulin, and sulfonylureas.

RESULTS

One hundred seventeen eligible randomized controlled trials (RCTs) with 221,364 participants were included in this study. Compared with placebo, trelagliptin (RR 3.51; 1.58-13.70) increased the risk of fracture, whereas albiglutide (RR 0.29; 0.04-0.93) and voglibose (RR 0.03; 0-0.11) decreased the risk of fracture. Other medications were comparable in terms of their effects on fracture risk, and no statistical significance was observed. In terms of fractures, voglibose (0.01%) may be the safest option, and trelagliptin (13.64%) may be the worst. Sensitivity analysis results were consistent with those of the main analysis. No statistically significant differences were observed in the regression coefficients of age (1.03; 0.32-2.1), follow-up duration (0.79; 0.27-1.64), and sex distribution (0.63; 0.15-1.56).

CONCLUSIONS

We found varied results on the association between the use of anti-diabetic drugs and fracture risk. Specifically, trelagliptin raised the risk of fracture, whereas voglibose and albiglutide showed benefit with statistical difference. Other drugs were comparable in terms of their effects on fracture risk. Some drugs (omarigliptin, sitagliptin, vildagliptin, saxagliptin, empagliflozin, ertugliflozin, rosiglitazone, pioglitazone, and nateglinide) may increase the risk of fracture, while others (such as dulaglutide, exenatide, liraglutide, semaglutide, lixisenatide, linagliptin, alogliptin, canagliflozin, dapagliflozin, glipizide, gliclazide, glibenclamide, glimepiride, metformin, and insulin) may show benefits. The risk of fracture was independent of age, sex distribution, and the duration of exposure to anti-diabetic drugs. When developing individualized treatment strategies, the clinical efficacy of anti-diabetic drugs must be weighed against their benefits and risks brought about by individual differences of patients.

SYSTEMATIC REVIEW REGISTRATION

This Systematic Review was prospectively registered on the PROSPERO (https://www.crd.york.ac.uk/PROSPERO/, registration number CRD42020189464).

Meta-Analysis with Few Studies and Binary Data: A Bayesian Model Averaging Approach

In meta-analysis, the existence of between-sample heterogeneity introduces model uncertainty, which must be incorporated into the inference. We argue that an alternative way to measure this heterogeneity is by clustering the samples and then determining the posterior probability of the cluster models. The meta-inference is obtained as a mixture of all the meta-inferences for the cluster models, where the mixing distribution is the posterior model probabilities. When there are few studies, the number of cluster configurations is manageable, and the meta-inferences can be drawn with BMA techniques. Although this topic has been relatively neglected in the meta-analysis literature, the inference thus obtained accurately reflects the cluster structure of the samples used. In this paper, illustrative examples are given and analysed, using real binary data.

The Effect of Dexmedetomidine on Emergence Agitation or Delirium in Children After Anesthesia-A Systematic Review and Meta-Analysis of Clinical Studies

Background: We conducted this systematic review and meta-analysis to investigate the clinical effect of dexmedetomidine in preventing pediatric emergence agitation (EA) or delirium (ED) following anesthesia compared with placebo or other sedatives. Methods: The databases of Pubmed, Embase, and Cochrane Library were searched until 8th January 2020. Inclusion criteria were participants with age<18 years and studies of comparison between dexmedetomidine and placebo or other sedatives. Exclusion criteria included adult studies; duplicate publications; management with dexmedetomidine alone; review or meta-analysis; basic research; article published as abstract, letter, case report, editorial, note, method, or protocol; and article presented in non-English language. Results: Fifty-eight randomized controlled trials (RCTs) and five case-control trials (CCTs) including 7,714 patients were included. The results showed that dexmedetomidine significantly decreased the incidence of post-anesthesia EA or ED compared with placebo [OR = 0.22, 95% CI: (0.16, 0.32), I 2 = 75, P < 0.00001], midazolam [OR = 0.36, 95% CI: (0.21, 0.63), I 2 = 57, P = 0.0003], and opioids [OR = 0.55, 95% CI: (0.33, 0.91), I 2 = 0, P = 0.02], whereas the significant difference was not exhibited compared with propofol (or pentobarbital) [OR = 0.56, 95% CI: (0.15, 2.14), I 2 = 58, P = 0.39], ketamine [OR = 0.43, 95% CI: (0.19, 1.00), I 2 = 0, P = 0.05], clonidine [OR = 0.54, 95% CI: (0.20, 1.45), P = 0.22], chloral hydrate [OR = 0.98, 95% CI: (0.26, 3.78), P = 0.98], melatonin [OR = 1.0, 95% CI: (0.13, 7.72), P = 1.00], and ketofol [OR = 0.55, 95% CI: (0.16, 1.93), P = 0.35]. Conclusion: Compared with placebo, midazolam, and opioids, dexmedetomidine significantly decreased the incidence of post-anesthesia EA or ED in pediatric patients. However, dexmedetomidine did not exhibit this superiority compared with propofol and ketamine. With regard to clonidine, chloral hydrate, melatonin, and ketofol, the results needed to be further tested due to the fact that only one trial was included for each control drug.

Perioperative Sleep Disturbances and Postoperative Delirium in Adult Patients: A Systematic Review and Meta-Analysis of Clinical Trials

Background: The aim of this systematic review and meta-analysis of clinical trials was to investigate the effects of perioperative sleep disturbances on postoperative delirium (POD). Methods: Authors searched for studies (until May 12, 2020) reporting POD in patients with sleep disturbances following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. Results: We identified 29 relevant trials including 55,907 patients. We divided these trials into three groups according to study design: Seven retrospective observational trials, 12 prospective observational trials, and 10 randomized controlled trials. The results demonstrated that perioperative sleep disturbances were significantly associated with POD occurrence in observational groups [retrospective: OR = 0.56, 95% CI: [0.33, 0.93], I ² = 91%, p for effect = 0.03; prospective: OR = 0.27, 95% CI: [0.20, 0.36], I ² = 25%, p for effect < 0.001], but not in the randomized controlled trial group [OR = 0.58, 95% CI: [0.34, 1.01], I ² = 68%, p for effect = 0.05]. Publication bias was assessed using Egger's test. We used a one-by-one literature exclusion method to address high heterogeneity. Conclusions: Perioperative sleep disturbances were potential risk factors for POD in observational trials, but not in randomized controlled trials.

Effect of Prophylactic Levosimendan on All-Cause Mortality in Pediatric Patients Undergoing Cardiac Surgery-An Updated Systematic Review and Meta-Analysis

Background: Levosimendan, a calcium sensitizer, enhances the myocardial function by generating more energy-efficient myocardial contractility than that achieved through adrenergic stimulation with catecholamines. We conducted this meta-analysis to primarily investigate the effects of levosimendan on all-cause mortality in pediatric patients undergoing cardiac surgery under cardiopulmonary bypass. Methods: The databases of Pubmed, Embase, and Cochrane Library were searched till 21st March 2020. The eligible criteria were participants with age<18 year and undergoing cardiac surgery for congenital heart disease (CHD), and studies of comparison between levosimendan and placebo or other inotropes. Stata version 12.0 was used to perform statistical analyses. Results: Six randomized controlled trials (RCTs) and 1 case-control trial (CCT) including 436 patients were included. The results showed that levosimendan did not significantly decrease all-cause mortality compared with control drugs (and placebo) in children undergoing cardiac surgery (P = 0.403). Perioperative prophylactic levosimendan administration strikingly decreased the low cardiac output syndrome (LCOS) incidence (P = 0.016) but did not significantly reduce acute kidney injury (AKI) incidence (P = 0.251) and shorten mechanical ventilation and ICU stay time compared with other inotropes and placebo by analyzing the included literatures [mechanical ventilation (or intubation) time: P = 0.188; ICU stay time: P = 0.620]. Conclusions: Compared with other inotropes and placebo, perioperative prophylactic administration of levosimendan did not decrease the rates of mortality and AKI and shorten the time of mechanical ventilation (or intubation) and ICU stay but demonstrated a significant reduction in LCOS incidence after corrective surgery in pediatric patients for CHD. Due to limited number of included studies, the current data were insufficient to make the conclusions.

Pitfalls of using the risk ratio in meta-analysis

For meta-analysis of studies that report outcomes as binomial proportions, the most popular measure of effect is the odds ratio (OR), usually analyzed as log(OR). Many meta-analyses use the risk ratio (RR) and its logarithm because of its simpler interpretation. Although log(OR) and log(RR) are both unbounded, use of log(RR) must ensure that estimates are compatible with study-level event rates in the interval (0, 1). These complications pose a particular challenge for random-effects models, both in applications and in generating data for simulations. As background, we review the conventional random-effects model and then binomial generalized linear mixed models (GLMMs) with the logit link function, which do not have these complications. We then focus on log-binomial models and explore implications of using them; theoretical calculations and simulation show evidence of biases. The main competitors to the binomial GLMMs use the beta-binomial (BB) distribution, either in BB regression or by maximizing a BB likelihood; a simulation produces mixed results. Two examples and an examination of Cochrane meta-analyses that used RR suggest bias in the results from the conventional inverse-variance-weighted approach. Finally, we comment on other measures of effect that have range restrictions, including risk difference, and outline further research.