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PurposeOveractive bladder (OAB) syndrome significantly impairs quality of life, often necessitating pharmacological interventions with associated risks. The fragility of OAB trial outcomes, as measured by the fragility index (FI: smallest number of event changes to reverse statistical significance) and quotient (FQ: FI divided by total sample size expressed as a percentage), is critical yet unstudied.Materials and methodsWe conducted a systematic search for randomized controlled trials on OAB medications published between January 2000 and August 2023. Inclusion criteria were trials with two parallel arms reporting binary outcomes related to OAB medications. We extracted trial details, outcomes, and statistical tests employed. We calculated FI and FQ, analyzing associations with trial characteristics through linear regression.ResultsWe included 57 trials with a median sample size of 211 participants and a 12% median lost to follow-up. Most studies investigated anticholinergics (37/57, 65%). The median FI/FQ was 5/3.5%. Larger trials were less fragile (median FI 8; FQ 1.0%) compared to medium (FI: 4; FQ 2.5%) and small trials (FI: 4; FQ 8.3%). Double-blinded studies exhibited higher FQs (median 2.9%) than unblinded trials (6.7%). Primary and secondary outcomes had higher FIs (median 5 and 6, respectively) than adverse events (FI: 4). Each increase in 10 participants was associated with a +0.19 increase in FI (p

Crude oil is a complex system with unique physical and chemical properties. One of the most important physical properties of crude oil is viscosity. This paper demonstrates that the temperature dependence of crude oil viscosity can be described using the universal scaling model for viscosity over a wide temperature range. For the first time, a correlation has been established between the API gravity of crude oil and the fragility index, which is a measure of viscosity change with temperature in the glass transition region. It has been demonstrated that this correlation can be replicated by a linear function: the higher the API gravity the lower the oil density and the poorer the oil forms an amorphous state. The temperature range has been determined, at which molecular cooperation in crude oil can occur. The obtained results allow us to estimate/predict the viscosity of any crude oil at low temperatures, correlated with the glass transition temperature, based on high temperature experimental measurements near the melting point. [ABSTRACT FROM AUTHOR]

Background: Esophageal cancer remains a significant global health challenge. Several treatment modalities were explored in randomized controlled trials (RCTs) in recent decades. This study evaluates the robustness of RCTs focusing on esophageal cancer treatment using the fragility index (FI) and reverse fragility index (RFI). Methods: A systematic review of RCTs studying different treatment modalities for esophageal cancer from 2000 to 2023 was conducted. The FI and RFI were utilized to gauge the robustness of statistically significant and non-significant outcomes, respectively. The FI represents the minimal number of patient outcomes that would need to alter to overturn a trial's statistical significance, while RFI indicates the minimal changes required to achieve significance in non-significant results. Results: Out of 4028 studies retrieved, 21 RCTs were included for final analysis. The studies spanned 2001 to 2023 with a mean followup of 66 months (range, 29–108 months) and median number of patients of 194 (range, 45–802). The most common treatment modalities examined in these studies were neoadjuvant chemoradiotherapy (n = 7, 33.3%), neoadjuvant chemotherapy (n = 4, 19.0%), and neoadjuvant immunotherapy (n = 2, 9.5%). Only 5 studies (23.8%) had a statistically significant primary outcome result with a median FI of 6 (IQR, 2.5–8.5). Non-significant primary outcomes were seen in 16 studies (76.2%) with a median RFI of 4 (IQR 1–11) and lost to followup of 0 (IQR 0–4). In the study with the highest FI (10), the FI was lower than the number of patients lost to followup (13). Conclusion: Our findings demonstrate that most RCTs on esophageal cancer treatments did not report significant primary outcomes. The few studies that reported significant results had a low fragility index, suggesting a vulnerability in their findings. [ABSTRACT FROM AUTHOR]

ABSTRACT The results of randomized clinical trials (RCTs) are frequently assessed with the fragility index (FI). Although the information provided by FI may supplement the p value, this indicator presents intrinsic weaknesses and shortcomings. In this article, we establish an analysis of fragility within a broader framework so that it can reliably complement the information provided by the p value. This perspective is named the analysis of strength. We first propose a new strength index (SI), which can be adopted in normal distribution settings. This measure can be obtained for both significance and nonsignificance and is straightforward to calculate, thus presenting compelling advantages over FI, starting from the presence of a threshold. The case of time‐to‐event outcomes is also addressed. Then, beyond the p value, we develop the analysis of strength using likelihood ratios from Royall's statistical evidence viewpoint. A new R package is provided for performing strength calculations, and a simulation study is conducted to explore the behavior of SI and the likelihood‐based indicator empirically across different settings. The newly proposed analysis of strength is applied in the assessment of the results of three recent trials involving the treatment of COVID‐19. [ABSTRACT FROM AUTHOR]

Network glasses composed of chalcogenide and modified oxides display three topological phases: the flexible, intermediate, and stressed-rigid. Modulated-DSC experiments, Raman scattering, and molar volume measurements along with topological constraint theory have shown that glass compositions in the flexible and stressed-rigid phases display glass transitions that age with time. The change of the enthalpy of relaxation (ΔHnr) at the glass transition temperature (Tg) steadily evolves with waiting time which can be traced to the presence of Open Degrees of Freedom (ODF). In the isostatically constrained intermediate phase (IP), glasses possess an enthalpy of relaxation which is substantially reduced in aging due to a lack of ODF. IP glasses are composed of self-organised Isostatically Rigid Local Structures (ISRLSs) which have no ODF. The melt fragility index (m) across the three topological phases displays a Gaussian-like global minimum of m = 15 near the IP centre composition, illustrating a super-strong melt behaviour leading to the realisation of the ideal Phillips glass condition where glass forming tendency is globally optimised as demonstrated in the present work. For melt compositions away from the IP centre and into the flexible and stressed-rigid phases, the fragility index steadily increases due to the increased presence of non-ISRLSs. The non-ISRLSs admix with the ISRLSs formed near the mid IP composition, thus promoting the melt networks to relax, age, and diffuse as one goes away from IP centre composition. [ABSTRACT FROM AUTHOR]

Abstract Objective The fragility index (FI), which is the minimum number of changes in status from “event” to “non-event” resulting in a loss of statistical significance, serves as a significant supplementary indicator for clinical physicians in interpreting clinical trial results and aids in understanding the outcomes of randomized controlled trials (RCTs). In this systematic literature survey, we evaluated the FI for RCTs evaluating Chinese herbal medicine (CHM) for irritable bowel syndrome (IBS), and explored potential associations between study characteristics and the robustness of RCTs. Methods A comprehensive search was conducted in four databases in Chinese and four databases in English from their inception to January 1, 2023. RCTs encompassed 1:1 ratio into two parallel arms and reported at least one binary outcome that demonstrated statistical significance were included. FI was calculated by the iterative reduction of a target outcome event in the treatment group and concomitant subtraction of a non-target event from that group, until positive significance (defined as P

Simple Summary: In this article, the authors introduce a new metric called the modified Fragility Index (mFI) to assess the accuracy of determining the maximum tolerated dose (MTD) in early oncology clinical trials. The mFI measures how sensitive the MTD decision is to the inclusion of a few more participants in the trial. The authors analyzed three published cancer trials and found that two trials were robust to adding more participants, indicating that the MTD estimate remained stable. However, in the other trial, the MTD estimate was more fragile and could have changed with just one or two more participants. The mFI metric helps researchers make more reliable decisions about the appropriate MTD. By considering the potential impact of additional participants, researchers can improve accuracy and confidence in dose determination, leading to better treatment outcomes for patients. Objectives: The sample sizes of phase I trials are typically small; some designs may lead to inaccurate estimation of the maximum tolerated dose (MTD). The objective of this study was to propose a metric assessing whether the MTD decision is sensitive to enrolling a few additional subjects in a phase I dose-finding trial. Methods: Numerous model-based and model-assisted designs have been proposed to improve the efficiency and accuracy of finding the MTD. The Fragility Index (FI) is a widely used metric quantifying the statistical robustness of randomized controlled trials by estimating the number of events needed to change a statistically significant result to non-significant (or vice versa). We propose a modified Fragility Index (mFI), defined as the minimum number of additional participants required to potentially change the estimated MTD, to supplement existing designs identifying fragile phase I trial results. Findings: Three oncology trials were used to illustrate how to evaluate the fragility of phase I trials using mFI. The results showed that two of the trials were not sensitive to additional subjects' participation while the third trial was quite fragile to one or two additional subjects. Conclusions: The mFI can be a useful metric assessing the fragility of phase I trials and facilitating robust identification of MTD. [ABSTRACT FROM AUTHOR]

Background: Based in part on the results of randomized controlled trials (RCTs) that suggest a beneficial effect over alternative treatment options, the use of platelet-rich plasma (PRP) for the management of knee osteoarthritis (OA) is widespread and increasing. However, the extent to which these studies are vulnerable to slight variations in the outcomes of patients remains unknown. Purpose: To evaluate the statistical fragility of conclusions from RCTs that reported outcomes of patients with knee OA who were treated with PRP versus alternative nonoperative management strategies. Study Design: Systematic review and meta-analysis; Level of evidence, 2. Methods: All RCTs comparing PRP with alternative nonoperative treatment options for knee OA were identified. The fragility index (FI) and reverse FI were applied to assess the robustness of conclusions regarding the efficacy of PRP for knee OA. Meta-analyses were performed to determine the minimum number of patients from ≥1 trials included in the meta-analysis for which a modification on the event status would change the statistical significance of the pooled treatment effect. Results: In total, this analysis included outcomes from 1993 patients with a mean ± SD age of 58.0 ± 3.8 years. The mean number of events required to reverse significance of individual RCTs (FI) was 4.57 ± 5.85. Based on random-effects meta-analyses, PRP demonstrated a significantly higher rate of successful outcomes when compared with hyaluronic acid (P =.002; odds ratio [OR], 2.19; 95% CI, 1.33-3.62), as well as higher rates of patient-reported symptom relief (P =.019; OR, 1.55; 95% CI, 1.07-2.24), not requiring a reintervention after the initial injection treatment (P =.002; OR, 2.17; 95% CI, 1.33-3.53), and achieving the minimal clinically important difference (MCID) for pain improvement (P =.007; OR, 6.19; 95% CI, 1.63-23.42) when compared with all alternative nonoperative treatments. Overall, the mean number of events per meta-analysis required to change the statistical significance of the pooled treatment effect was 8.67 ± 4.50. Conclusion: Conclusions drawn from individual RCTs evaluating PRP for knee OA demonstrated slight robustness. On meta-analysis, PRP demonstrated a significant advantage over hyaluronic acid as well as improved symptom relief, lower rates of reintervention, and more frequent achievement of the MCID for pain improvement when compared with alternative nonoperative treatment options. Statistically significant pooled treatment effects evaluating PRP for knee OA are more robust than approximately half of all comparable meta-analyses in medicine and health care. Future RCTs and meta-analyses should consider reporting FIs and fragility quotients to facilitate interpretation of results in their proper context. [ABSTRACT FROM AUTHOR]

* OBJECTIVE: To determine the Fragility Index of hamstring injury risk factors, defined as the minimum number of participants who would need to change classification to make a hamstring injury risk factor statistically nonsignificant. * DESIGN: Retrospective secondary data analysis. * METHODS: Studies that investigated 1 or more risk factors for hamstring injury, and presented sufficient data to develop a 2 x 2 contingency table were included. A systematic literature search and reference screening of a recent hamstring injury systematic review were conducted to identify 78 articles. Relative risk and 95% confidence intervals were determined and then systematically recalculated by removing 1 observation from the high-risk injury count and adding it to the high-risk noninjury count. The Fragility Index for a risk factor was the number of observations required to be moved between groups until the relative risk was no longer significant. * RESULTS: The median Fragility Index of all hamstring injury risk factors was 3 (Q1-Q3 = 2-6). The Fragility Index for nonmodifiable risk factors was 3 (Q1-Q3 = 2-6) and 3 (Q1-Q3 = 2-5) for modifiable risk factors. Over 35% of all included hamstring injury risk factors had a Fragility Index of ≤2. * CONCLUSION: Most statistically significant hamstring injury risk factors are fragile associations. The interpretation of significant hamstring injury risk factors should consider a range of statistical metrics, and while the Fragility Index should never be considered in isolation, it is an intuitive measure to help assess the robustness of findings. [ABSTRACT FROM AUTHOR]

Background: Randomized controlled trials (RCTs) are the gold standard for treatment efficacy, but foot and ankle RCTs are often small or inconsistent. The Fragility Index (FI) evaluates the stability of significant findings. This study assessed the fragility of RCT outcomes for Achilles tendon pathology (ATP) interventions. Methods: This systematic review queried PubMed up to May 14, 2024, for RCTs on ATP interventions. RCTs with significant binary outcomes were included. Two reviewers assessed eligibility, extracted data, calculated FIs, and evaluated risk of bias. Frequency-weighted means were used for narrative synthesis. Results: Eleven RCTs with 4506 patients (mean cohort size: 409.64 ± 160.54) and a mean age of 36.97 ± 13.51 years (n = 4356; 96.67%) were included, covering 24 binary outcomes. The median FI across all outcomes was 3 (interquartile range 1-4; mean 3.92), indicating that changing the outcome of just a few patients could shift a study's results from statistically significant to nonsignificant. Trials having an FI ≤3 comprised 58.33%. Three outcomes (12.5%) had an FI of zero after recalculating P values using the two-sided Fisher exact test. Half of the outcomes were robust. No RCT reported FIs or adjusted significance for multiple testing. Most studies (81.82%) performed 2 or more statistical tests, with an average of 30.81 ± 41.28 P values reported per study. The overall risk of bias was low in 1 study (9.09%) and moderate in 7 (63.64%). Most studies had low risk of bias in randomization (72.73%) and missing outcome data (90.91%). Conclusion: The FI assesses the fragility of statistically significant binary results, revealing that many ATP RCTs have fragile outcomes due to small sample sizes. A median FI of 3 means that changing the outcome of 3 patients could shift a study's results from statistically significant to nonsignificant. [ABSTRACT FROM AUTHOR]

Objective: The fragility index (FI), which is the minimum number of changes in status from "event" to "non-event" resulting in a loss of statistical significance, serves as a significant supplementary indicator for clinical physicians in interpreting clinical trial results and aids in understanding the outcomes of randomized controlled trials (RCTs). In this systematic literature survey, we evaluated the FI for RCTs evaluating Chinese herbal medicine (CHM) for irritable bowel syndrome (IBS), and explored potential associations between study characteristics and the robustness of RCTs. Methods: A comprehensive search was conducted in four databases in Chinese and four databases in English from their inception to January 1, 2023. RCTs encompassed 1:1 ratio into two parallel arms and reported at least one binary outcome that demonstrated statistical significance were included. FI was calculated by the iterative reduction of a target outcome event in the treatment group and concomitant subtraction of a non-target event from that group, until positive significance (defined as P < 0.05 by Fisher's exact test) is lost. The lower the FI (minimum 1) of a trial outcome, the more fragile the positive result of the outcome was. Linear regression models were adopted to explore influence factors of the value of FI. Results: A total of 30 trials from 2 4118 potentially relevant citations were finally included. The median FI of total trials included was 1.5 (interquartile range [IQR], 1–5), and half of the trials (n = 15) had a FI equal to 1. In 12 trials (40%), the total number of participants lost to follow-up surpassed the respective FI. The study also identified that increased FI was significantly associated with no TCM syndrome differentiation for inclusion criteria of the patients, larger total sample size, low risk of bias, and larger numbers of events. Conclusions: The majority of CHM IBS RCTs with positive results were found to be fragile. Ensuring adequate sample size, scientifically rigorous study design, proper control of confounding factors, and a quality control calibration for consistency of TCM diagnostic results among clinicians should be addressed to increase the robustness of the RCTs. We recommend reporting the FI as one of the components of sensitivity analysis in future RCTs to facilitate the assessment of the fragility of trials. [ABSTRACT FROM AUTHOR]

Background: Evidence-based care relies on robust research. The fragility index (FI) is used to assess the robustness of statistically significant findings in randomized controlled trials (RCTs). While the traditional FI is limited to dichotomous outcomes, a novel tool, the continuous fragility index (CFI), allows for the assessment of the robustness of continuous outcomes. Purpose: To calculate the CFI of statistically significant continuous outcomes in RCTs evaluating interventions for managing anterior shoulder instability (ASI). Study Design: Meta-analysis; Level of evidence, 2. Methods: A search was conducted across the MEDLINE, Embase, and CENTRAL databases for RCTs assessing management strategies for ASI from inception to October 6, 2022. Studies that reported a statistically significant difference between study groups in ≥1 continuous outcome were included. The CFI was calculated and applied to all available RCTs reporting interventions for ASI. Multivariable linear regression was performed between the CFI and various study characteristics as predictors. Results: There were 27 RCTs, with a total of 1846 shoulders, included. The median sample size was 61 shoulders (IQR, 43). The median CFI across 27 RCTs was 8.2 (IQR, 17.2; 95% CI, 3.6-15.4). The median CFI was 7.9 (IQR, 21; 95% CI, 1-22) for 11 studies comparing surgical methods, 22.6 (IQR, 16; 95% CI, 8.2-30.4) for 6 studies comparing nonsurgical reduction interventions, 2.8 for 3 studies comparing immobilization methods, and 2.4 for 3 studies comparing surgical versus nonsurgical interventions. Significantly, 22 of 57 included outcomes (38.6%) from studies with completed follow-up data had a loss to follow-up exceeding their CFI. Multivariable regression demonstrated that there was a statistically significant positive correlation between a trial's sample size and the CFI of its outcomes (r = 0.23 [95% CI, 0.13-0.33]; P <.001). Conclusion: More than a third of continuous outcomes in ASI trials had a CFI less than the reported loss to follow-up. This carries the significant risk of reversing trial findings and should be considered when evaluating available RCT data. We recommend including the FI, CFI, and loss to follow-up in the abstracts of future RCTs. [ABSTRACT FROM AUTHOR]

Background: A P value of <.05 is often used to denote statistical significance; however, in many scenarios, this threshold is vulnerable to a small number of outcome reversals. This study joins a body of studies within the orthopaedic literature that evaluate the statistical fragility of existing research via metrics such as fragility index (FI) and fragility quotient (FQ). Purpose/Hypothesis: The purpose of this study was to investigate the statistical fragility of randomized controlled trials (RCTs) and comparative studies on the topic, given the resurgent interest in lateral extra-articular tenodesis (LET) to augment primary or revision anterior cruciate ligament reconstruction (ACLR). It was hypothesized that the outcomes reported in these studies would be statistically fragile. Study Design: Systematic review; Level of evidence, 4. Methods: Comparative studies and RCTs regarding LET as an adjunct procedure to ACLR published between 2000 and 2022 were analyzed. Descriptive characteristics, dichotomous outcomes, and continuous outcomes were extracted. The FI and continuous FI (CFI) were calculated by the number of event reversals to change significance; the FQ and continuous FQ (CFQ) were calculated to normalize the fragility metrics per sample size. Results: Of 455 studies screened, 29 studies were included (9 RCTs, 20 comparative); 79.3% of included studies were published after 2020. A total of 48 dichotomous and 265 continuous outcomes were analyzed. The median FI was 9.0 (IQR, 7.0-13.3), with FQ of 0.1 (IQR, 0.04-0.17); the median CFI was 7.8 (IQR, 4.2-19.6), with CFQ of 0.12 (IQR, 0.08-0.19). The FQ and CFQ for studies on LET with revision ACLR were larger (0.117 and 0.113, respectively) than those focused on primary ACLR (0.042 and 0.095, respectively). Conclusion: Studies focused on LET with primary ACLR were more fragile than those on LET with revision, which suggests that further research on the indications for LET with primary ACLR is necessary. Future orthopaedic comparative research should include fragility metrics alongside traditional P values. [ABSTRACT FROM AUTHOR]

Purpose: FDA investigational device exemption (IDE) studies are considered a gold standard of assessing safety and efficacy of novel devices through RCTs. The fragility index (FI) has emerged as a means to assess robustness of statistically significant study results and inversely, the reverse fragility index (RFI) for non-significant differences. Previous authors have defined results as fragile if loss to follow up is greater than the FI or RFI. The aim of this study was to assess the FI, RFI, and robustness of data supplied by IDE studies in spinal surgery. Methods: This was a systematic review of the literature. Inclusion criteria included randomized controlled trials with dichotomous outcome measures conducted under IDE guidelines between 2000 and 2023. FI and RFI were calculated through successively changing events to non-events until the outcome changed to non-significance or significance, respectively. The fragility quotient (FQ) and reverse fragility quotient (RFQ) were calculated by dividing the FI and RFI, respectively, by the sample size. Results: Thirty-two studies met inclusion criteria with a total of 40 unique outcome measures; 240 outcomes were analyzed. Twenty-six studies reported 96 statistically significant results. The median FI was 6 (IQR: 3-9.25), and patients lost to follow up was greater than the FI in 99.0% (95/96) of results. The average FQ was 0.027. Thirty studies reported 144 statistically insignificant results and a median RFI of 6 (IQR: 4-8). The average RFQ extrapolated was 0.021, and loss to follow up was greater than the RFI in 98.6% (142/144) of results. Conclusions: IDE studies in spine surgery are surprisingly fragile given their reputations, large sample sizes, and intent to establish safety in investigational devices. This study found a median FI and RFI of 6. The number of patients lost to follow-up was greater than FIand RFI in 98.8% (237/240) of reported outcomes. FQ and RFQ tell us that changes of two to three patients per hundred can flip the significance of reported outcomes. This is an important reminder of the limitations of RCTs. Analysis of fragility in future studies may help clarify the strength of the relationship between reported data and their conclusions. [ABSTRACT FROM AUTHOR]

Purpose: The P value has been used as a statistical tool in randomized controlled trials (RCTs) to establish significance but does not provide information on the robustness of a study when used alone. The fragility index (FI) provides a supplemental approach for demonstrating robustness in RCTs that report dichotomous outcomes. This study aims to determine the statistical fragility of RCTs that compare minimally invasive techniques with open techniques in managing benign and malignant colorectal diseases. Methods: Dichotomous outcomes of minimally invasive surgery versus open surgery in RCTs from 2000 to 2023 were assessed. The overall FI and fragility quotient (FQ) of each study were calculated. Results: Of the 1377 screened studies, 50 met the inclusion criteria. In total, 820 outcomes were recorded with 747 outcomes reported as not significant (P ≥.05) and 73 as significant (P <.05). The overall FI for all studies including all outcomes was 5 (interquartile range [IQR] 4–7) with a FQ of 0.031 (IQR 0.014–0.062). Of the 50 RCTs, 6 (12%) reported a loss to follow-up that was greater than the overall FI of 5. Conclusions: As RCTs are judged increasingly beyond just the P value, practicing colorectal surgeons will benefit from using and interpreting the FI, FQ, and the P value of studies both in analyzing future RCTs and in determining whether or not to make a change in their clinical practice if there is an efficiently true discovery. [ABSTRACT FROM AUTHOR]

Fragility analysis is a method of further characterizing outcomes in terms of the stability of statistical findings. This study assesses the statistical fragility of recent randomized controlled trials (RCTs) evaluating robotic-assisted versus conventional total knee arthroplasty (RA-TKA versus C-TKA). We queried PubMed for RCTs comparing alignment, function, and outcomes between RA-TKA and C-TKA. Fragility index (FI) and reverse fragility index (RFI) (collectively, "FI") were calculated for dichotomous outcomes as the number of outcome reversals needed to change statistical significance. Fragility quotient (FQ) was calculated by dividing the FI by the sample size for that outcome event. Median FI and FQ were calculated for all outcomes collectively as well as for each individual outcome. Subanalyses were performed to assess FI and FQ based on outcome event type and statistical significance, as well as study loss to follow-up and year of publication. The overall median FI was 3.0 (interquartile range, [IQR] 1.0 to 6.3) and the median reverse fragility index was 3.0 (IQR 2.0 to 4.0). The overall median FQ was 0.027 (IQR 0.012 to 0.050). Loss to follow-up was greater than FI for 23 of the 38 outcomes assessed. A small number of alternative outcomes is often enough to reverse the statistical significance of findings in RCTs evaluating dichotomous outcomes in RA-TKA versus C-TKA. We recommend reporting FI and FQ alongside P values to improve the interpretability of RCT results. [ABSTRACT FROM AUTHOR]

Reverse total shoulder arthroplasty (RTSA) has seen increasing utilization as an effective intervention for a wide variety of shoulder pathologies. The scope and indications for growth are often driven by findings from randomized controlled trials (RCTs) guiding surgical decision-making for RTSA. In this study, we utilized the fragility index (FI), reverse fragility index (rFI), and fragility quotient (FQ) to assess the robustness of outcomes reported in RCTs in the RTSA literature. PubMed, Embase, and MEDLINE were queried for RCTs (Jan. 1, 2010-Mar. 31, 2023) in the RTSA literature reporting dichotomous outcomes. The FI and rFI were defined as the number of outcome reversals required to alter statistical significance for significant and nonsignificant outcomes, respectively. The FQ was determined by dividing the FI by the sample size of each study. Subgroup analysis was performed based on outcome category. One hundred seventy-six RCTs were screened with 18 studies included. The median FI across 59 total outcomes was 4 (interquartile range [IQR]: 3-5) with an associated FQ of 0.051 (IQR: 0.029-0.065). Thirteen outcomes were statistically significant with a median FI of 3 (IQR: 1-4) and FQ of 0.033 (IQR: 0.012-0.066). Forty-six outcomes were nonsignificant with a median rFI of 4 (IQR: 3-5) and FQ of 0.055 (IQR: 0.032-0.065). The most fragile outcome category was revision/reoperations with a median FI of 2.50 (IQR: 1.00-3.25), followed by clinical score/outcome (median FI: 3.00), complications (median FI: 4.00), "other" (median FI: 4.00), and radiographic findings (median FI: 5.00). Notably, the number of patients lost to follow-up was greater than or equal to the FI for 59% of outcomes. The statistical findings in RTSA RCTs are fragile and should be interpreted with caution. Reversal of only a few outcomes, or maintaining postoperative follow-up, may be sufficient to alter significance of study findings. We recommend standardized reporting of P values with FI and FQ metrics to allow clinicians to effectively assess the robustness of study findings. [ABSTRACT FROM AUTHOR]

Purpose: This study employs both the fragility index (FI) and fragility quotient (FQ) to assess the level of robustness in the cervical disc arthroplasty (CDA) literature. We hypothesize that dichotomous outcomes involving CDA would exhibit statistical vulnerability. Methods: A PubMed search was conducted to evaluate dichotomous data for randomized controlled trials (RCTs) in CDA literature from 2000 to 2023. The FI of each outcome was calculated through the reversal of a single outcome event until significance was reversed. The FQ was calculated by dividing each fragility index by the study sample size. The interquartile range (IQR) was also calculated for the FI and FQ. Results: Of the 1561 articles screened, 111 met the search criteria, with 35 RCTs evaluating CDA included for analysis. Six hundred and ninety-three outcome events with 130 significant (P < 0.05) outcomes and 563 nonsignificant (P ≥ 0.05) outcomes were identified. The overall FI and FQ for all 693 outcomes were 5 (IQR 3–7) and 0.019 (IQR 0.011–0.043). Fragility analysis of statistically significant outcomes and nonsignificant outcomes both revealed an FI of 5. All of the studies reported loss to follow-up (LTF) data where 65.7% (23) did not report or reported an LTF greater or equal to 5. Conclusions: The literature regarding CDA RCTs lacks statistical robustness and may misrepresent the conclusions with the sole use of the P value. By implementing the FI and FQ along with the P value, we believe the interpretation and contextualization of the clinical data surrounding CDA will be better understood. [ABSTRACT FROM AUTHOR]

Study Design. Meta-analysis. Objective. To assess the robustness of randomized controlled trials (RCTs) that compared cervical disc arthroplasty (CDA) and anterior cervical discectomy and fusion (ACDF) for the treatment of symptomatic degenerative cervical pathology by using fragility indices. Summary of Background Data. RCTs comparing these surgical approaches have shown that CDA may be equivalent or even superior to ACDF due to better preservation of normal spinal kinematics. Materials and Methods. RCTs reporting clinical outcomes after CDA versus ACDF for degenerative cervical disc disease were evaluated. Data for outcome measures were classified as continuous or dichotomous. Continuous outcomes included: Neck Disability Index, overall pain, neck pain, radicular arm pain, and modified Japanese Orthopedic Association scores. Dichotomous outcomes included: any adjacent segment disease (ASD), superior-level ASD, and inferior-level ASD. The fragility index (FI) and continuous FI (CFI) were determined for dichotomous and continuous outcomes, respectively. The corresponding fragility quotient (FQ) and continuous FQ were calculated by dividing FI/CFI by sample size. Results. Twenty-five studies (78 outcome events) were included. Thirteen dichotomous events had a median FI of 7 [interquartile range (IQR): 3–10], and the median FQ was 0.043 (IQR: 0.035–0.066). Sixty-five continuous events had a median CFI of 14 (IQR: 9–22) and a median continuous FQ of 0.145 (IQR: 0.074–0.188). This indicates that, on average, altering the outcome of 4.3 patients out of 100 for the dichotomous outcomes and 14.5 out of 100 for continuous outcomes would reverse trial significance. Of the 13 dichotomous events that included a loss to follow-up data, 8 (61.5%) represented ≥7 patients lost. Of the 65 continuous events reporting the loss to follow-up data, 22 (33.8%) represented ≥ 14 patients lost. Conclusion. RCTs comparing ACDF and CDA have fair to moderate statistical robustness and do not suffer from statistical fragility. [ABSTRACT FROM AUTHOR]

Abstract Background The fragility index is a statistical measure of the robustness or “stability” of a statistically significant result. It has been adapted to assess the robustness of statistically significant outcomes from randomized controlled trials. By hypothetically switching some non-responders to responders, for instance, this metric measures how many individuals would need to have responded for a statistically significant finding to become non-statistically significant. The purpose of this study is to assess the fragility index of randomized controlled trials evaluating opioid substitution and antagonist therapies for opioid use disorder. This will provide an indication as to the robustness of trials in the field and the confidence that should be placed in the trials’ outcomes, potentially identifying ways to improve clinical research in the field. This is especially important as opioid use disorder has become a global epidemic, and the incidence of opioid related fatalities have climbed 500% in the past two decades. Methods Six databases were searched from inception to September 25, 2021, for randomized controlled trials evaluating opioid substitution and antagonist therapies for opioid use disorder, and meeting the necessary requirements for fragility index calculation. Specifically, we included all parallel arm or two-by-two factorial design RCTs that assessed the effectiveness of any opioid substitution and antagonist therapies using a binary primary outcome and reported a statistically significant result. The fragility index of each study was calculated using methods described by Walsh and colleagues. The risk of bias of included studies was assessed using the Revised Cochrane Risk of Bias tool for randomized trials. Results Ten studies with a median sample size of 82.5 (interquartile range (IQR) 58, 179, range 52–226) were eligible for inclusion. Overall risk of bias was deemed to be low in seven studies, have some concerns in two studies, and be high in one study. The median fragility index was 7.5 (IQR 4, 12, range 1–26). Conclusions Our results suggest that approximately eight participants are needed to overturn the conclusions of the majority of trials in opioid use disorder. Future work should focus on maximizing transparency in reporting of study results, by reporting confidence intervals, fragility indexes, and emphasizing the clinical relevance of findings. Trial registration PROSPERO CRD42013006507. Registered on November 25, 2013.

BackgroundThe statistical significance of randomized controlled trials (RCTs) and comparative studies is often conveyed utilizing the P value. However, P values are an imperfect measure and may be vulnerable to a small number of outcome reversals to alter statistical significance. The interpretation of the statistical strength of these studies may be aided by the inclusion of a Fragility Index (FI) and Fragility Quotient (FQ). This study examines the statistical stability of studies comparing operative vs nonoperative management for Achilles tendon rupture.MethodsA systematic search was performed of 10 orthopaedic journals between 2000 and 2021 for comparative studies focusing on management of Achilles tendon rupture reporting dichotomous outcome measures. FI for each outcome was determined by the number of event reversals necessary to alter significance (P < .05). FQ was calculated by dividing the FI by the respective sample size. Additional subgroup analyses were performed.ResultsOf 8020 studies screened, 1062 met initial search criteria with 17 comparative studies ultimately included for analysis, 10 of which were RCTs. A total of 40 outcomes were examined. Overall, the median FI was 2.5 (interquartile range [IQR] 2-4), the mean FI was 2.90 (±1.58), the median FQ was 0.032 (IQR 0.012-0.069), and the mean FQ was 0.049 (±0.062). The FI was less than the number of patients lost to follow-up for 78% of outcomes.ConclusionStudies examining the efficacy of operative vs nonoperative management of Achilles tendon rupture may not be as statistically stable as previously thought. The average number of outcome reversals needed to alter the significance of a given study was 2.90. Future analyses may benefit from the inclusion of a fragility index and a fragility quotient in their statistical analyses.

The study is dedicated to the investigation of thermo-physical characteristics of Se95Te5 chalcogenide glassy semiconductor during its glass formation and crystallization processes, employing various scanning rates of 5, 10, 15 and 20 K/min in non-isothermal modes through DSC measurement. Analysis of the structural relaxation kinetics involves the Kissinger's, Augis and Bennett's, as well as Matusita's approaches. Experimental data yield contains the determination of crucial parameters such as glass transition (Tg), crystallization (Tc), and melting temperatures alongside factors like reduced temperature of glass transition (Trg), Hruby's parameter (Kgl), fragility index (Fi), Avrami exponents (n, m), glass transition ((140.24 kJ/mol) and crystallization (Ec = 95.11 kJ/mol) energies, respectively. The results confirm that Se95Te5 chalcogenide system as an efficient glass former. Matusita's method reveals that the crystallization mechanism (n = 2.51, m = 1.9) corresponds to volumetric nucleation with two-dimensional growth. [ABSTRACT FROM AUTHOR]

Background: There is a lack of consensus in the use of open reduction internal fixation (ORIF) vs primary arthrodesis (PA) in the management of Lisfranc injuries. Statistical fragility represents the number of events needed to flip statistical significance and provides context to interpret P values of outcomes from conflicting studies. The current study evaluates the statistical fragility of existing research with an outcome-specific approach to provide statistical clarity to the ORIF vs PA discussion. We hypothesized that statistical fragility analysis would offer clinically relevant insight when interpreting conflicting outcomes regarding ORIF vs PA management of Lisfranc injuries. Methods: All comparative studies, RCTs, and case-series investigating ORIF vs PA management of Lisfranc injuries published through October 5, 2023, were identified. Descriptive characteristics, dichotomous outcomes, and continuous outcomes were extracted. Fragility index and continuous fragility index were calculated by the number of event reversals needed to alter significance. Outcomes were categorized by clinical relevance, and median FI and CFI were reported. Results: A total of 244 studies were screened. Ten studies and 67 outcomes (44 dichotomous, 23 continuous) were included in the fragility analysis. Of the 10 studies, 4 studies claimed PA to correlate with superior outcomes compared to ORIF with regard to functional scores and return to function outcomes. Of these 4 studies, 3 were statistically robust. Six studies claimed PA and ORIF to have no differences in outcomes, in which only 2 studies were statistically robust. Conclusion: The overall research regarding ORIF vs PA is relatively robust compared with other orthopaedic areas of controversy. Although the full statistical context of each article must be considered, studies supporting PA superiority with regard to functional scores and return to function metrics were found to be statistically robust. Outcome-specific analysis revealed moderate fragility in several clinically relevant outcomes such as functional score, return to function, and wound complications. [ABSTRACT FROM AUTHOR]

Acellular dermal matrix (ADM) is commonly used in plastic and reconstructive surgery. With the abundance of randomized controlled trials (RCTs) reporting P -values for ADM outcomes, this study used the fragility index (FI), reverse fragility index (rFI), and fragility quotient (FQ) to evaluate the statistical stability of the outcomes in ADM RCTs. PubMed, Embase, SCOPUS, Medline, and Cochrane databases were reviewed for ADM RCTs (2003-present) reporting a dichotomous, categorical outcome. FI and rFI (event reversals influencing outcome significance) and FQ (standardized fragility) were calculated and reported as median. Subgroup analysis was performed based on intervention types. Among the 127 studies screened, 56 RCTs with 579 outcomes were included. The median FI stood at 4 (3−5) and FQ was 0.04 (0.03−0.07). Only 101 outcomes were statistically significant with a median FI of 3 (1−6) and FQ of 0.04 (0.02−0.08). The nonsignificant outcomes had a median FI of 4 (3−5) and FQ of 0.04 (0.03−0.07). Notably, 26% of the outcomes had several patients lost to follow up equal to or surpassing the FI. Based on the intervention type, the median FIs showed minor fluctuations but remained low. Outcomes from ADM-related RCTs were statistically fragile. Slight outcome reversals or maintenance of patient follow-up can alter the significance of results. Therefore, future researchers are recommended to jointly report FI, FQ, and P- values to offer a comprehensive view of the robustness in ADM literature. [ABSTRACT FROM AUTHOR]

BackgroundComparative studies and randomized controlled trials (RCTs) often use the P (probability) value to convey the statistical significance of their findings. P values are an imperfect measure, however, and are vulnerable to a small number of outcome reversals to alter statistical significance. The inclusion of a fragility index (FI) and fragility quotient (FQ) may aid in the interpretation of a study's statistical strength.Purpose/hypothesisThe purpose of this study was to examine the statistical stability of studies comparing single-row to double-row rotator cuff repair. It was hypothesized that the findings of these studies would be vulnerable to a small number of outcome event reversals, often fewer than the number of patients lost to follow-up.Study designSystematic review; Level of evidence, 3.MethodsWe analyzed comparative studies and RCTs on primary single-row versus double-row rotator cuff repair that were published between 2000 and 2021 in 10 leading orthopaedic journals. Statistical significance was defined as a P < .05. The FI for each outcome was determined by the number of event reversals necessary to alter significance. The FQ was calculated by dividing the FI by the respective sample size.ResultsOf 4896 studies screened, 22 comparative studies, 10 of which were RCTs, were ultimately included for analysis. A total of 74 outcomes were examined. Overall, the median FI was 2 (interquartile range [IQR], 1-3), and the median FQ was 0.035 (IQR, 0.020-0.057). The mean FI was 2.55 ± 1.29, and the mean FQ was 0.043 ± 0.027. In 64% of outcomes, the FI was less than the number of patients lost to follow-up.) Additionally, 81% of significant outcomes needed just a single outcome reversal to lose their significance.ConclusionOver half of the studies currently used to guide clinical practice have a number of patients lost to follow-up greater than their FI. The results of these studies should be interpreted within the context of these limitations. Future analyses may benefit from the inclusion of the FI and the FQ in their statistical analyses.

AimsRecent trials have evaluated sodium-glucose co-transporter 2 inhibitors in patients with heart failure (HF). We sought to assess the robustness of findings from these trials using the fragility index (FI).Methods and resultsFragility index is defined as the minimum number of patients that must be moved from the 'non-event' to the 'event' group to turn a statistically significant result to non-significant. In addition to FI, fragility quotient [(FQ); FI divided by the sample size] was calculated to assess the proportion of events that must be moved to change the significance. For statistically non-significant outcomes, reverse fragility index (RFI) and reverse fragility quotient (RFQ) were calculated. Robustness of findings after pooling data from all three trials was also assessed. A robust reduction in first HF hospitalization or cardiovascular mortality was seen with dapagliflozin (FI = 62 and FQ = 0.013), empagliflozin (FI = 50 and FQ = 0.013), and sotagliflozin (FI = 60 and FQ = 0.049). Dapagliflozin nominally improved all-cause and cardiovascular mortality, with modest FI (n = 8 and 5) and FQ (0.002 and 0.001). Empagliflozin and sotagliflozin did not demonstrate statistically significant reductions in all-cause mortality, with modest RFI (empagliflozin: RFI = 26 and RFQ = 0.007; sotagliflozin: RFI = 6 and RFQ = 0.005). A similar trend was seen with cardiovascular mortality (empagliflozin: RFI = 24 and RFQ = 0.006; sotagliflozin: RFI = 7 and RFQ = 0.006). Upon meta-analysis, the result for first HF hospitalization or cardiovascular mortality was robust (FI = 95 and FQ = 0.010). The reductions in all-cause (FI = 12 and FQ = 0.001) and cardiovascular mortality (FI = 9 and FQ = 0.001), while statistically significant, were fragile.ConclusionImprovement in the composite outcome of first HF hospitalization or cardiovascular death was highly concordant and robust across sodium-glucose co-transporter 2 inhibitor trials. In contrast, secondary endpoints of all-cause and cardiovascular mortality were statistically fragile, underscoring the need to power trials for mortality to fully understand the benefit of therapies on fatal events.

Reverse shoulder arthroplasty (RSA) is used in the treatment of traumatic and arthritic pathologies, with expanding clinical indications and as a result there has been an increase in clinical research on the topic. The purpose of this study was to examine the statistical fragility of randomized control trials (RCTs) reporting outcomes from RSA. A systematic search was undertaken to find RCTs investigating RSA. The Fragility Index (FI) was calculated using Fisher’s exact test, by sequentially altering the number of events until there was a reversal of significance. The Fragility Quotient (FQ) was calculated by dividing the FI by the trial population. Each trial was assigned an overall FI and FQ calculated as the median result of its reported findings. Overall, 19 RCTs warranted inclusion in the review, representing 1146 patients, of which 41.2% were male, with a mean age of 74.2 ± 4.3 years and mean follow-up of 22.1 ± 9.9 months. The median RCT population was 59, with a median of 9 patients lost to follow-up. The median FI was 4.5, and median FQ was 0.083, indicating more patients did not complete the trial than the number of outcomes which would have to change to reverse the finding of significance. This review found that the RCT evidence for RSA management may be vulnerable to statistical fragility, with a handful of events required to reverse a finding of significance.

Purpose: To identify and assess the clinical impact of randomised controlled trials (RCTs) assessing the surgical management of femoroacetabular impingement syndrome (FAIS) through a citation analysis. Methods: MEDLINE, EMBASE and CENTRAL were searched from inception to April 22, 2023 for RCTs assessing the surgical management of FAIS. Study characteristics were directly abstracted from included trials and citation metrics were obtained from the Clarivate Web of Knowledge database on May 19, 2023. The continuous fragility index (CFI) was calculated for eligible outcomes. Univariate regression models were used to explore correlations between total citations per year and various study characteristics. Results: Ten studies comprising one thousand two hundred ninetypatients were eligible for analysis. Studies were published from 2013 to 2023. Eight countries were represented across various trials with 91% being either North American or European. The mean journal impact factor of published studies was 39.684 (median 2.982; range 1.31–202.73). The mean citation density was 14.17 (range 0.33–48.67). The median CFI was 4.8 (range 1–32.2). Correlation analysis demonstrated strong and statistically significant correlations to study sample size (R = 0.75, p = 0.012), journal impact factor (R = 0.80, p = 0.006) and continuous fragility index (R = 0.95, p = 0.015). Conclusion: Trials assessing the surgical management of FAIS present with a wide range of clinical uptake based on citation density and are published in journals of broadly variable impact factor. Despite promising citation metrics, high-quality evidence on arthroscopy for FAIS is limited to the United States and Europe with an unclear international impact. Future knowledge translation efforts are warranted to maximise the international uptake of evidence regarding arthroscopic management of FAIS. Level of evidence: I. [ABSTRACT FROM AUTHOR]

Purpose: To report the statistical stability of prospective clinical trials evaluating the effect of intramedullary reaming on rates of non-union in tibial fractures through calculation of the fragility metrics for non-union rates and all other dichotomous outcomes. Methods: Literature search was conducted for prospective clinical trials evaluating the effect of intramedullary reaming on non-union rates in tibial nailing. All dichotomous outcomes were extracted from the manuscripts. The fragility index (FI) and reverse fragility index (RFI) were calculated by determining the number of event reversals required for a statistically significant outcome to lose significance and vice-versa. The fragility quotient (FQ) and reverse fragility quotient (RFQ) were calculated by dividing the FI or RFI by the sample size, respectively. Outcomes were defined as "fragile" if the FI or RFI was found to be less than or equal to the number of patients lost to follow-up. Results: Literature search identified 579 results which produced ten studies meeting the criteria for review. There were 111 outcomes identified for analysis, of which 89 (80%) exhibited statistical fragility. For reported outcomes across the studies the median and mean FI was 2, the median FQ was 0.019, the mean FQ was 0.030, the median RFI was 4, the mean RFI was 3.95, the median RFQ was 0.045, and the mean RFQ was 0.030. Four studies reported outcomes which were found to have an FI of 0. Conclusions: The studies evaluating the effect of intramedullary reaming on tibial nail fixation demonstrate considerable fragility. On average, two event reversals for significant findings, and four event reversals for insignificant findings are sufficient to alter statistical significance. Level of evidence: Level II, systematic review of Level I and Level II studies. [ABSTRACT FROM AUTHOR]

PURPOSEThe fragility index (FI) measures the robustness of randomized controlled trials (RCTs). It complements the P value by taking into account the number of outcome events. In this study, the authors measured the FI for major interventional radiology RCTs.METHODSInterventional radiology RCTs published between January 2010 and December 2022 relating to trans-jugular intrahepatic portosystemic shunt, trans-arterial chemoembolization, needle biopsy, angiography, angioplasty, thrombolysis, and nephrostomy tube insertion were analyzed to measure the FI and robustness of the studies.RESULTSA total of 34 RCTs were included. The median FI of those studies was 4.5 (range 1–68). Seven trials (20.6%) had a number of patients lost to follow-up that was higher than their FI, and 15 (44.1%) had a FI of 1–3.CONCLUSIONThe median FI, and hence the reproducibility of interventional radiology RCTs, is low compared to other medical fields, with some having a FI of 1, which should be interrupted cautiously.

OBJECTIVE: To study ICU trials published in the four highest-impact general medicine journals by comparing them with concurrently published non-ICU trials in the same journals. DATA SOURCES: PubMed was searched for randomized controlled trials (RCTs) published between January 2014 and October 2021 in the New England Journal of Medicine, The Lancet, the Journal of the American Medical Association, and the British Medical Journal. STUDY SELECTION: Original RCT publications investigating any type of intervention in any patient population. DATA EXTRACTION: ICU RCTs were defined as RCTs exclusively including patients admitted to the ICU. Year and journal of publication, sample size, study design, funding source, study outcome, type of intervention, Fragility Index (FI), and Fragility Quotient were collected. DATA SYNTHESIS: A total of 2,770 publications were screened. Of 2,431 original RCTs, 132 (5.4%) were ICU RCTs, gradually rising from 4% in 2014 to 7.5% in 2021. ICU RCTs and non-ICU RCTs included a comparable number of patients (634 vs 584, p = 0.528). Notable differences for ICU RCTs were the low occurrence of commercial funding (5% vs 36%, p < 0.001), the low number of RCTs that reached statistical significance (29% vs 65%, p < 0.001), and the low FI when they did reach significance (3 vs 12, p = 0.008). CONCLUSIONS: In the last 8 years, RCTs in ICU medicine made up a meaningful, and growing, portion of RCTs published in high-impact general medicine journals. In comparison with concurrently published RCTs in non-ICU disciplines, statistical significance was rare and often hinged on the outcome events of just a few patients. Increased attention should be paid to realistic expectations of treatment effects when designing ICU RCTs to detect differences in treatment effects that are reliable and clinically relevant. [ABSTRACT FROM AUTHOR]

• Fragility index analysis reveals low robustness of significant outcomes in PAH RCTs. • Included RCTs had a median FI of 10, indicating fragility of the results. • Moderate correlation was found between FI and sample size or journal impact factor. Randomized clinical trials (RCTs) are considered the gold standard for evidence-based medicine. The Fragility Index (FI) is a tool to assess the robustness of RCT results. FI was validated for dichotomous outcomes and recent work expanded its use to continuous outcomes. Studying the robustness of RCTs in Pulmonary Arterial Hypertension (PAH) treatments is crucial due to the severity and mortality risks associated with this rare condition. Analyze FI and Fragility quotient (FQ) of significant primary outcomes in PAH RCTs and study FI correlation with sample size and journal impact factor. FI and FQ calculation followed by Spearman correlation to assess the correlation between FI and sample size, and FI and impact factor. The median sample size of the 21 trials was 202 patients (IQR 106–267), with 6 trials reporting primary outcomes as dichotomous and 15 reporting continuous primary outcomes. The median FI was 10 (IQR 3–20), and the median FQ was 0.044 (0.026–0.097). A moderate correlation was found between FI and sample size, with r = 0.56; P = 0.008 and FI and journal impact factor (r =0.50; P =0.019). The FI for continuous outcomes was similar to that for dichotomous outcomes. This study represents the first analysis of the FI and FQ of PAH treatment RCTs, and expands the use of FI to continuous outcomes in this context. The moderate correlation between FI and sample size suggests that increasing sample size alone is partially correlated to a higher FI. The similarity between FI for continuous and dichotomous outcomes supports the broader use of FI in PAH RCTs. [ABSTRACT FROM AUTHOR]

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Purpose: The purpose of this study was to apply both the fragility index (FI) and fragility quotient (FQ) to evaluate the degree of statistical fragility in the distal femur fracture (DFF) literature. We hypothesized that the dichotomous outcomes within the DFF literature are statistically fragile. Methods: Using preferred reporting items for systematic reviews and meta-analyses, we performed a PubMed search for distal femur fractures clinical trials from 2000 to 2022 reporting dichotomous outcomes. The FI of each outcome was calculated through the reversal of a single outcome event until significance was reversed. The FQ was calculated by dividing each fragility index by study sample size. The interquartile range (IQR) was also calculated for the FI and FQ. Results: Of the 4258 articles screened, 92 met the search criteria, with eleven RCTs included for analysis. Ninety eight outcome events with 25 significant (P < 0.05) outcomes and 73 nonsignificant (P > 0.05) outcomes were identified. The overall FI and FQ for all 98 outcomes were 5 (IQR 4–6) and 0.130 (IQR 0.087–0.174), respectively. Three studies (33.3%) reported loss to follow (LTF) greater than 5. Conclusions: The randomized controlled trials in the peer-reviewed distal femur fracture literature may not be as robust as previously thought, as incorporating statistical analyses solely on a P value threshold is misleading. Standardized reporting of the P value, FI and FQ can help the clinician reliably draw conclusions based on the fragility of outcome measures. [ABSTRACT FROM AUTHOR]

Aim: The aim of this work was to evaluate the robustness of randomized controlled trials (RCTs) on anal fistula management using the news tools of Fragility Index (FI), Reverse Fragility Index (RFI) and their corresponding fragility quotients. Method: A systematic search was conducted based on the Preferred Reporting Items for Systematic Reviews and Meta‐analysis (PRISMA) guidelines which utilized MEDLINE, EMBASE, Cochrane Library and Web of Science databases. Inclusion criteria included RCTs related to the management of anal fistula published from 2000 to 2022 with dichotomous outcomes measures and 1:1 allocation. Calculation of FI and RFI was performed by creating 2 × 2 contingency tables by successively changing one nonevent to an event for each outcome measure until the result was made nonsignificant or significant, respectively. The Fragility Quotients were calculated by dividing the FI or RFI by the total sample size. Fragile results were defined as those with a FI or RFI equal to or less than the number of patients lost to follow‐up. Additionally, those with a FI or RFI less than 3 were also considered fragile. Studies were considered extremely fragile if FI was ≤1 or FQ was ≤0.01. Results: There were 36 RCTs that met our criteria, with 3223 patients. Among these, 19 (53%) were positive RCTs (p < 0.005) and 17 (47%) were negative RCTs (p > 0.05). The median FI was 2 (0–5). The analysis by categorical subgroup showed a strong correlation between FI and the p‐value (p = 0.000) and the number of events (p = 0.011). The median RFI was 5 (3.5–9.5) and the subgroup analysis showed a strong correlation between RFI and the p‐value (p = 0.000), sample size (0.021) and number needed to treat/number needed to harm (0.000). We considered 63.2% of positive RCTs to be fragile and 35.3% of negative RCTs. Conclusions: In the present study we demonstrated the lack of robustness of study findings in published RCTs in the field of anal fistula. [ABSTRACT FROM AUTHOR]

In the present paper, the study of amorphous-crystalline transformation in (Se80Te20)94−x Ge6Bix (x = 0, 1, 2, 4, 6, 8, 10 and 12 at.%) chalcogenide alloys has been done using non-isothermal differential scanning calorimetry (DSC). Characteristic temperatures indicate that the samples with x = 1 at.% and x = 6 at.% can be considered as a critical configurations at which the system becomes a chemically ordered alloy. Kissinger and Moynihan approaches which utilized dependence of glass transition temperature (Tg) on heating rate (α) are used to deduce activation energy of glass transition (Eg). Crystallization process is characterized by various kinetic parameters such as activation energy and frequency factor deduced using different methods. Dietzel, Hruby, Saad and Poulin criteria are employed to assess glass forming ability and thermal stability of investigated alloys. The alloy with x = 12 at.% of Bi content has highest ∆T confirms maximum thermal stability, further validated from the values of Hruby parameter (Kgl) and thermal stability parameter (S). The fragility index infers that the composition studied in the present study is made from strong glass forming liquids. [ABSTRACT FROM AUTHOR]

In this paper we derive a characterization of the distribution of the number of exceedances among the components of a random vector in terms of order statistics of generators of D-norms (GOD). The computation of the fragility index is an immediate consequence. [ABSTRACT FROM AUTHOR]

Abstract Purpose Significant results of randomized controlled trials (RCTs) should be properly weighed. This study adopted fragility index (FI) to evaluate the robustness of significant dichotomous outcomes from RCTs on coronavirus disease 2019 (COVID-19) treatment. Materials and methods ClinicalTrials.gov and PubMed were searched from inception to July 31, 2021. FIs were calculated and their distribution was depicted. FI’s categorical influential factors were analyzed. Spearman correlation coefficient (r s) was reported for the relationship between FI and the continuous characteristics of RCTs. Results Fifty RCTs with 120 outcomes in 7869 patients were included. The FI distribution was abnormal with median 3 (interquartile range 1–7, P = 0.0001). The FIs and robustness were affected by the outcomes of interest, various patient populations, and interventions (T = 18.215,16.667, 23.107; P = 0.02,0.0001, 0.001, respectively). A cubic relationship between the FIs and absolute difference of events between groups with R square of 0.848 (T = 215.828, P = 0.0001, R square = 0.865) was observed. A strong negative logarithmic relationship existed between FI and the P value with R square = – 0.834. Conclusion The robustness of significant dichotomous outcomes of COVID-19 treatments was fragile and affected by the outcomes of interest, patients, interventions, P value, and absolute difference of events between the groups. FI was an useful quantitative metric for the binary significant outcomes on COVID-19 treatments. Registration PROSPERO (CRD42021272455).

Background: Debate centering on the management of anterior shoulder instability (ASI) in recent years has led to many randomized controlled trials (RCTs) being published on the topic. The fragility index (FI) has subsequently emerged as a novel method of assessing significant findings reported in RCTs, particularly those with small sample sizes. Purpose: To evaluate the FI of statistically significant findings in RCTs that reported the outcomes of management strategies of patients with ASI. Study Design: Systematic review; Level of evidence, 1. Methods: Using PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) guidelines, 2 independent reviewers performed a systematic review of RCTs focusing on the outcomes of management strategies of patients with ASI. There were 3 main categories of RCTs included: (1) nonoperative management in internal rotation (IR) versus external rotation (ER), (2) nonoperative management versus a surgical intervention, and (3) surgical management with arthroscopic Bankart repair versus open Bankart repair. The Fisher exact test was utilized to calculate the FI for the reversal of statistical significance in all statistically significant dichotomous outcomes. Results: A total of 21 RCTs were included, including 1589 shoulders (mean age, 29.4 years) with a mean follow–up of 26.8 months. There were 10 RCTs (831 shoulders) that reported outcomes after the nonoperative management of ASI in IR versus ER, with a mean FI of 6.8. There were 5 RCTs (324 shoulders) that reported outcomes comparing the nonoperative and operative management of ASI, with a mean FI of 3.5. There were 6 RCTs (434 shoulders) that reported outcomes after the operative management of ASI with either arthroscopic Bankart repair or open Bankart repair, with a mean FI of 9.6. Conclusion: The overall FI of RCTs reporting the outcomes of management strategies for patients with ASI was high, suggesting a moderate fragility of statistically significant outcomes including recurrence, revision stabilization, and return to play. [ABSTRACT FROM AUTHOR]

Thermal characterization of different compositions of Ge30−xSbxTe10Se60 (x = 0, 5, 10, 15, 20 at.%) glassy materials has been investigated through differential scanning calorimetry (DSC). The tested glasses have been synthesized by melt-quench technique. Glassy materials display compositional phase separation at x = 0, 5, 10, 15 at.%. For additional increase in Sb content at x = 20 at.%, the separation of phases combines in the glass matrix. The glass transition temperature (Tg), initial temperature of crystallization (Tc), peak crystallization temperature (Tp) and melting temperature (Tm) were found to be affected by both heating rate and composition. It is noticed that the increasing of antimony mass percentage in the glassy matrix is leading to decrease in Tg, Tc, Tp and Tm values. The melting temperature (Tm) of these glasses was found in the range 733–746 K for the first phase and in the range 740–792 K for the second phase. The activation energy of glass transition (Eg), activation energy for crystallization (Ec), Avrami index (n) and fragility index (Fi) were calculated using these specific temperatures. Eg decreases with increasing Sb content in all studied samples, but Eg is increasing in the sample with Sb content of 20%, and hence, it varies between 102.7 and 110.6 kJ approximately, whereas (Ec) decreases with the increase in the Sb content in all the tested samples and varies between 283 and 339 kJ. The fragility index varies between 10 and 26 indicating that the melts of these glasses are strong, and the fragility is minimum. The results were discussed in terms of the average coordination number NC and chemical bond approach. [ABSTRACT FROM AUTHOR]

Background: Clinical decision-making often relies on evidence-based medicine, derived from objective data with conventional and rigorous statistical tests to evaluate significance. The literature surrounding rehabilitation after rotator cuff repair (RCR) is conflicting, with no defined standard of practice. Purpose: To determine the fragility index (FI) and the fragility quotient (FQ) of randomized controlled trials (RCTs) evaluating rehabilitation protocols after RCR. Study Design: Systematic review. Methods: A systematic review was performed according to PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) guidelines by searching the PubMed, Cochrane Library, and Embase databases for RCTs evaluating rehabilitation protocols after arthroscopic RCRs from 2000 to June 1, 2022. The FI was determined by manipulating the dichotomous outcome events from each article until a reversal of significance with 2 × 2 contingency tables was achieved. The FQ was determined by dividing the FI by the sample size. Results: Fourteen RCTs with 48 dichotomous outcomes were ultimately included for analysis. The mean FI for the included dichotomous outcomes was 4 (interquartile range, 3-6), suggesting that the reversal of 4 events is required to change study significance. The mean FQ was 0.048. Of the RCTs that reported data regarding loss to follow-up, most studies (58.5%) indicated that >4 patients had been lost to follow-up. Conclusion: The results of RCT studies of RCR rehabilitation protocols are moderately fragile, something clinicians should be aware of when implementing study results into practice. We recommend the inclusion of FI and FQ in addition to standard P values when reporting statistical results in future RCTs with dichotomous outcome variables on this topic. [ABSTRACT FROM AUTHOR]

Background: Utility of robotic over laparoscopic approach has been an area of debate across all surgical specialties over the past decade. The fragility index (FI) is a metric that evaluates the frailty of randomized controlled trials (RCTs) findings by altering the status of patients from an event to non-event until significance is lost. This study aims to evaluate the robustness of RCTs comparing laparoscopic and robotic abdominopelvic surgeries through the FI. Methods: A search was conducted in MEDLINE and EMBASE for RCTs with dichotomous outcomes comparing laparoscopic and robot-assisted surgery in general surgery, gynecology, and urology. The FI and reverse fragility Index (RFI) metrics were used to assess the strength of findings reported by RCTs, and bivariate correlation was conducted to analyze relationships between FI and trial characteristics. Results: A total of 21 RCTs were included, with a median sample size of 89 participants (Interquartile range [IQR] 62–126). The median FI was 2 (IQR 0–15) and median RFI 5.5 (IQR 4–8.5). The median FI was 3 (IQR 1–15) for general surgery (n = 7), 2 (0.5–3.5) for gynecology (n = 4), and 0 (IQR 0–8.5) for urology RCTs (n = 4). Correlation was found between increasing FI and decreasing p-value, but not sample size, number of outcome events, journal impact factor, loss to follow-up, or risk of bias. Conclusion: RCTs comparing laparoscopic and robotic abdominal surgery did not prove to be very robust. While possible advantages of robotic surgery may be emphasized, it remains novel and requires further concrete RCT data. [ABSTRACT FROM AUTHOR]

The purpose of this study was to apply both the fragility index (FI) and fragility quotient (FQ) to evaluate the degree of statistical fragility in the distal fibular fracture (DFF) literature. We hypothesized that the dichotomous outcomes within the DFF literature are statistically fragile. We performed a PubMed search for distal fibular fractures clinical trials from 2000 to 2022 reporting dichotomous outcomes. The FI of each outcome was calculated through the reversal of a single outcome event until significance was reversed. The FQ was calculated by dividing each fragility index by study sample size. The interquartile range (IQR) was also calculated for the FI and FQ. Of the 1158 articles screened, 23 met the search criteria, with six RCTs included for analysis. Forty-five outcome events with 5 significant (p < 0.05) outcomes and 40 nonsignificant (p ≥ 0.05) outcomes were identified. The overall FI and FQ was 5 (IQR 4–6) and 0.089 (IQR 0.061–0.107), respectively. The randomized controlled trials in the peer-reviewed distal fibular fracture literature may not be as robust as previously thought, as incorporating statistical analyses solely on a P value threshold is misleading. Standardized reporting of the P value, FI and FQ can help the clinician reliably draw conclusions based on the fragility of outcome measures. [ABSTRACT FROM AUTHOR]