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Multivariate meta-analysis is becoming increasingly popular and official routines or self-programmed functions have been included in many statistical software. In this article, we review the statistical methods and the related software for multivariate meta-analysis. Emphasis is placed on Bayesian methods using Markov chain Monte Carlo, and codes in WinBUGS are provided. The various model-fitting options are illustrated in two examples and specific guidance is provided on how to run a multivariate meta-analysis using various software packages.

The question of which antipsychotic drug should be preferred for the treatment of schizophrenia is controversial, and conventional pairwise meta-analyses cannot provide a hierarchy based on the randomised evidence. We aimed to integrate the available evidence to create hierarchies of the comparative efficacy, risk of all-cause discontinuation, and major side-effects of antipsychotic drugs. We did a Bayesian-framework, multiple-treatments meta-analysis (which uses both direct and indirect comparisons) of randomised controlled trials to compare 15 antipsychotic drugs and placebo in the acute treatment of schizophrenia. We searched the Cochrane Schizophrenia Group's specialised register, Medline, Embase, the Cochrane Central Register of Controlled Trials, and ClinicalTrials.gov for reports published up to Sept 1, 2012. Search results were supplemented by reports from the US Food and Drug Administration website and by data requested from pharmaceutical companies. Blinded, randomised controlled trials of patients with schizophrenia or related disorders were eligible. We excluded trials done in patients with predominant negative symptoms, concomitant medical illness, or treatment resistance, and those done in stable patients. Data for seven outcomes were independently extracted by two reviewers. The primary outcome was efficacy, as measured by mean overall change in symptoms. We also examined all-cause discontinuation, weight gain, extrapyramidal side-effects, prolactin increase, QTc prolongation, and sedation. We identified 212 suitable trials, with data for 43 049 participants. All drugs were significantly more effective than placebo. The standardised mean differences with 95% credible intervals were: clozapine 0·88, 0·73–1·03; amisulpride 0·66, 0·53–0·78; olanzapine 0·59, 0·53–0·65; risperidone 0·56, 0·50–0·63; paliperidone 0·50, 0·39–0·60; zotepine 0·49, 0·31–0·66; haloperidol 0·45, 0·39–0·51; quetiapine 0·44, 0·35–0·52; aripiprazole 0·43, 0·34–0·52; sertindole 0·39, 0·26–0·52; ziprasidone 0·39, 0·30–0·49; chlorpromazine 0·38, 0·23–0·54; asenapine 0·38, 0·25–0·51; lurasidone 0·33, 0·21–0·45; and iloperidone 0·33, 0·22–0·43. Odds ratios compared with placebo for all-cause discontinuation ranged from 0·43 for the best drug (amisulpride) to 0·80 for the worst drug (haloperidol); for extrapyramidal side-effects 0·30 (clozapine) to 4·76 (haloperidol); and for sedation 1·42 (amisulpride) to 8·82 (clozapine). Standardised mean differences compared with placebo for weight gain varied from −0·09 for the best drug (haloperidol) to −0·74 for the worst drug (olanzapine), for prolactin increase 0·22 (aripiprazole) to −1·30 (paliperidone), and for QTc prolongation 0·10 (lurasidone) to −0·90 (sertindole). Efficacy outcomes did not change substantially after removal of placebo or haloperidol groups, or when dose, percentage of withdrawals, extent of blinding, pharmaceutical industry sponsorship, study duration, chronicity, and year of publication were accounted for in meta-regressions and sensitivity analyses. Antipsychotics differed substantially in side-effects, and small but robust differences were seen in efficacy. Our findings challenge the straightforward classification of antipsychotics into first-generation and second-generation groupings. Rather, hierarchies in the different domains should help clinicians to adapt the choice of antipsychotic drug to the needs of individual patients. These findings should be considered by mental health policy makers and in the revision of clinical practice guidelines. None.

Network meta-analysis synthesizes direct and indirect evidence in a network of trials that compare multiple interventions and has the potential to rank the competing treatments according to the studied outcome. Despite its usefulness network meta-analysis is often criticized for its complexity and for being accessible only to researchers with strong statistical and computational skills. The evaluation of the underlying model assumptions, the statistical technicalities and presentation of the results in a concise and understandable way are all challenging aspects in the network meta-analysis methodology. In this paper we aim to make the methodology accessible to non-statisticians by presenting and explaining a series of graphical tools via worked examples. To this end, we provide a set of STATA routines that can be easily employed to present the evidence base, evaluate the assumptions, fit the network meta-analysis model and interpret its results.

Selection models Selection models focus on the selection process, that is, the mechanism by which trials are selected for publication. 1 Using selection models, researchers can estimate the likely impact the missing studies would have, had they been included in the meta-analysis. In meta-analysis, selection models condition the observed effect size in each study to its propensity for publication and they estimate the unconditional summary that pertains to all studies that have been carried out, either published or unpublished.

Percutaneous coronary intervention (PCI) with drug-eluting stents is the standard of care for treatment of native coronary artery stenoses, but optimum treatment strategies for bare metal stent and drug-eluting stent in-stent restenosis (ISR) have not been established. We aimed to compare and rank percutaneous treatment strategies for ISR. We did a network meta-analysis to synthesise both direct and indirect evidence from relevant trials. We searched PubMed, the Cochrane Library Central Register of Controlled Trials, and Embase for randomised controlled trials published up to Oct 31, 2014, of different PCI strategies for treatment of any type of coronary ISR. The primary outcome was percent diameter stenosis at angiographic follow-up. This study is registered with PROSPERO, number CRD42014014191. We deemed 27 trials eligible, including 5923 patients, with follow-up ranging from 6 months to 60 months after the index intervention. Angiographic follow-up was available for 4975 (84%) of 5923 patients 6–12 months after the intervention. PCI with everolimus-eluting stents was the most effective treatment for percent diameter stenosis, with a difference of −9·0% (95% CI −15·8 to −2·2) versus drug-coated balloons (DCB), −9·4% (–17·4 to −1·4) versus sirolimus-eluting stents, −10·2% (–18·4 to −2·0) versus paclitaxel-eluting stents, −19·2% (–28·2 to −10·4) versus vascular brachytherapy, −23·4% (–36·2 to −10·8) versus bare metal stents, −24·2% (–32·2 to −16·4) versus balloon angioplasty, and −31·8% (–44·8 to −18·6) versus rotablation. DCB were ranked as the second most effective treatment, but without significant differences from sirolimus-eluting (–0·2% [95% CI −6·2 to 5·6]) or paclitaxel-eluting (–1·2% [–6·4 to 4·2]) stents. These findings suggest that two strategies should be considered for treatment of any type of coronary ISR: PCI with everolimus-eluting stents because of the best angiographic and clinical outcomes, and DCB because of its ability to provide favourable results without adding a new stent layer. None.

The comparative efficacy and safety of pharmacological agents to lower blood pressure in adults with diabetes and kidney disease remains controversial. We aimed to investigate the benefits and harms of blood pressure-lowering drugs in this population of patients. We did a network meta-analysis of randomised trials from around the world comparing blood pressure-lowering agents in adults with diabetic kidney disease. Electronic databases (the Cochrane Collaboration, Medline, and Embase) were searched systematically up to January, 2014, for trials in adults with diabetes and kidney disease comparing orally administered blood pressure-lowering drugs. Primary outcomes were all-cause mortality and end-stage kidney disease. We also assessed secondary safety and cardiovascular outcomes. We did random-effects network meta-analysis to obtain estimates for primary and secondary outcomes and we presented these estimates as odds ratios or standardised mean differences with 95% CIs. We ranked the comparative effects of all drugs against placebo with surface under the cumulative ranking (SUCRA) probabilities. 157 studies comprising 43 256 participants, mostly with type 2 diabetes and chronic kidney disease, were included in the network meta-analysis. No drug regimen was more effective than placebo for reducing all-cause mortality. However, compared with placebo, end-stage renal disease was significantly less likely after dual treatment with an angiotensin-receptor blocker (ARB) and an angiotensin-converting-enzyme (ACE) inhibitor (odds ratio 0·62, 95% CI 0·43–0·90) and after ARB monotherapy (0·77, 0·65–0·92). No regimen significantly increased hyperkalaemia or acute kidney injury, although combined ACE inhibitor and ARB treatment had the lowest rank among all interventions because of borderline increases in estimated risks of these harms (odds ratio 2·69, 95% CI 0·97–7·47 for hyperkalaemia; 2·69, 0·98–7·38 for acute kidney injury). No blood pressure-lowering strategy prolonged survival in adults with diabetes and kidney disease. ACE inhibitors and ARBs, alone or in combination, were the most effective strategies against end-stage kidney disease. Any benefits of combined ACE inhibitor and ARB treatment need to be balanced against potential harms of hyperkalaemia and acute kidney injury. Canterbury Medical Research Foundation, Italian Medicines Agency.

Many healthcare interventions are complex, consisting of multiple, possibly interacting, components. Several methodological articles addressing complex interventions in the meta-analytical context have been published. We hereby provide an overview of methods used to evaluate the effects of complex interventions with meta-analytical models. We summarized the methodology, highlighted new developments, and described the benefits, drawbacks, and potential challenges of each identified method. We expect meta-analytical methods focusing on components of several multicomponent interventions to become increasingly popular due to recently developed, easy-to-use, software tools that can be used to conduct the relevant analyses. The different meta-analytical methods are illustrated through two examples comparing psychotherapies for panic disorder.

Objective Systematic reviewers often need to choose between two statistical methods when synthesising evidence in a meta-analysis: the fixed effect and the random effects models. The two approaches entail different assumptions about the treatment effect in the included studies. The aim of this paper was to explain the assumptions underlying each model and their implications in the interpretation of summary results. Methods We discussed the key assumptions underlying the two methods and the subsequent implications on interpreting results. We used two illustrative examples from a published meta-analysis and highlighted differences in results. Results The two meta-analytic approaches may yield similar or contradicting results. Even if results between the two models are similar, summary estimates should be interpreted in a different way. Conclusions Selection between fixed or random effects should be based on the clinical relevance of the assumptions that characterise each approach. Researchers should consider the implications of the analysis model in the interpretation of the findings and use prediction intervals in the random effects meta-analysis.

Background There is still no approved medication for the core symptoms of autism spectrum disorder (ASD). This network meta-analysis investigated pharmacological and dietary-supplement treatments for ASD. Methods We searched for randomized-controlled-trials (RCTs) with a minimum duration of seven days in ClinicalTrials.gov, EMBASE, MEDLINE, PsycINFO, WHO-ICTRP (from inception up to July 8, 2018), CENTRAL and PubMed (up to November 3, 2021). The co-primary outcomes were core symptoms (social-communication difficulties-SCD, repetitive behaviors-RB, overall core symptoms-OCS) measured by validated scales and standardized-mean-differences (SMDs). Associated symptoms, e.g., irritability/aggression and attention-deficit/hyperactivity disorder (ADHD) symptoms, dropouts and important side-effects, were investigated as secondary outcomes. Studies in children/adolescents and adults were analyzed separately in random-effects pairwise and network meta-analyses. Results We analyzed data for 41 drugs and 17 dietary-supplements, from 125 RCTs ( n  = 7450 participants) in children/adolescents and 18 RCTs ( n  = 1104) in adults. The following medications could improve at least one core symptom domain in comparison with placebo: aripiprazole ( k  = 6 studies in analysis, SCD: SMD = 0.27 95% CI [0.09, 0.44], RB: 0.48 [0.26, 0.70]), atomoxetine ( k  = 3, RB:0.49 [0.18, 0.80]), bumetanide ( k  = 4, RB: 0.35 [0.09, 0.62], OCS: 0.61 [0.31, 0.91]), and risperidone ( k  = 4, SCM: 0.31 [0.06, 0.55], RB: 0.60 [0.29, 0.90]; k  = 3, OCS: 1.18 [0.75, 1.61]) in children/adolescents; fluoxetine ( k  = 1, RB: 1.20 [0.45, 1.96]), fluvoxamine ( k  = 1, RB: 1.04 [0.27, 1.81]), oxytocin ( k  = 6, RB:0.41 [0.16, 0.66]) and risperidone ( k  = 1, RB: 0.97 [0.21,1.74]) in adults. There were some indications of improvement by carnosine, haloperidol, folinic acid, guanfacine, omega-3-fatty-acids, probiotics, sulforaphane, tideglusib and valproate, yet imprecise and not robust. Confidence in these estimates was very low or low, except moderate for oxytocin. Medications differed substantially in improving associated symptoms, and in their side-effect profiles. Limitations Most of the studies were inadequately powered (sample sizes of 20–80 participants), with short duration (8–13 weeks), and about a third focused on associated symptoms. Networks were mainly star-shaped, and there were indications of reporting bias. There was no optimal rating scale measuring change in core symptoms. Conclusions Some medications could improve core symptoms, although this could be likely secondary to the improvement of associated symptoms. Evidence on their efficacy and safety is preliminary; therefore, routine prescription of medications for the core symptoms cannot be recommended. Trial registration PROSPERO-ID CRD42019125317.

Background Network meta-analysis estimates all relative effects between competing treatments and can produce a treatment hierarchy from the most to the least desirable option according to a health outcome. While about half of the published network meta-analyses present such a hierarchy, it is rarely the case that it is related to a clinically relevant decision question. Methods We first define treatment hierarchy and treatment ranking in a network meta-analysis and suggest a simulation method to estimate the probability of each possible hierarchy to occur. We then propose a stepwise approach to express clinically relevant decision questions as hierarchy questions and quantify the uncertainty of the criteria that constitute them. The steps of the approach are summarized as follows: a) a question of clinical relevance is defined, b) the hierarchies that satisfy the defined question are collected and c) the frequencies of the respective hierarchies are added; the resulted sum expresses the certainty of the defined set of criteria to hold. We then show how the frequencies of all possible hierarchies relate to common ranking metrics. Results We exemplify the method and its implementation using two networks. The first is a network of four treatments for chronic obstructive pulmonary disease where the most probable hierarchy has a frequency of 28%. The second is a network of 18 antidepressants, among which Vortioxetine, Bupropion and Escitalopram occupy the first three ranks with frequency 19%. Conclusions The developed method offers a generalised approach of producing treatment hierarchies in network meta-analysis, which moves towards attaching treatment ranking to a clear decision question, relevant to all or a subset of competing treatments.