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Objective: The purpose of this study was to utilize fragility analysis to assess the robustness of randomized controlled trials (RCTs) evaluating the management of articular cartilage defects of the knee. We hypothesize that the cartilage restorative literature will be fragile with the reversal of only a few outcome events required to change statistical significance., Design: RCTs from 11 orthopedic journals indexed on PubMed from 2000 to 2020 reporting dichotomous outcome measures relating to the management of articular cartilage defects of the knee were included. The Fragility Index (FI) for each outcome was calculated through the iterative reversal of a single outcome event until significance was reversed. The Fragility Quotient (FQ) was calculated by dividing each FI by study sample size. Additional statistical analysis was performed to provide median FI and FQ across subgroups., Results: Nineteen RCTs containing 60 dichotomous outcomes were included for analysis. The FI and FQ of all outcomes was 4 (IQR 2-7) and 0.067 (IQR 0.034-0.096), respectively. The average number of patients lost to follow-up (LTF) was 3.9 patients with 15.8% of the included studies reporting LTF greater than or equal to 4, the FI of all included outcomes., Conclusions: The orthopedic literature evaluating articular cartilage defects of the knee is fragile as the reversal of relatively few outcome events may alter the significance of statistical findings. We therefore recommend comprehensive fragility analysis and triple reporting of the P value, FI, and FQ to aid in the interpretation and contextualization of clinical findings reported in the cartilage restoration literature.

Objective: The fragility index is a clinically interpretable metric increasingly used to interpret the robustness of clinical trials results that is generally not incorporated in sample size calculation and applied post-hoc. In this manuscript, we propose to base the sample size calculation on the fragility index in a way that supplements the classical prefixed alpha and power cutoffs and we provide a dedicated R software package for the design and analysis tools., Study Design and Setting: This approach follows from a novel hypothesis testing framework that is based on the fragility index and builds on the classical testing approach. As case studies, we re-analyse the design of two important trials in cardiovascular medicine, the FAME and FAMOUS-NSTEMI trials., Results: The analyses show that approach returns sample sizes which results in a higher power for the P value based test and most importantly a lower and context dependent Type I error rate for the fragility index based test compared to standard tests., Conclusion: Our method allows clinicians to control for the fragility index during clinical trial design., (Copyright © 2021. Published by Elsevier Inc.)

Background: The Fragility Index (FI) is a method for evaluating the robustness of statistically significant findings from randomized controlled trials (RCTs) beyond the P value in trials with dichotomous outcomes. The FI is defined as the number of patients in one arm of a trial that would have to have a different outcome to change the results of the trial from statistically significant to nonsignificant. This review assessed the FI in arthroplasty RCTs.Methods: A systematic search was conducted in MEDLINE, Embase, and Web of Science for RCTs related to primary total joint arthroplasty (TJA) from 2010 to 2020. Trials with a statistically significant dichotomous primary outcome were included. The FI was calculated using Fisher's exact test to determine how many events would need to be reversed to change a study from statistically significant to nonsignificant.Results: A total of 34 RCTs were included. The median sample size was 103 patients (range 24-791). The median FI was 1 (range 0-45), meaning that reversing the outcome of just one patient in either treatment group of each trial would change it from a significant to a nonsignificant result.Conclusion: Hip and knee arthroplasty RCTs with statistically significant dichotomous outcomes in TJA are fragile. The median FI in TJA is lower than the FI in any of the other previously reported orthopedic subspecialties. Fragility is another reason to be cautious when conducting or interpreting small trials, and to continue to strive toward large trials to answer important questions in TJA.Level Of Evidence: Level I. [ABSTRACT FROM AUTHOR]

Viscosity is one of the most important properties of disordered matter. The temperature-dependence of viscosity is used to adjust process variables for glass-making, from melting to annealing. The aim of this work was to develop a physics-informed machine learning model capable of predicting the temperature-dependence of the viscosity of oxide liquids, inspired by the recent Neural Network (NN) reported by Tandia and co-authors. Instead of predicting the viscosity itself, the NN predicts the parameters of the MYEGA viscosity equation: the liquid's fragility index, the glass transition temperature, and the asymptotic viscosity. With these parameters, viscosity can be computed at any temperature of interest, with the advantage of good extrapolation capabilities inherent to the MYEGA equation. The viscosity dataset was collected from the SciGlass database; only oxide liquids with enough data points in the "high" and "low" viscosity regions were selected, resulting in a final dataset with 17,584 data points containing 847 different liquids. About 600 features were engineered from the liquids' chemical composition and 35 of these features were selected using a feature selection protocol. The hyperparameter (HP) tuning of the NN was performed in a set of experiments using both random search and Bayesian strategies, where a total of 700 HP sets were tested. The most successful HP sets were further tested using 10-fold cross-validation, and the one with the lowest average validation loss was selected as the best set. The final trained NN was tested with a test dataset of 85 liquids with different compositions than those used for training and validating the NN. The coefficient of determination (R 2) for the test dataset's prediction was 0.97. This work introduces three advantages: the model can predict viscosity as well as the liquids' glass transition temperature and fragility index; the model is designed and trained with a focus on extrapolation; finally, the model is available as free and open-source software licensed under the GPL3. [ABSTRACT FROM AUTHOR]

Background: The Fragility Indexquantifies the reliability of positive trials by estimating the number of events, which would change statistically significant results to non-significant results.Methods: We identified randomized trials supporting drug approvals by the US FDA between 2009 and 2019 in lung, breast, prostate, and colon cancers and in melanoma. We reconstructed survival tablesand calculated the number of events, which would result in a non-significant result for the primary endpoint. The FI was then compared to the number of patients in each trial who withdrew consent or were lost to follow-up. Regression analyses were used to explore associations between RCT characteristics and FI and trials in which FI was lower or equal to number of participants who withdrew consent or were lost to follow-up.Results: Among 81 RCTs, the median FI was 28. The median number of patients who withdrew consent or were lost to follow up was 27. FI was equal or lower than the number of patients who withdrew consent or were lost to follow-up in 47 trials (58%). There was a modest increase in FI over time (p = 0.02). Trials with overall survival as the primary endpoint (p = 0.006) and those in the palliative setting (p < 0.001) had lower FI. There was no association with trial sample size or duration of follow-up.Findings: Statistical significance of RCTs in common solid tumours can be reversed often with a small number of additional events. Post-approval RCTs or real-world data analyses should be performed to ensure results of registration trials are robust. [ABSTRACT FROM AUTHOR]

In this study, the molecular mobility of acetylated starch (AS) with degree of substitution (DS) 1.5 and 3, representing partial and complete substitution of hydroxyl groups with acetyl groups, was investigated. The glass transition region and the onset of long-range cooperative molecular motions were examined using temperature-modulated-DSC (TMDSC). A potential analogy between the relaxation time of hole formation and the α -relaxation time was observed. The deviation in the temperature dependence of the α -relaxation time from the Arrhenius relationship, obtained with the fragility index, revealed differences according to DS. The cooperative rearranging region (CRR) characteristics differed according to DS and estimation method. Smaller size of the CRR for AS with DS 3 compared to AS with DS 1.5 suggest disruption of hydrogen bonds at high acetylation level. TMDSC experimental data at moderate temperature and predictions and SS-NMR results at ambient temperature, indicate different mobility of AS according to DS and temperature conditions. Image 1 • Acetylation of starch alters its chain dynamics. • Relaxation time of hole formation can represent α-relaxation time. • Crystallinity and hydrogen bonding control chain dynamics in acetylated starch. [ABSTRACT FROM AUTHOR]

Background: The Fragility Index (FI) and Reverse Fragility Index are powerful tools to supplement the P value in evaluation of randomized clinical trial (RCT) outcomes. These metrics are defined as the number of patients needed to change the significance level of an outcome. The purpose of this study was to calculate these metrics for published RCTs in total joint arthroplasty (TJA)., Methods: We performed a systematic review of RCTs in TJA over the last decade. For each study, we calculated the FI (for statistically significant outcomes) or Reverse Fragility Index (for nonstatistically significant outcomes) for all dichotomous, categorical outcomes. We also used the Pearson correlation coefficient to evaluate publication-level variables., Results: We included 104 studies with 473 outcomes; 92 were significant, and 381 were nonstatistically significant. The median FI was 6 overall and 4 and 7 for significant and nonsignificant outcomes, respectively. There was a positive correlation between FI and sample size (R = 0.14, P  = .002) and between FI and P values (R = 0.197, P  = .000012)., Conclusions: This study is the largest evaluation of FI in orthopedics literature to date. We found a median FI that was comparable to or higher than FIs calculated in other orthopedic subspecialties. Although the mean and median FIs were greater than the 2 recommended by the American Academy of Orthopaedic Surgeons Clinical Practice Guidelines to demonstrate strong evidence, a large percentage of studies have an FI < 2. This suggests that the TJA literature is on par or slightly better than other subspecialties, but improvements must be made., Level of Evidence: Level I; Systematic Review., (© 2021 Published by Elsevier Inc. on behalf of The American Association of Hip and Knee Surgeons.)

Objective: Clinicians' overdependence on p-values to determine significance in clinical trials is common yet potentially misleading. The Fragility Index (FI) describes how robust a significant result is by determining the number of events the statistical significance hinges on. However, this concept cannot be applied to nondichotomous variables. We describe a method to calculate a Continuous Fragility Index (CFI) for continuous variables. We further provide a method to estimate CFI when original data is not available., Study Design and Setting: An iterative substitution algorithm is described to calculate CFI prospectively from data or retrospectively from summary statistics and its response to variations in the data is reported. We then apply this method to a previously published review as a proof-of-concept., Results: The CFI increases linearly with sample size, logarithmically with mean difference, and decreases exponentially with standard deviation. Forty-eight studies were included of which 30 had significant non-dichotomous outcomes. CFI and FI were uncorrelated and mean CFI was significantly higher than FI (9 vs. 2, P< 0.001)., Conclusion: Our algorithm extends fragility to continuous outcomes, expanding the applications of the fragility concept. The fragility of outcomes within a single study may vary based on variable type and should be evaluated independently., (Copyright © 2021 Elsevier Inc. All rights reserved.)

Randomized controlled trials (RCTs) are often used to inform clinical practice and it is desirable that their results be robust. A fragility index (FI), defined as the smallest number of participants in whom an outcome change from non-event to event would turn a statistically significant result to a non-significant result, can be computed to measure robustness. We sought to determine the distribution of fragility indices across various research areas and summarized the factors associated with fragility. We searched PubMed between February 2014 and May 2019 and included reviews that reported on fragility indices and the associated factors. Two investigators independently screened articles for eligibility and extracted all relevant data from each review. Fragility indices were pooled using random effects meta-analysis. Twenty-four (24) reviews met the inclusion criteria. They contained a median of 41 trials (first quartile [Q1]-third quartile [Q3]: 17–120). The overall mean FI across different fields of research was 4 (95% confidence interval [CI] 3–5), indicating a high level of fragility. Higher journal impact factor, larger sample size, bigger effect size, more outcome events, a lower p -value, and adequate allocation concealment were reported to be associated with the higher FI. The ecological correlation between median FI and median sample size (22 studies) was 0.95 (95% CI 0.58–0.99). Trials across various fields of research are frequently fragile. We also identified some factors associated with fragility. Researchers should consider strategies to enhance the robustness of studies and minimize fragility. • The fragility index measures how robust trial results are. • Larger studies with more events and lower p -values are less likely to be fragile. • Trials are frequently fragile and hinge on few events regardless of the area of research. [ABSTRACT FROM AUTHOR]

The concepts of fragility index (FI) and fragility quotient (FQ) have been previously described. PlumX metrics encompass online "footprints" of research in addition to traditional citations. Herein we explore PlumX metrics against the quality of BBD literature. To explore altmetrics against the quality of bladder and bowel dysfunction (BBD) literature. A literature search was conducted using Pubmed, Medline, Embase for BBD and related terms. A total of 54,045 abstracts were screened, followed by 693 full text reviews and data extraction from 126. Studies were included if they reported on 2 groups being compared, had dichotomous outcomes, and had significant results. The median FI score was 4 (0–500) and there were 20 studies which had a FI of 0. The FQ had a median of 0.04 (0–0.32). PlumX usage was 263 ± 540, captures were 45 ± 60 and social media attention was 2 ± 2. Overall, 42% of papers were clinical trials (RCTs). When compared to other study designs, we noted a significant difference in PlumX captures (57 ± 72 RCT vs. 35 ± 47 other; p = 0.03). RCTs had higher usage, social media engagement and citations however, the differences were not significant. H-Index had a significant correlation with FI (p = 0.036), however correlations for PlumX usage and captures, while modestly positive (0.04–0.10) for the FI and FQ, were not significant. A comparison of FI and FQ by topic can be reviewed in the Summary Table. When considering the FI and FQ robustness indicators of the BBD literature, we found similarities when compared to other studies. It was reported that overall, the hydronephrosis literature was fragile with many studies requiring only a few events to nullify significance, regardless of the study design. Similarly, in a review of pediatric vesicoureteral reflux (VUR) clinical trials, results were also fragile. When comparing fragility measures to altmetric variables we noted that despite the growing popularity of altmetrics, citation counts, and h-indices remain the traditional measures to monitor research consumption. There has been a reported correlation between manuscript citation counts, author h-index, altmetrics measures in several specialties and across many domains of research including medical sciences, arts, and the humanities, however in the present study only weak correlations were noted. The body of BBD comparative studies is fragile in keeping with other pediatric urology literature populations. Despite fragile results, RCTs generate slightly moreattention as measured by select PlumX metrics. These results suggest the need for including fragility measures in our literature, aiming to focus attention towards more robust articles. Table 1 Comparison of Fragility Index and Fragility Quotient by BBD topic. Table 1 Topic Fragility Index Fragility Quotient Nocturnal Enuresis 5 (1) 0.05 (0.06) Urinary Tract Infection 4.5 (7) 0.044 (0.08) Overactive Bladder 2 (5) 0.013 (0.03) Dysfunctional Voiding 2 (5) 0.029 (0.06) Incontinence 4 (7) 0.045 (0.06) Values in table show median and interquartile range. There were no statistically significant differences using Kruskal–Wallis (KW) test. [ABSTRACT FROM AUTHOR]

Poly(dimethylosiloxane) (PDMS) cross-linked by metal-ligand coordination has a potential functionality for electronic devices applications. In this work, the molecular dynamics of bipyridine (bpy)–PDMS-MeCl2 (Me: Mn2+, Fe2+, Ni2+, and Zn2+) are investigated by means of broadband dielectric spectroscopy and supported by differential scanning calorimetry and density functional theory calculations. The study of molecular motions covered a broad range of temperatures and frequencies and was performed for the first time for metal-ligand cross-linked PDMS. It was found that the incorporation of bpy moieties into PDMS chain prevents its crystallization. The dielectric permittivity of studied organometallic systems was elevated and almost two times higher (ε′ ~4 at 1 MHz) than in neat PDMS. BpyPDMS-MeCl2 complexes exhibit slightly higher glass transition temperature and fragility as compared to a neat PDMS. Two segmental type relaxations (α and αac) were observed in dielectric studies, and their origin was discussed in relation to the molecular structure of investigated complexes. The αac relaxation was observed for the first time in amorphous metal-ligand complexes. It originates from the lower mobility of PDMS polymer chains, which are immobilized by metal-ligand coordination centers via bipyridine moieties. [ABSTRACT FROM AUTHOR]

Thermal analysis of chalcogenide glass similar to other materials is of great importance in order to increase the knowledge about its phase transitions, thermal stability, etc. The current study reports on the thermal kinetics of melt-quenched Zn 5 Se 95 chalcogenide glass using differential thermal analysis (DTA) techniques under non-isothermal conditions. The glass-forming ability (GFA) and the relation between the glass transition and onset crystallization temperatures are found to show a linear behavior. In addition, Moynihan et al. Kissinger's, and other approaches of Johnson-Mehl-Avrami utilized to determine the activation energy of the amorphous-crystalline and glass transition. It is found that the glass transition process cannot be concluded in terms of single activation energy, and that variation with the extent of conversion was analyzed using various iso-conventional methods. Therefore, the observed change of the activation energy throughout the glass transition reveals that the transition from amorphous to the supercooled liquid phase of Zn 5 Se 95 glass is a complex process. The crystallization process at different heating rates is simulated using the Málek method, and Šesták–Berggren SB(M,N) model, in which the SB model show fairly good matching with the experimental DTA data. Moreover; the fragility index is a measure of the GFA of Zn 5 Se 95 chalcogenide glass, which has been estimated using the glass transitions and activation energy values. We have found that the fragility index of Zn 5 Se 95 glass values in between ∼13 and 30, depending on the heating rate, revealing that the synthesized glass is a strong liquid with excellent GFA. • Thermal kinetics ofZn 5 Se 95 using DTA under non-isothermal conditions is studied. • The glass transition process cannot be concluded in terms of single activation energy. • The calculated DTA curves by SB(M,N) model show fairly good consistency with the experimental DTA curves.. • The fragility index of Zn 5 Se 95 has been calculated using the glass transitions and activation energy values.. [ABSTRACT FROM AUTHOR]

Background: Results of randomized clinical trials may not be entirely applicable to clinical practice. The present manuscript aims to explore the pragmatism and robustness of the evidence that supports the European Society for Medical Oncology (ESMO) follicular lymphoma (FL) guidelines. Methods & design: Analysis of all trials used to support positive, therapeutic, oncological recommendations in the 2020 ESMO FL guidelines. Predefined data points were extracted from each trial. Pragmatism was assessed by means of the PRECIS-2 tool, the difference in overall survival in the interventions compared and the source of funding. Robustness was assessed by means of the fragility index and the p value. Results: 28 trials were included. The full protocol or a protocol summary was provided for 12 (43%). Based on the PRECIS-2 domains, trials were considered pragmatic in organization, analysis and flexibility and explanatory in eligibility. Robustness was high, with 4/24 (17%) trials with p values between 0.05 and 0.005 and a median fragility index of 18. Conclusions: Results of trials to support ESMO recommendations in FL were robust. Pragmatism was high in some domains but modest to low in others and the pattern was similar across trials. Transparency in the publication of trial protocols was suboptimal.

Background and Objectives: The network meta-analysis (NMA) is frequently used to synthesize evidence for multiple treatment comparisons, but its complexity may affect the robustness (or fragility) of the results. The fragility index (FI) is recently proposed to assess the fragility of the results from clinical studies and from pairwise meta-analyses. We extend the FI to NMAs with binary outcomes., Methods: We define the FI for each treatment comparison in NMAs. It quantifies the minimal number of events necessary to be modified for altering the comparison's statistical significance. We introduce an algorithm to derive the FI and visualizations of the process. A worked example of smoking cessation data is used to illustrate the proposed methods., Results: Some treatment comparisons had small FIs; their significance (or nonsignificance) could be altered by modifying a few events' status. They were related to various factors, such as P-values, event counts, and sample sizes, in the original NMA. After modifying event status, treatment ranking measures were also changed to different extents., Conclusion: Many NMAs include insufficiently compared treatments, small event counts, or small sample sizes; their results are potentially fragile. The FI offers a useful tool to evaluate treatment comparisons' robustness and reliability., (Copyright © 2020 Elsevier Inc. All rights reserved.)

Background: Efficacy of an intervention is commonly evaluated using P values, in addition to effect size measures such as absolute risk reduction, relative risk reduction, and numbers needed to treat. However, these measures are not always intuitive to clinicians. The fragility index (FI) is a more intuitive number that can facilitate interpretation but can only be used with binary outcomes. FI is the minimum number of patients who must be moved from the nonevent group to the event group to turn a significant result nonsignificant. In this retrospective analysis, we assessed the robustness of cardiovascular randomized controlled trials (RCTs), which report a positive (statistically significant) primary outcome by using the FI.Methods and Results: We searched Medline from 2007 to 2017 to identify cardiovascular RCTs published in 6 high impact journals (The Lancet, New England Journal of Medicine, Journal of the American Medical Association, Circulation, Journal of the American College of Cardiology and European Heart Journal). Only RCTs with sample sizes >500 and a 2-by-2 factorial design or dichotomous primary outcomes were selected. FI was calculated using a defined approach. Among the cohort of 123 RCTs that met inclusion criteria, median FI was 13 (interquartile range, 5-26). In 28 trials (22.8%), FI ranged between 1 and 4. In 37 trials (30.1%), number of patients lost to follow-up was higher than the FI. Pharmaceutical interventions had higher FI compared with other interventions, FI=19 (7-52; P=0.002). Median FI varied according to subspecialty (electrophysiology=2; heart failure=11; interventional cardiology=8; P=0.020) and multiregional RCTs had higher FI=22 (12-53.25; P=0.023). FI did not differ based on risk of bias indicators, funding, or publication year.Conclusions: Considerable variations in FI were observed among cardiovascular trials, suggesting the need for careful interpretation of results, particularly when number of patients lost to follow-up exceeds FI. [ABSTRACT FROM AUTHOR]

The reduced glass transition temperature (Trg) and fragility index (m) are both used to predict the critical cooling rate (Rc). When either Trg or m is individually used to predict log10(Rc), a large deviation occurrs in the prediction of log10(Rc) because both of the corresponding correlations have low coefficients of determination (R2). The R2 value increases from either 0.33 (by using only Trg) or 0.68 (by using only m) to 0.91 by using both Trg and m. Therefore, the glass‐forming ability (GFA) is estimated more accurately when Trg and m are both applied to predict log10(Rc) through a binary linear regression analysis. [ABSTRACT FROM AUTHOR]

Randomized controlled trials (RCTs) are the gold standard for comparing clinical interventions. Statistical significance as reported via a P value has been used to determine if a difference between clinical interventions exists in an RCT. However, P values do not clearly convey information about the robustness of a study's conclusions. An emerging metric, called the fragility index (the number of subjects who would need to change outcome category to raise the P value above the.05 threshold), is an indirect measure of how likely a repeat of the trial would reach the same conclusions. This study addressed the fragility of RCTs using dichotomous outcomes in hand surgery. Using systematic searching of the MEDLINE database, we identified hand surgery RCTs published in 11 high-impact journals published in the last decade (2007–2017). Studies were identified that involved 2 parallel arms, allocated patients to treatment and control in a 1:1 ratio, and reported statistical significance for a dichotomous variable. The fragility index was calculated using Fisher's exact test, using previously published methods. Five hand surgery RCTs were identified for inclusion reporting a range of fragility indices from 0 to 26. Two of the trials (40%) had a fragility index of 2 or less. Two of the trials (40%) reported that the number of patients lost to follow-up exceeded the fragility index, meaning that results of the patients lost to follow-up could theoretically completely reverse the study conclusions. The range of fragility indices reported in the recent hand surgery literature is consistent with previous reporting within orthopedic surgery. The fragility index is a useful metric to analyze the robustness of the study conclusions that should complement other methods of critical evaluation including the P value or effect sizes. Our results emphasize the need for future efforts to strengthen the robustness of RCT conclusions. [ABSTRACT FROM AUTHOR]

The author reflects on the noted changes in clinical practice due to the changes in the study, analysis of data, dissemination and understanding of results. Topics covered include the use of complicated statistical tests in providing research results, the highlights of the article "The Fragility Index in Multicenter Randomized Controlled Critical Care Trials" by E. E. Ridgeon and others published in the journal "Critical Care Medicine," and the advantages of using Fragility Index in research.

Objectives: Meta-analyses inform clinical practice by summarizing treatment effect estimates based on results from several trials. However, the statistical significance of a meta-analysis (i.e., whether the pooled treatment effect is statistically significant or not) may rely on the outcome of only a few patients from specific trials in the meta-analysis. We aimed to evaluate the extent to which the statistical significance of meta-analyses can be changed (from statistically significant to nonsignificant, or vice versa) after modifying the event status of patients in specific arms of specific trials., Methods: We conducted a cross-sectional analysis of meta-analyses of trials with a binary outcome from Cochrane Systematic Reviews. We defined the fragility index of meta-analyses as the minimum number of patients from one or more trials included in the meta-analysis for whom an event-status modification (i.e., changing an event to nonevent or a nonevent to event) would change the statistical significance of the pooled treatment effect. For statistically significant and nonsignificant meta-analyses, we evaluated the fragility index, the ratio between the fragility index and the total number of participants included in the trials, and the ratio between the fragility index and the total number of events., Results: Our sample comprised 906 meta-analyses: 400 and 506 had statistically significant and nonsignificant pooled treatment effects, respectively. For statistically significant meta-analyses, the median fragility index was 12 (Q1-Q3: 4-33); for 29% the fragility index was 5 or less. Overall, 43% and 9% meta-analyses would have become nonsignificant if the event status was modified for less than 1% of the total participants in one or several specific trials, and for less than 1% of the total number of events, respectively. These proportions were similar for statistically nonsignificant meta-analyses. Overall, the statistical significance of 33% of all meta-analyses depended on the event status of five or fewer participants from one or more specific trials., Conclusion: The statistical significance of meta-analyses often depends on the outcome of a few patients. The fragility index of meta-analyses may help in interpreting the conclusions of meta-analyses., (Copyright © 2019 Elsevier Inc. All rights reserved.)