Letter to the Director
The inclusion of Bayes factor and the conversion of effect size in anesthesiology and reanimation research
La inclusión del factor Bayes y la conversión del tamaño de efecto en la investigación en anestesiología y reanimación
C. Ramos-Vera
Corresponding author
Área de investigación, Facultad de Ciencias de la Salud, Universidad Cesar Vallejo, Lima, Peru
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"apellidos" => "Aso Escario" ] ] ] ] ] "idiomaDefecto" => "en" "Traduccion" => array:1 [ "es" => array:9 [ "pii" => "S0034935621001845" "doi" => "10.1016/j.redar.2021.05.013" "estado" => "S300" "subdocumento" => "" "abierto" => array:3 [ "ES" => false "ES2" => false "LATM" => false ] "gratuito" => false "lecturas" => array:1 [ "total" => 0 ] "idiomaDefecto" => "es" "EPUB" => "https://multimedia.elsevier.es/PublicationsMultimediaV1/item/epub/S0034935621001845?idApp=UINPBA00004N" ] ] "EPUB" => "https://multimedia.elsevier.es/PublicationsMultimediaV1/item/epub/S234119292200083X?idApp=UINPBA00004N" "url" => "/23411929/0000006900000005/v1_202206100555/S234119292200083X/v1_202206100555/en/main.assets" ] "en" => array:14 [ "idiomaDefecto" => true "cabecera" => "<span class="elsevierStyleTextfn">Letter to the Director</span>" "titulo" => "The inclusion of Bayes factor and the conversion of effect size in anesthesiology and reanimation research" "tieneTextoCompleto" => true "paginas" => array:1 [ 0 => array:2 [ "paginaInicial" => "313" "paginaFinal" => "314" ] ] "autores" => array:1 [ 0 => array:4 [ "autoresLista" => "C. Ramos-Vera" "autores" => array:1 [ 0 => array:4 [ "nombre" => "C." "apellidos" => "Ramos-Vera" "email" => array:1 [ 0 => "cristony_777@hotmail.com" ] "referencia" => array:1 [ 0 => array:2 [ "etiqueta" => "<span class="elsevierStyleSup">*</span>" "identificador" => "cor0005" ] ] ] ] "afiliaciones" => array:1 [ 0 => array:2 [ "entidad" => "Área de investigación, Facultad de Ciencias de la Salud, Universidad Cesar Vallejo, Lima, Peru" "identificador" => "aff0005" ] ] "correspondencia" => array:1 [ 0 => array:3 [ "identificador" => "cor0005" "etiqueta" => "⁎" "correspondencia" => "Corresponding author." ] ] ] ] "titulosAlternativos" => array:1 [ "es" => array:1 [ "titulo" => "La inclusión del factor Bayes y la conversión del tamaño de efecto en la investigación en anestesiología y reanimación" ] ] "textoCompleto" => "<span class="elsevierStyleSections"><p id="par0005" class="elsevierStylePara elsevierViewall">La presente investigación no ha recibido ayudas específicas provenientes de agencias del sector público, sector comercial o entidades sin ánimo de lucro</p><p id="par0010" class="elsevierStylePara elsevierViewall">In number 8 of volume 67 of this journal, an important study was published reporting a statistically significant correlation between acute renal failure and risk of mortality in the intensive care unit in 270 critically ill patients with COVID-19. This study in question was a significance/hypothesis testing study (<span class="elsevierStyleItalic">p</span><span class="elsevierStyleHsp" style=""></span><<span class="elsevierStyleHsp" style=""></span>0.05) based on calculating the odds ratio (OR).<a class="elsevierStyleCrossRef" href="#bib0005"><span class="elsevierStyleSup">1</span></a></p><p id="par0015" class="elsevierStylePara elsevierViewall">The importance replicating hypothesis testing studies (<span class="elsevierStyleItalic">p</span><span class="elsevierStyleHsp" style=""></span><<span class="elsevierStyleHsp" style=""></span>0.05) in clinical research cannot be overstressed, and researchers should be encouraged to test the reproducibility of conclusive study findings in future anaesthesiology and resuscitation using Bayesian inference.<a class="elsevierStyleCrossRefs" href="#bib0010"><span class="elsevierStyleSup">2,3</span></a></p><p id="par0020" class="elsevierStylePara elsevierViewall">This can be done using the Bayes factor (BF), which quantifies the degree to which the data are more likely under one model versus another (null hypothesis vs. alternative hypothesis).<a class="elsevierStyleCrossRefs" href="#bib0010"><span class="elsevierStyleSup">2,3</span></a> This allowed us to reanalyse the significant finding reported by Ferrando et al.<a class="elsevierStyleCrossRef" href="#bib0005"><span class="elsevierStyleSup">1</span></a> and quantify the degree to which the data support either the null hypothesis or the alternative hypothesis beyond the dichotomous interpretation of the rejection or acceptance of the null hypothesis.<a class="elsevierStyleCrossRefs" href="#bib0010"><span class="elsevierStyleSup">2,3</span></a> Statistical replication of significant findings through BF can strengthen the practical credibility of articles in this journal (clinical trials, interventions and treatments, among others) that is required when Bayesian inference reports conclusive (strong) or superior (FB<span class="elsevierStyleInf">10</span><span class="elsevierStyleHsp" style=""></span>><span class="elsevierStyleHsp" style=""></span>10) evidence, based on Jeffreys’ classification of BF values<a class="elsevierStyleCrossRef" href="#bib0020"><span class="elsevierStyleSup">4</span></a> as weak, moderate, strong and very strong (<a class="elsevierStyleCrossRef" href="#tbl0005">Table 1</a>).</p><elsevierMultimedia ident="tbl0005"></elsevierMultimedia><p id="par0025" class="elsevierStylePara elsevierViewall">The purpose of this letter is to report a simple example of Bayesian reanalysis to determine the degree of probative strength of the statistical hypotheses. Therefore, the OR (2,468) was first converted to an effect size (r) using the Lenhard and Lenhard online calculator,<a class="elsevierStyleCrossRef" href="#bib0025"><span class="elsevierStyleSup">5</span></a> which returned a value of r<span class="elsevierStyleHsp" style=""></span>=<span class="elsevierStyleHsp" style=""></span>0.242, and the sample size (270) was also defined for Bayesian replication.<a class="elsevierStyleCrossRef" href="#bib0010"><span class="elsevierStyleSup">2</span></a> This method considers 2 interpretations: BF<span class="elsevierStyleInf">10</span> (proving the alternative hypothesis) and BF<span class="elsevierStyleInf">01</span> (proving the null hypothesis), with a 95% confidence interval (CI).<a class="elsevierStyleCrossRefs" href="#bib0010"><span class="elsevierStyleSup">2,3</span></a> The BF results are: BF<span class="elsevierStyleInf">10</span><span class="elsevierStyleHsp" style=""></span>=<span class="elsevierStyleHsp" style=""></span>233 and BF<span class="elsevierStyleInf">01</span><span class="elsevierStyleHsp" style=""></span>=<span class="elsevierStyleHsp" style=""></span>0.004 with a 95% CI of 0.125–0.350, which supported the significant finding reported by Ferrando et al.<a class="elsevierStyleCrossRef" href="#bib0005"><span class="elsevierStyleSup">1</span></a> with very strong evidence in favour of the alternative hypothesis (correlation). Likewise, the size of the maximum BF (maxFB<span class="elsevierStyleInf">10</span><span class="elsevierStyleHsp" style=""></span>=<span class="elsevierStyleHsp" style=""></span>483.8) supports the robustness of the reported estimates.</p><p id="par0030" class="elsevierStylePara elsevierViewall">BF is a useful statistical method that can make a practical contribution to decision-making by confirming the conclusiveness of reported results.</p><span id="sec0005" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0005">Funding</span><p id="par0035" class="elsevierStylePara elsevierViewall">The authors declare that they have not received specific aid from agencies in the public sector, commercial sector or non-profit entities.</p></span><span id="sec0010" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0010">Conflict of interests</span><p id="par0040" class="elsevierStylePara elsevierViewall">The authors have no conflict of interest to declare.</p></span></span>" "textoCompletoSecciones" => array:1 [ "secciones" => array:3 [ 0 => array:2 [ "identificador" => "sec0005" "titulo" => "Funding" ] 1 => array:2 [ "identificador" => "sec0010" "titulo" => "Conflict of interests" ] 2 => array:1 [ "titulo" => "References" ] ] ] "pdfFichero" => "main.pdf" "tienePdf" => true "NotaPie" => array:1 [ 0 => array:2 [ "etiqueta" => "☆" "nota" => "<p class="elsevierStyleNotepara" id="npar0005">Please cite this article as: Ramos-Vera C, La inclusión del factor Bayes y la conversión del tamaño de efecto en la investigación en anestesiología y reanimación, Revista Española de Anestesiología y Reanimación. 2022;69:313–314.</p>" ] ] "multimedia" => array:1 [ 0 => array:8 [ "identificador" => "tbl0005" "etiqueta" => "Table 1" "tipo" => "MULTIMEDIATABLA" "mostrarFloat" => true "mostrarDisplay" => false "detalles" => array:1 [ 0 => array:3 [ "identificador" => "at0030" "detalle" => "Table " "rol" => "short" ] ] "tabla" => array:2 [ "leyenda" => "<p id="spar0010" class="elsevierStyleSimplePara elsevierViewall">Based on Jeffreys.<a class="elsevierStyleCrossRef" href="#bib0020"><span class="elsevierStyleSup">4</span></a></p>" "tablatextoimagen" => array:1 [ 0 => array:1 [ "tabla" => array:1 [ 0 => """ <table border="0" frame="\n \t\t\t\t\tvoid\n \t\t\t\t" class=""><tbody title="tbody"><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">>30 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Very strong \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Alternative hypothesis \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">10–30 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Strong \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Alternative hypothesis \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">3.1–10 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Moderate \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Alternative hypothesis \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">1.1–3 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Weak \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Alternative hypothesis \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">1 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">0 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">No evidence \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">0.3–0.99 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Weak \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Null hypothesis \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">0.3–0.1 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Moderate \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Null hypothesis \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">0.1–0.03 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Strong \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Null hypothesis \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t"><0.03 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Very strong \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Null hypothesis \t\t\t\t\t\t\n \t\t\t\t</td></tr></tbody></table> """ ] ] ] ] "descripcion" => array:1 [ "en" => "<p id="spar0005" class="elsevierStyleSimplePara elsevierViewall">Interpretation of Bayes factor values.</p>" ] ] ] "bibliografia" => array:2 [ "titulo" => "References" "seccion" => array:1 [ 0 => array:2 [ "identificador" => "bibs0005" "bibliografiaReferencia" => array:5 [ 0 => array:3 [ "identificador" => "bib0005" "etiqueta" => "1" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Características, evolución clínica y factores asociados a la mortalidad en UCI de los pacientes críticos infectados por SARS-CoV-2 en España: estudio prospectivo, de cohorte y multicéntrico" "autores" => array:1 [ 0 => array:2 [ "etal" => true "autores" => array:6 [ 0 => "C. 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