Assessing the influence of after-hours surgery: concerns with the confounders and conclusion

IF 7.5 1区 医学 Q1 ANESTHESIOLOGY Anaesthesia Pub Date : 2025-03-09 DOI:10.1111/anae.16591
Kotaro Sakurai, Chikashi Takeda
{"title":"Assessing the influence of after-hours surgery: concerns with the confounders and conclusion","authors":"Kotaro Sakurai, Chikashi Takeda","doi":"10.1111/anae.16591","DOIUrl":null,"url":null,"abstract":"<p>Oh et al. [<span>1</span>] used a large sample size to analyse short-term complications and long-term outcomes of after-hours surgery, providing valuable insights into operating theatre management. The use of propensity scores to adjust for the higher likelihood of high-urgency patients and those with severe comorbidities being managed after-hours is commendable. However, critical potential confounders and analytical errors introduce complexities that hinder clear interpretation of the results.</p>\n<div>First, there are concerns regarding clinicopathological characteristics and their adjustment. As expected, emergency surgeries were performed more frequently after-hours. However, Table S5 reveals that, even after adjustment, there was a four-fold higher rate of emergency procedures after-hours (4.1% vs. 16.0%) [<span>1</span>]. The authors report that the absolute standardised mean difference was &gt;0.1 after adjustment, but our calculations using the following formula show that the absolute standardised mean difference for emergency surgery was 0.40 (<span data-altimg=\"/cms/asset/b4471c89-b539-472d-a509-d6dd18695275/anae16591-math-0001.png\"></span><mjx-container ctxtmenu_counter=\"3\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/anae16591-math-0001.png\"><mjx-semantics><mjx-mrow><mjx-msub data-semantic-children=\"2,8\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"ModifyingAbove p With ̂ Subscript italic after minus italic hours\" data-semantic-type=\"subscript\"><mjx-mover data-semantic-children=\"0,1\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mjx-over style=\"padding-bottom: 0.105em; padding-left: 0.335em; margin-bottom: -0.551em;\"><mjx-mo data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" style=\"width: 0px; margin-left: -0.278em;\"><mjx-c></mjx-c></mjx-mo></mjx-over><mjx-base><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-base></mjx-mover><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-children=\"3,4,5\" data-semantic-collapsed=\"(8 (c 6 7) 3 4 5)\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"text\" data-semantic-type=\"punctuated\" size=\"s\"><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"unknown\" data-semantic-type=\"text\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mtext><mjx-mo data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"unknown\" data-semantic-type=\"text\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mtext></mjx-mrow></mjx-script></mjx-msub></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00032409:media:anae16591:anae16591-math-0001\" display=\"inline\" location=\"graphic/anae16591-math-0001.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msub data-semantic-=\"\" data-semantic-children=\"2,8\" data-semantic-role=\"latinletter\" data-semantic-speech=\"ModifyingAbove p With ̂ Subscript italic after minus italic hours\" data-semantic-type=\"subscript\"><mover accent=\"true\" data-semantic-=\"\" data-semantic-children=\"0,1\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">p</mi><mo data-semantic-=\"\" data-semantic-parent=\"2\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" stretchy=\"true\">̂</mo></mover><mrow data-semantic-=\"\" data-semantic-children=\"3,4,5\" data-semantic-collapsed=\"(8 (c 6 7) 3 4 5)\" data-semantic-parent=\"9\" data-semantic-role=\"text\" data-semantic-type=\"punctuated\"><mtext data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic-parent=\"8\" data-semantic-role=\"unknown\" data-semantic-type=\"text\" mathvariant=\"italic\">after</mtext><mo data-semantic-=\"\" data-semantic-parent=\"8\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\">−</mo><mtext data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic-parent=\"8\" data-semantic-role=\"unknown\" data-semantic-type=\"text\" mathvariant=\"italic\">hours</mtext></mrow></msub></mrow>$$ {\\hat{p}}_{after- hours} $$</annotation></semantics></math></mjx-assistive-mml></mjx-container> and <span data-altimg=\"/cms/asset/22c24e70-1d16-48dc-a2b6-53088deca046/anae16591-math-0002.png\"></span><mjx-container ctxtmenu_counter=\"4\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/anae16591-math-0002.png\"><mjx-semantics><mjx-mrow><mjx-msub data-semantic-children=\"2,8\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"ModifyingAbove p With ̂ Subscript italic in minus italic hours\" data-semantic-type=\"subscript\"><mjx-mover data-semantic-children=\"0,1\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mjx-over style=\"padding-bottom: 0.105em; padding-left: 0.335em; margin-bottom: -0.551em;\"><mjx-mo data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" style=\"width: 0px; margin-left: -0.278em;\"><mjx-c></mjx-c></mjx-mo></mjx-over><mjx-base><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-base></mjx-mover><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-children=\"3,4,5\" data-semantic-collapsed=\"(8 (c 6 7) 3 4 5)\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"text\" data-semantic-type=\"punctuated\" size=\"s\"><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"unknown\" data-semantic-type=\"text\"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mtext><mjx-mo data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"unknown\" data-semantic-type=\"text\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mtext></mjx-mrow></mjx-script></mjx-msub></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00032409:media:anae16591:anae16591-math-0002\" display=\"inline\" location=\"graphic/anae16591-math-0002.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msub data-semantic-=\"\" data-semantic-children=\"2,8\" data-semantic-role=\"latinletter\" data-semantic-speech=\"ModifyingAbove p With ̂ Subscript italic in minus italic hours\" data-semantic-type=\"subscript\"><mover accent=\"true\" data-semantic-=\"\" data-semantic-children=\"0,1\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">p</mi><mo data-semantic-=\"\" data-semantic-parent=\"2\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" stretchy=\"true\">̂</mo></mover><mrow data-semantic-=\"\" data-semantic-children=\"3,4,5\" data-semantic-collapsed=\"(8 (c 6 7) 3 4 5)\" data-semantic-parent=\"9\" data-semantic-role=\"text\" data-semantic-type=\"punctuated\"><mtext data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic-parent=\"8\" data-semantic-role=\"unknown\" data-semantic-type=\"text\" mathvariant=\"italic\">in</mtext><mo data-semantic-=\"\" data-semantic-parent=\"8\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\">−</mo><mtext data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic-parent=\"8\" data-semantic-role=\"unknown\" data-semantic-type=\"text\" mathvariant=\"italic\">hours</mtext></mrow></msub></mrow>$$ {\\hat{p}}_{in- hours} $$</annotation></semantics></math></mjx-assistive-mml></mjx-container>, denoting the prevalence of the dichotomous variables in the after-hours and in-hours groups, respectively) [<span>2</span>]. <div><span><!--FIGURE-->\n<span data-altimg=\"/cms/asset/bfa7fd37-9dad-44f2-b657-8e8a59381ca6/anae16591-math-0003.png\"></span><mjx-container ctxtmenu_counter=\"5\" ctxtmenu_oldtabindex=\"1\" display=\"true\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" display=\"true\" location=\"graphic/anae16591-math-0003.png\" style=\"margin-left: 0px; margin-right: 0px;\"><mjx-semantics><mjx-mrow data-semantic-children=\"0,96\" data-semantic-content=\"1\" data-semantic- data-semantic-role=\"equality\" data-semantic-speech=\"d equals StartFraction left parenthesis ModifyingAbove p With ̂ Subscript italic after minus italic hours Baseline minus ModifyingAbove p With ̂ Subscript italic in minus italic hours Baseline right parenthesis Over StartRoot StartFraction ModifyingAbove p With ̂ Subscript italic after minus italic hours Baseline left parenthesis 1 minus ModifyingAbove p With ̂ Subscript italic after minus italic hours Baseline right parenthesis plus ModifyingAbove p With ̂ Subscript italic in minus italic hours Baseline left parenthesis 1 minus ModifyingAbove p With ̂ Subscript italic in minus italic hours Baseline right parenthesis Over 2 EndFraction EndRoot EndFraction\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"97\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"97\" data-semantic-role=\"equality\" data-semantic-type=\"relation\" rspace=\"5\" space=\"5\"><mjx-c></mjx-c></mjx-mo><mjx-mfrac data-semantic-children=\"28,95\" data-semantic- data-semantic-parent=\"97\" data-semantic-role=\"division\" data-semantic-type=\"fraction\"><mjx-frac type=\"d\"><mjx-num><mjx-nstrut type=\"d\"></mjx-nstrut><mjx-mrow data-semantic-children=\"25\" data-semantic-content=\"26,27\" data-semantic- data-semantic-parent=\"96\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"28\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"11,24\" data-semantic-content=\"13\" data-semantic- data-semantic-parent=\"28\" data-semantic-role=\"subtraction\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"4,10\" data-semantic- data-semantic-parent=\"25\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mover data-semantic-children=\"2,3\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mjx-over style=\"padding-bottom: 0.105em; padding-left: 0.335em; margin-bottom: -0.551em;\"><mjx-mo data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" style=\"width: 0px; margin-left: -0.278em;\"><mjx-c></mjx-c></mjx-mo></mjx-over><mjx-base><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-base></mjx-mover><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-children=\"5,6,7\" data-semantic-collapsed=\"(10 (c 8 9) 5 6 7)\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"text\" data-semantic-type=\"punctuated\" size=\"s\"><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"unknown\" data-semantic-type=\"text\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mtext><mjx-mo data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"unknown\" data-semantic-type=\"text\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mtext></mjx-mrow></mjx-script></mjx-msub><mjx-mspace style=\"width: 0.278em;\"></mjx-mspace><mjx-mo data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"25\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" rspace=\"4\" space=\"4\"><mjx-c></mjx-c></mjx-mo><mjx-mspace style=\"width: 0.278em;\"></mjx-mspace><mjx-msub data-semantic-children=\"17,23\" data-semantic- data-semantic-parent=\"25\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mover data-semantic-children=\"15,16\" data-semantic- data-semantic-parent=\"24\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mjx-over style=\"padding-bottom: 0.105em; padding-left: 0.335em; margin-bottom: -0.551em;\"><mjx-mo data-semantic- data-semantic-parent=\"17\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" style=\"width: 0px; margin-left: -0.278em;\"><mjx-c></mjx-c></mjx-mo></mjx-over><mjx-base><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"17\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-base></mjx-mover><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-children=\"18,19,20\" data-semantic-collapsed=\"(23 (c 21 22) 18 19 20)\" data-semantic- data-semantic-parent=\"24\" data-semantic-role=\"text\" data-semantic-type=\"punctuated\" size=\"s\"><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"23\" data-semantic-role=\"unknown\" data-semantic-type=\"text\"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mtext><mjx-mo data-semantic- data-semantic-parent=\"23\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"23\" data-semantic-role=\"unknown\" data-semantic-type=\"text\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mtext></mjx-mrow></mjx-script></mjx-msub></mjx-mrow><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"28\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo></mjx-mrow></mjx-num><mjx-dbox><mjx-dtable><mjx-line type=\"d\"></mjx-line><mjx-row><mjx-den><mjx-dstrut type=\"d\"></mjx-dstrut><mjx-msqrt data-semantic-children=\"94\" data-semantic- data-semantic-parent=\"96\" data-semantic-role=\"unknown\" data-semantic-type=\"sqrt\"><mjx-sqrt><mjx-surd><mjx-mo><mjx-c></mjx-c></mjx-mo></mjx-surd><mjx-box style=\"padding-top: 0.141em;\"><mjx-mfrac data-semantic-children=\"92,93\" data-semantic- data-semantic-parent=\"95\" data-semantic-role=\"division\" data-semantic-type=\"fraction\"><mjx-frac><mjx-num><mjx-nstrut></mjx-nstrut><mjx-mrow data-semantic-children=\"89,91\" data-semantic-content=\"58\" data-semantic- data-semantic-parent=\"94\" data-semantic-role=\"addition\" data-semantic-type=\"infixop\" size=\"s\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"38,56\" data-semantic-content=\"88\" data-semantic- data-semantic-parent=\"92\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"31,37\" data-semantic- data-semantic-parent=\"89\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mover data-semantic-children=\"29,30\" data-semantic- data-semantic-parent=\"38\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mjx-over style=\"padding-bottom: 0.105em; padding-left: 0.335em; margin-bottom: -0.551em;\"><mjx-mo data-semantic- data-semantic-parent=\"31\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" style=\"width: 0px; margin-left: -0.278em;\"><mjx-c></mjx-c></mjx-mo></mjx-over><mjx-base><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"31\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-base></mjx-mover><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-children=\"32,33,34\" data-semantic-collapsed=\"(37 (c 35 36) 32 33 34)\" data-semantic- data-semantic-parent=\"38\" data-semantic-role=\"text\" data-semantic-type=\"punctuated\" size=\"s\"><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"37\" data-semantic-role=\"unknown\" data-semantic-type=\"text\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mtext><mjx-mo data-semantic- data-semantic-parent=\"37\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"37\" data-semantic-role=\"unknown\" data-semantic-type=\"text\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mtext></mjx-mrow></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"89\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"53\" data-semantic-content=\"54,55\" data-semantic- data-semantic-parent=\"89\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"56\" data-semantic-role=\"open\" data-semantic-type=\"fence\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"39,52\" data-semantic-content=\"41\" data-semantic- data-semantic-parent=\"56\" data-semantic-role=\"subtraction\" data-semantic-type=\"infixop\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"53\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn><mjx-mspace style=\"width: 0.278em;\"></mjx-mspace><mjx-mo data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"53\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" rspace=\"1\" space=\"1\"><mjx-c></mjx-c></mjx-mo><mjx-mspace style=\"width: 0.278em;\"></mjx-mspace><mjx-msub data-semantic-children=\"45,51\" data-semantic- data-semantic-parent=\"53\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mover data-semantic-children=\"43,44\" data-semantic- data-semantic-parent=\"52\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mjx-over style=\"padding-bottom: 0.105em; padding-left: 0.335em; margin-bottom: -0.551em;\"><mjx-mo data-semantic- data-semantic-parent=\"45\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" style=\"width: 0px; margin-left: -0.278em;\"><mjx-c></mjx-c></mjx-mo></mjx-over><mjx-base><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"45\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-base></mjx-mover><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-children=\"46,47,48\" data-semantic-collapsed=\"(51 (c 49 50) 46 47 48)\" data-semantic- data-semantic-parent=\"52\" data-semantic-role=\"text\" data-semantic-type=\"punctuated\" size=\"s\"><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"51\" data-semantic-role=\"unknown\" data-semantic-type=\"text\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mtext><mjx-mo data-semantic- data-semantic-parent=\"51\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"51\" data-semantic-role=\"unknown\" data-semantic-type=\"text\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mtext></mjx-mrow></mjx-script></mjx-msub></mjx-mrow><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"56\" data-semantic-role=\"close\" data-semantic-type=\"fence\"><mjx-c></mjx-c></mjx-mo></mjx-mrow></mjx-mrow><mjx-mspace style=\"width: 0.278em;\"></mjx-mspace><mjx-mo data-semantic- data-semantic-operator=\"infixop,+\" data-semantic-parent=\"92\" data-semantic-role=\"addition\" data-semantic-type=\"operator\" rspace=\"1\" space=\"1\"><mjx-c></mjx-c></mjx-mo><mjx-mspace style=\"width: 0.278em;\"></mjx-mspace><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"69,87\" data-semantic-content=\"90\" data-semantic- data-semantic-parent=\"92\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"62,68\" data-semantic- data-semantic-parent=\"91\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mover data-semantic-children=\"60,61\" data-semantic- data-semantic-parent=\"69\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mjx-over style=\"padding-bottom: 0.105em; padding-left: 0.335em; margin-bottom: -0.551em;\"><mjx-mo data-semantic- data-semantic-parent=\"62\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" style=\"width: 0px; margin-left: -0.278em;\"><mjx-c></mjx-c></mjx-mo></mjx-over><mjx-base><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"62\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-base></mjx-mover><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-children=\"63,64,65\" data-semantic-collapsed=\"(68 (c 66 67) 63 64 65)\" data-semantic- data-semantic-parent=\"69\" data-semantic-role=\"text\" data-semantic-type=\"punctuated\" size=\"s\"><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"68\" data-semantic-role=\"unknown\" data-semantic-type=\"text\"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mtext><mjx-mo data-semantic- data-semantic-parent=\"68\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"68\" data-semantic-role=\"unknown\" data-semantic-type=\"text\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mtext></mjx-mrow></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"91\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"84\" data-semantic-content=\"85,86\" data-semantic- data-semantic-parent=\"91\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"87\" data-semantic-role=\"open\" data-semantic-type=\"fence\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"70,83\" data-semantic-content=\"72\" data-semantic- data-semantic-parent=\"87\" data-semantic-role=\"subtraction\" data-semantic-type=\"infixop\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"84\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn><mjx-mspace style=\"width: 0.278em;\"></mjx-mspace><mjx-mo data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"84\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" rspace=\"1\" space=\"1\"><mjx-c></mjx-c></mjx-mo><mjx-mspace style=\"width: 0.278em;\"></mjx-mspace><mjx-msub data-semantic-children=\"76,82\" data-semantic- data-semantic-parent=\"84\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mover data-semantic-children=\"74,75\" data-semantic- data-semantic-parent=\"83\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mjx-over style=\"padding-bottom: 0.105em; padding-left: 0.335em; margin-bottom: -0.551em;\"><mjx-mo data-semantic- data-semantic-parent=\"76\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" style=\"width: 0px; margin-left: -0.278em;\"><mjx-c></mjx-c></mjx-mo></mjx-over><mjx-base><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"76\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-base></mjx-mover><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-children=\"77,78,79\" data-semantic-collapsed=\"(82 (c 80 81) 77 78 79)\" data-semantic- data-semantic-parent=\"83\" data-semantic-role=\"text\" data-semantic-type=\"punctuated\" size=\"s\"><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"82\" data-semantic-role=\"unknown\" data-semantic-type=\"text\"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mtext><mjx-mo data-semantic- data-semantic-parent=\"82\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"82\" data-semantic-role=\"unknown\" data-semantic-type=\"text\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mtext></mjx-mrow></mjx-script></mjx-msub></mjx-mrow><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"87\" data-semantic-role=\"close\" data-semantic-type=\"fence\"><mjx-c></mjx-c></mjx-mo></mjx-mrow></mjx-mrow></mjx-mrow></mjx-num><mjx-dbox><mjx-dtable><mjx-line></mjx-line><mjx-row><mjx-den><mjx-dstrut></mjx-dstrut><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"94\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c></mjx-c></mjx-mn></mjx-den></mjx-row></mjx-dtable></mjx-dbox></mjx-frac></mjx-mfrac></mjx-box></mjx-sqrt></mjx-msqrt></mjx-den></mjx-row></mjx-dtable></mjx-dbox></mjx-frac></mjx-mfrac></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"block\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00032409:media:anae16591:anae16591-math-0003\" display=\"block\" location=\"graphic/anae16591-math-0003.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-children=\"0,96\" data-semantic-content=\"1\" data-semantic-role=\"equality\" data-semantic-speech=\"d equals StartFraction left parenthesis ModifyingAbove p With ̂ Subscript italic after minus italic hours Baseline minus ModifyingAbove p With ̂ Subscript italic in minus italic hours Baseline right parenthesis Over StartRoot StartFraction ModifyingAbove p With ̂ Subscript italic after minus italic hours Baseline left parenthesis 1 minus ModifyingAbove p With ̂ Subscript italic after minus italic hours Baseline right parenthesis plus ModifyingAbove p With ̂ Subscript italic in minus italic hours Baseline left parenthesis 1 minus ModifyingAbove p With ̂ Subscript italic in minus italic hours Baseline right parenthesis Over 2 EndFraction EndRoot EndFraction\" data-semantic-type=\"relseq\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"97\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">d</mi><mo data-semantic-=\"\" data-semantic-operator=\"relseq,=\" data-semantic-parent=\"97\" data-semantic-role=\"equality\" data-semantic-type=\"relation\" linebreak=\"goodbreak\">=</mo><mfrac data-semantic-=\"\" data-semantic-children=\"28,95\" data-semantic-parent=\"97\" data-semantic-role=\"division\" data-semantic-type=\"fraction\"><mrow data-semantic-=\"\" data-semantic-children=\"25\" data-semantic-content=\"26,27\" data-semantic-parent=\"96\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"fenced\" data-semantic-parent=\"28\" data-semantic-role=\"open\" data-semantic-type=\"fence\">(</mo><mrow data-semantic-=\"\" data-semantic-children=\"11,24\" data-semantic-content=\"13\" data-semantic-parent=\"28\" data-semantic-role=\"subtraction\" data-semantic-type=\"infixop\"><msub data-semantic-=\"\" data-semantic-children=\"4,10\" data-semantic-parent=\"25\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mover accent=\"true\" data-semantic-=\"\" data-semantic-children=\"2,3\" data-semantic-parent=\"11\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">p</mi><mo data-semantic-=\"\" data-semantic-parent=\"4\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" stretchy=\"true\">̂</mo></mover><mrow data-semantic-=\"\" data-semantic-children=\"5,6,7\" data-semantic-collapsed=\"(10 (c 8 9) 5 6 7)\" data-semantic-parent=\"11\" data-semantic-role=\"text\" data-semantic-type=\"punctuated\"><mtext data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic-parent=\"10\" data-semantic-role=\"unknown\" data-semantic-type=\"text\" mathvariant=\"italic\">after</mtext><mo data-semantic-=\"\" data-semantic-parent=\"10\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\">−</mo><mtext data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic-parent=\"10\" data-semantic-role=\"unknown\" data-semantic-type=\"text\" mathvariant=\"italic\">hours</mtext></mrow></msub><mspace width=\"0.277778em\"></mspace><mo data-semantic-=\"\" data-semantic-operator=\"infixop,−\" data-semantic-parent=\"25\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" linebreak=\"goodbreak\">−</mo><mspace width=\"0.277778em\"></mspace><msub data-semantic-=\"\" data-semantic-children=\"17,23\" data-semantic-parent=\"25\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mover accent=\"true\" data-semantic-=\"\" data-semantic-children=\"15,16\" data-semantic-parent=\"24\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"17\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">p</mi><mo data-semantic-=\"\" data-semantic-parent=\"17\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" stretchy=\"true\">̂</mo></mover><mrow data-semantic-=\"\" data-semantic-children=\"18,19,20\" data-semantic-collapsed=\"(23 (c 21 22) 18 19 20)\" data-semantic-parent=\"24\" data-semantic-role=\"text\" data-semantic-type=\"punctuated\"><mtext data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic-parent=\"23\" data-semantic-role=\"unknown\" data-semantic-type=\"text\" mathvariant=\"italic\">in</mtext><mo data-semantic-=\"\" data-semantic-parent=\"23\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\">−</mo><mtext data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic-parent=\"23\" data-semantic-role=\"unknown\" data-semantic-type=\"text\" mathvariant=\"italic\">hours</mtext></mrow></msub></mrow><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"fenced\" data-semantic-parent=\"28\" data-semantic-role=\"close\" data-semantic-type=\"fence\">)</mo></mrow><msqrt data-semantic-=\"\" data-semantic-children=\"94\" data-semantic-parent=\"96\" data-semantic-role=\"unknown\" data-semantic-type=\"sqrt\"><mfrac data-semantic-=\"\" data-semantic-children=\"92,93\" data-semantic-parent=\"95\" data-semantic-role=\"division\" data-semantic-type=\"fraction\"><mrow data-semantic-=\"\" data-semantic-children=\"89,91\" data-semantic-content=\"58\" data-semantic-parent=\"94\" data-semantic-role=\"addition\" data-semantic-type=\"infixop\"><mrow data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"38,56\" data-semantic-content=\"88\" data-semantic-parent=\"92\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><msub data-semantic-=\"\" data-semantic-children=\"31,37\" data-semantic-parent=\"89\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mover accent=\"true\" data-semantic-=\"\" data-semantic-children=\"29,30\" data-semantic-parent=\"38\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"31\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">p</mi><mo data-semantic-=\"\" data-semantic-parent=\"31\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" stretchy=\"true\">̂</mo></mover><mrow data-semantic-=\"\" data-semantic-children=\"32,33,34\" data-semantic-collapsed=\"(37 (c 35 36) 32 33 34)\" data-semantic-parent=\"38\" data-semantic-role=\"text\" data-semantic-type=\"punctuated\"><mtext data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic-parent=\"37\" data-semantic-role=\"unknown\" data-semantic-type=\"text\" mathvariant=\"italic\">after</mtext><mo data-semantic-=\"\" data-semantic-parent=\"37\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\">−</mo><mtext data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic-parent=\"37\" data-semantic-role=\"unknown\" data-semantic-type=\"text\" mathvariant=\"italic\">hours</mtext></mrow></msub><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"89\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\">⁢</mo><mrow data-semantic-=\"\" data-semantic-children=\"53\" data-semantic-content=\"54,55\" data-semantic-parent=\"89\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"fenced\" data-semantic-parent=\"56\" data-semantic-role=\"open\" data-semantic-type=\"fence\">(</mo><mrow data-semantic-=\"\" data-semantic-children=\"39,52\" data-semantic-content=\"41\" data-semantic-parent=\"56\" data-semantic-role=\"subtraction\" data-semantic-type=\"infixop\"><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"53\" data-semantic-role=\"integer\" data-semantic-type=\"number\">1</mn><mspace width=\"0.277778em\"></mspace><mo data-semantic-=\"\" data-semantic-operator=\"infixop,−\" data-semantic-parent=\"53\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" linebreak=\"goodbreak\">−</mo><mspace width=\"0.277778em\"></mspace><msub data-semantic-=\"\" data-semantic-children=\"45,51\" data-semantic-parent=\"53\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mover accent=\"true\" data-semantic-=\"\" data-semantic-children=\"43,44\" data-semantic-parent=\"52\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"45\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">p</mi><mo data-semantic-=\"\" data-semantic-parent=\"45\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" stretchy=\"true\">̂</mo></mover><mrow data-semantic-=\"\" data-semantic-children=\"46,47,48\" data-semantic-collapsed=\"(51 (c 49 50) 46 47 48)\" data-semantic-parent=\"52\" data-semantic-role=\"text\" data-semantic-type=\"punctuated\"><mtext data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic-parent=\"51\" data-semantic-role=\"unknown\" data-semantic-type=\"text\" mathvariant=\"italic\">after</mtext><mo data-semantic-=\"\" data-semantic-parent=\"51\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\">−</mo><mtext data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic-parent=\"51\" data-semantic-role=\"unknown\" data-semantic-type=\"text\" mathvariant=\"italic\">hours</mtext></mrow></msub></mrow><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"fenced\" data-semantic-parent=\"56\" data-semantic-role=\"close\" data-semantic-type=\"fence\">)</mo></mrow></mrow><mspace width=\"0.277778em\"></mspace><mo data-semantic-=\"\" data-semantic-operator=\"infixop,+\" data-semantic-parent=\"92\" data-semantic-role=\"addition\" data-semantic-type=\"operator\">+</mo><mspace width=\"0.277778em\"></mspace><mrow data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"69,87\" data-semantic-content=\"90\" data-semantic-parent=\"92\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><msub data-semantic-=\"\" data-semantic-children=\"62,68\" data-semantic-parent=\"91\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mover accent=\"true\" data-semantic-=\"\" data-semantic-children=\"60,61\" data-semantic-parent=\"69\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"62\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">p</mi><mo data-semantic-=\"\" data-semantic-parent=\"62\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" stretchy=\"true\">̂</mo></mover><mrow data-semantic-=\"\" data-semantic-children=\"63,64,65\" data-semantic-collapsed=\"(68 (c 66 67) 63 64 65)\" data-semantic-parent=\"69\" data-semantic-role=\"text\" data-semantic-type=\"punctuated\"><mtext data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic-parent=\"68\" data-semantic-role=\"unknown\" data-semantic-type=\"text\" mathvariant=\"italic\">in</mtext><mo data-semantic-=\"\" data-semantic-parent=\"68\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\">−</mo><mtext data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic-parent=\"68\" data-semantic-role=\"unknown\" data-semantic-type=\"text\" mathvariant=\"italic\">hours</mtext></mrow></msub><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"91\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\">⁢</mo><mrow data-semantic-=\"\" data-semantic-children=\"84\" data-semantic-content=\"85,86\" data-semantic-parent=\"91\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"fenced\" data-semantic-parent=\"87\" data-semantic-role=\"open\" data-semantic-type=\"fence\">(</mo><mrow data-semantic-=\"\" data-semantic-children=\"70,83\" data-semantic-content=\"72\" data-semantic-parent=\"87\" data-semantic-role=\"subtraction\" data-semantic-type=\"infixop\"><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"84\" data-semantic-role=\"integer\" data-semantic-type=\"number\">1</mn><mspace width=\"0.277778em\"></mspace><mo data-semantic-=\"\" data-semantic-operator=\"infixop,−\" data-semantic-parent=\"84\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" linebreak=\"goodbreak\">−</mo><mspace width=\"0.277778em\"></mspace><msub data-semantic-=\"\" data-semantic-children=\"76,82\" data-semantic-parent=\"84\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mover accent=\"true\" data-semantic-=\"\" data-semantic-children=\"74,75\" data-semantic-parent=\"83\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"76\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">p</mi><mo data-semantic-=\"\" data-semantic-parent=\"76\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" stretchy=\"true\">̂</mo></mover><mrow data-semantic-=\"\" data-semantic-children=\"77,78,79\" data-semantic-collapsed=\"(82 (c 80 81) 77 78 79)\" data-semantic-parent=\"83\" data-semantic-role=\"text\" data-semantic-type=\"punctuated\"><mtext data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic-parent=\"82\" data-semantic-role=\"unknown\" data-semantic-type=\"text\" mathvariant=\"italic\">in</mtext><mo data-semantic-=\"\" data-semantic-parent=\"82\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\">−</mo><mtext data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"italic\" data-semantic-parent=\"82\" data-semantic-role=\"unknown\" data-semantic-type=\"text\" mathvariant=\"italic\">hours</mtext></mrow></msub></mrow><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"fenced\" data-semantic-parent=\"87\" data-semantic-role=\"close\" data-semantic-type=\"fence\">)</mo></mrow></mrow></mrow><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"94\" data-semantic-role=\"integer\" data-semantic-type=\"number\">2</mn></mfrac></msqrt></mfrac></mrow>$$ d=\\frac{\\left({\\hat{p}}_{after- hours}\\kern0.277778em -\\kern0.277778em {\\hat{p}}_{in- hours}\\right)}{\\sqrt{\\frac{{\\hat{p}}_{after- hours}\\left(1\\kern0.277778em -\\kern0.277778em {\\hat{p}}_{after- hours}\\right)\\kern0.277778em +\\kern0.277778em {\\hat{p}}_{in- hours}\\left(1\\kern0.277778em -\\kern0.277778em {\\hat{p}}_{in- hours}\\right)}{2}}} $$</annotation></semantics></math></mjx-assistive-mml></mjx-container>\n</span><span></span></div>\n</div>\n<p>Given the well-established impact of emergency surgeries on patient outcomes [<span>3, 4</span>], it is likely that the increased frequency of emergency surgeries contributed to the poorer after-hours outcomes observed. Additional discrepancies between the exposure rates and absolute standardised mean difference results for other factors, such as solid organ transplantation or surgeries for severe trauma, highlight the need for further clarification. Table S5 includes the essential background factors for discussing the generalisability of the results [<span>1</span>]. We hope that these errors will be addressed.</p>\n<p>Second, the dataset lacks detailed information on the surgical procedures. Certain surgeries, particularly life-saving ones, are more likely to occur after-hours [<span>5</span>], which could lead to an overestimation of the association between after-hours surgery and increased 90-day and 1-year mortalities. The authors should consider identifying the most common surgeries performed in-hours and after-hours. If this is not feasible owing to database limitations, it should be explicitly acknowledged as a significant constraint.</p>\n<p>Finally, the conclusion, “<i>The results of our study serve as evidence to inform policy decisions on which surgeries should be performed after-hours, considering patient safety</i>”, may not apply to this patient group, which includes emergency surgeries. These, by nature, require immediate intervention regardless of the time of the day, making it challenging to derive policy recommendations based on this dataset. A more appropriate approach would be to analyse patient groups restricted to elective surgeries. As they can be scheduled flexibly, obtaining similar results in these cases would provide a stronger foundation for policy decisions. To address the concern regarding the influence of emergency surgeries on outcomes, an additional analysis could further strengthen the validity of the conclusions.</p>\n<p>We concur with the authors that their discussion on the impact of anaesthetist and surgeon fatigue, limited night-time resources and circadian rhythm effects is crucial for optimising surgical scheduling to improve patient safety. Fixing the errors and adding more analyses would strengthen this argument greatly.</p>","PeriodicalId":7742,"journal":{"name":"Anaesthesia","volume":"19 1","pages":""},"PeriodicalIF":7.5000,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Anaesthesia","FirstCategoryId":"3","ListUrlMain":"https://doi.org/10.1111/anae.16591","RegionNum":1,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ANESTHESIOLOGY","Score":null,"Total":0}
引用次数: 0

Abstract

Oh et al. [1] used a large sample size to analyse short-term complications and long-term outcomes of after-hours surgery, providing valuable insights into operating theatre management. The use of propensity scores to adjust for the higher likelihood of high-urgency patients and those with severe comorbidities being managed after-hours is commendable. However, critical potential confounders and analytical errors introduce complexities that hinder clear interpretation of the results.

First, there are concerns regarding clinicopathological characteristics and their adjustment. As expected, emergency surgeries were performed more frequently after-hours. However, Table S5 reveals that, even after adjustment, there was a four-fold higher rate of emergency procedures after-hours (4.1% vs. 16.0%) [1]. The authors report that the absolute standardised mean difference was >0.1 after adjustment, but our calculations using the following formula show that the absolute standardised mean difference for emergency surgery was 0.40 (p̂afterhours$$ {\hat{p}}_{after- hours} $$ and p̂inhours$$ {\hat{p}}_{in- hours} $$, denoting the prevalence of the dichotomous variables in the after-hours and in-hours groups, respectively) [2].
d=(p̂afterhoursp̂inhours)p̂afterhours(1p̂afterhours)+p̂inhours(1p̂inhours)2$$ d=\frac{\left({\hat{p}}_{after- hours}\kern0.277778em -\kern0.277778em {\hat{p}}_{in- hours}\right)}{\sqrt{\frac{{\hat{p}}_{after- hours}\left(1\kern0.277778em -\kern0.277778em {\hat{p}}_{after- hours}\right)\kern0.277778em +\kern0.277778em {\hat{p}}_{in- hours}\left(1\kern0.277778em -\kern0.277778em {\hat{p}}_{in- hours}\right)}{2}}} $$

Given the well-established impact of emergency surgeries on patient outcomes [3, 4], it is likely that the increased frequency of emergency surgeries contributed to the poorer after-hours outcomes observed. Additional discrepancies between the exposure rates and absolute standardised mean difference results for other factors, such as solid organ transplantation or surgeries for severe trauma, highlight the need for further clarification. Table S5 includes the essential background factors for discussing the generalisability of the results [1]. We hope that these errors will be addressed.

Second, the dataset lacks detailed information on the surgical procedures. Certain surgeries, particularly life-saving ones, are more likely to occur after-hours [5], which could lead to an overestimation of the association between after-hours surgery and increased 90-day and 1-year mortalities. The authors should consider identifying the most common surgeries performed in-hours and after-hours. If this is not feasible owing to database limitations, it should be explicitly acknowledged as a significant constraint.

Finally, the conclusion, “The results of our study serve as evidence to inform policy decisions on which surgeries should be performed after-hours, considering patient safety”, may not apply to this patient group, which includes emergency surgeries. These, by nature, require immediate intervention regardless of the time of the day, making it challenging to derive policy recommendations based on this dataset. A more appropriate approach would be to analyse patient groups restricted to elective surgeries. As they can be scheduled flexibly, obtaining similar results in these cases would provide a stronger foundation for policy decisions. To address the concern regarding the influence of emergency surgeries on outcomes, an additional analysis could further strengthen the validity of the conclusions.

We concur with the authors that their discussion on the impact of anaesthetist and surgeon fatigue, limited night-time resources and circadian rhythm effects is crucial for optimising surgical scheduling to improve patient safety. Fixing the errors and adding more analyses would strengthen this argument greatly.

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来源期刊
Anaesthesia
Anaesthesia 医学-麻醉学
CiteScore
21.20
自引率
9.30%
发文量
300
审稿时长
6 months
期刊介绍: The official journal of the Association of Anaesthetists is Anaesthesia. It is a comprehensive international publication that covers a wide range of topics. The journal focuses on general and regional anaesthesia, as well as intensive care and pain therapy. It includes original articles that have undergone peer review, covering all aspects of these fields, including research on equipment.
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