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Methodological letter
Fragility Index, Reverse Fragility Index, Fragility Quotients, and Susceptibility Index. Novel tools for assessing of randomized clinical trials
Indice de Fragilidad, Indice Inverso de Fragilidad, Cocientes de Fragilidad e Indice de susceptibilidad. Nuevas herramientas para la valoración de los ensayos clínicos aleatorizados
Carlos Placer-Galán
Corresponding author
carlos943313762@gmail.com

Corresponding author.
, Elisabet Bollo Arocena
Servicio de Cirugía General y Digestiva, Hospital Universitario Donostia, San Sebastián, Spain
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    "textoCompleto" => "<span class="elsevierStyleSections"><p id="par0005" class="elsevierStylePara elsevierViewall">Randomized clinical trials &#40;RCTs&#41; represent the paradigm of Evidence-Based Medicine &#40;EBM&#41; and are the primary methods used to evaluate the efficacy and safety of treatment studies&#46; Additionally&#44; they constitute the primary support for testing causality in interventions&#46; Randomization and its concealment&#44; both for researchers and trial participants&#44; are the primary tools used to avoid biases&#46; However&#44; RCTs present some limitations&#44; particularly those conducted during surgery&#46;<a class="elsevierStyleCrossRef" href="#bib0005"><span class="elsevierStyleSup">1</span></a> One of the main problems in the correct interpretation of results is the loss of participants during the process&#46; Different approaches such as protocol and intention-to-treat analyses have been proposed to overcome these difficulties&#46; The external validity of these studies may be compromised by some factors&#44; including professionals &#40;varying degrees of competence in the aspect of study&#41;&#44; participants &#40;difficulty in selecting them&#41;&#44; and intervention &#40;most RCTs are conducted in third-level centers with experience that is difficult to extrapolate to other settings&#41;&#46; In the field of surgery&#44; RCTs present some more specific problems&#44; including variations in surgical technique&#44; learning curve&#44; and comparison between study groups &#40;patients with previous surgeries&#63;&#41; and difficulty in blinding the treatment performed &#40;for both professionals and participants&#41;&#46;<a class="elsevierStyleCrossRef" href="#bib0010"><span class="elsevierStyleSup">2</span></a></p><p id="par0010" class="elsevierStylePara elsevierViewall">Traditionally&#44; <span class="elsevierStyleItalic">P</span>-values have been used to determine the statistical significance between two or more options in RCTs&#46; This methodology has been criticized for not providing the strength of the associations and reducing their clinical importance&#46; To overcome these deficiencies&#44; most scientific journals require the incorporation of other statistics&#44; such as relative risks&#44; odds ratios&#44; and confidence intervals&#44; which help determine the true size of the effect achieved&#46; For an average reader&#44; these tests are not easy to interpret&#44; and other metrics have been designed to facilitate the task&#46; The number needed to treat &#40;NNT&#41; and number needed to harm &#40;NNH&#41; are two tools that provide a simpler and more practical response to interpreting the results of RCTs&#46;</p><p id="par0015" class="elsevierStylePara elsevierViewall">In recent years&#44; new tools have appeared to evaluate RCTs more intuitively and make decisions about their fragility or robustness&#46; These included the Fragility Index &#40;FI&#41;&#44; Reverse Fragility Index &#40;RFI&#41;&#44; Fragility Quotient&#44; Reverse Fragility Quotient &#40;FQ and RFQ&#41;&#44; and Susceptibility Index &#40;SI&#41;&#46;</p><span id="sec0005" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0005">Fragility Index&#44; Fragility Quotient and Susceptibility Index</span><p id="par0020" class="elsevierStylePara elsevierViewall">FI is defined as the minimum number of outcomes of a trial that would need to be changed to reverse statistical significance&#46;<a class="elsevierStyleCrossRef" href="#bib0015"><span class="elsevierStyleSup">3</span></a> This test can only be used in RCTs with a dichotomous outcome &#40;death or no death&#44; recurrence&#44; or no recurrence&#41; and a significant <span class="elsevierStyleItalic">P</span>-value &#40;<span class="elsevierStyleItalic">P</span>&#8201;&#60;&#8201;&#46;05&#41;&#46; In practice&#44; FI is the number of &#8220;no events&#8221; in the experimental group with the smallest number of events that should be changed to &#8220;event&#8221; to change the <span class="elsevierStyleItalic">P</span>-value to &#62;&#46;05 without modifying the total number of participants &#40;using Fisher&#39;s exact method&#41;&#46;</p><p id="par0025" class="elsevierStylePara elsevierViewall">Let us now examine an example&#46; One trial compared two treatments&#58; A &#40;experimental group&#41; and B &#40;control group&#41;&#46; The sample size of the study was 50 participants&#46; In group A&#44; there were 2 recurrences out of 25&#44; and in group B&#44; there were 9 recurrences out of 25 with a <span class="elsevierStyleItalic">P</span>-value of &#46;037 &#40;Fisher&#39;s exact test&#41;&#44; which was statistically significant&#46; If we increase the number of events in group A from two to three&#44; the <span class="elsevierStyleItalic">P</span>-value would be &#46;095&#44; and therefore&#44; significance would be lost&#46; It can be concluded that the FI is 1&#46; The smaller the FI value&#44; the more fragile the study&#46; A cutoff point defining the degree of fragility&#47;robustness of a trial has not yet been defined&#44; but studies with FI&#8201;&#60;&#8201;3 are usually considered fragile&#46;</p><p id="par0030" class="elsevierStylePara elsevierViewall">The sample size has a significant influence on the external validity of a randomized controlled trial&#44; and the Fragility Quotient &#40;FQ&#41; has been defined by dividing the FI by the sample size&#46;<a class="elsevierStyleCrossRef" href="#bib0020"><span class="elsevierStyleSup">4</span></a> In our example&#44; it would be 1&#47;50 &#40;0&#46;02&#41;&#46; The interpretation is in terms of the number of patients per 100&#46; In other words&#44; in our example&#44; a 2&#37; change in the results of the study would rule out the superiority of Treatment A&#46;</p><p id="par0035" class="elsevierStylePara elsevierViewall">Given that FI is the minimum number of events that would change the significance&#44; it is crucial to consider the value of lost patients during the study&#46; Furthermore&#44; if the number of patients lost is equal to or greater than the FI&#44; the study can be considered fragile&#46; This new concept has been incorporated into the Susceptibility Index&#46;<a class="elsevierStyleCrossRef" href="#bib0025"><span class="elsevierStyleSup">5</span></a> Its calculation follows the following formula&#58; SI&#8201;&#61;&#8201;&#40;number of lost patients&#8211;FI&#41;&#47;&#40;number of lost patients&#41;&#46; Higher values indicate that the results are highly susceptible to alteration by the number of patients lost during follow-up and facilitate comparison between studies&#46;</p></span><span id="sec0010" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0010">Reverse fragility index and reverse fragility quotient</span><p id="par0040" class="elsevierStylePara elsevierViewall">As already mentioned&#44; FI can only be used in RCTs that have demonstrated the superiority of one treatment over another&#46; However&#44; what happens in trials in which statistical significance is not achieved &#40;<span class="elsevierStyleItalic">P</span>&#8201;&#62;&#8201;&#46;05&#41;&#63; Recently&#44; the RFI has been described&#44; which is calculated in a similar way as the FI&#44; subtracting events from the group with fewer events while adding &#8220;no events&#8221; to the same group&#44; maintaining the total number of participants until the <span class="elsevierStyleItalic">P</span>-value was &#60;&#46;05&#46;<a class="elsevierStyleCrossRef" href="#bib0030"><span class="elsevierStyleSup">6</span></a> Its interpretation is very similar to that of FI&#46; A low RFI value indicated a weaker or more fragile trial&#46; Its Rverse Fragility Quotient &#40;RFQ&#41; was also designed&#44; which was calculated as the QF&#44; that is&#44; by dividing the RFI value by the sample size&#44; and whose interpretation is the same as the fragility quotient&#46;</p><p id="par0045" class="elsevierStylePara elsevierViewall">An index of susceptibility has not yet been published or validated for studies with a <span class="elsevierStyleItalic">P</span>-value of &#62;&#46;05&#46;</p><p id="par0050" class="elsevierStylePara elsevierViewall">The development and validation of a susceptibility index for studies with a <span class="elsevierStyleItalic">P</span>-value &#62;&#46;05 has not yet been published&#46;</p></span><span id="sec0015" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0015">Limitations and strengths of FI&#44; RFI&#44; FQ&#44; RFQ</span><p id="par0055" class="elsevierStylePara elsevierViewall">All indices discussed can only be used in studies with binary outcomes and a 1&#58;1 design&#46; Therefore&#44; they cannot be used in trials that compare three or more treatments or continuous variables &#40;e&#46;g&#46;&#44; pain scales&#41;&#46; Additionally&#44; they did not provide information on the clinical significance and importance of these differences&#46;</p><p id="par0060" class="elsevierStylePara elsevierViewall">However&#44; these new tools are useful and intuitive measures that allow for the evaluation of RCTs and comparisons between them&#46; Moreover&#44; they can be applied to meta-analyses&#44; where they can substantially change the conclusions&#46;</p></span><span id="sec0020" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0020">How to the calculate simply</span><p id="par0065" class="elsevierStylePara elsevierViewall">To perform these simple calculations&#44; any spreadsheet &#40;Excel&#44; etc&#46;&#41; or statistical software &#40;SPSS&#44; STATA&#44; SAS&#44; R&#44; etc&#46;&#41; can be used to construct a 2&#8201;&#215;&#8201;2 contingency table &#40;two study groups and two outcomes&#41;&#46; The change in statistical significance was determined using Fisher&#39;s exact test&#46; In cases where the authors of the study used &#967;2 and a <span class="elsevierStyleItalic">P</span>-value of &#60;&#46;05&#44; sometimes the exact Fisher test results in a <span class="elsevierStyleItalic">P</span>-value of &#62;&#46;05&#46; In these cases&#44; the FI was 0&#46;</p><p id="par0070" class="elsevierStylePara elsevierViewall">For interested readers&#44; there is a website that automatically calculates the FI &#40;<a href="https://clincalc.com/Stats/FragilityIndex.aspx">https&#58;&#47;&#47;clincalc&#46;com&#47;Stats&#47;FragilityIndex&#46;aspx</a>&#41;&#46; Additionally&#44; R software has a specific package for performing all the calculations described in this paper &#40;R software version 4&#46;2&#46;2&#44; R package Fragility Index&#41;&#46;</p></span><span id="sec0025" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0025">Conflict of interest</span><p id="par0075" class="elsevierStylePara elsevierViewall">The authors have no conflict of interest in this study&#46;</p></span></span>"
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