Table 3

Minimum volume threshold estimation and assessment of population impact

Logistic regression coefficients of hospital volumeVARL Minimum volume threshold (95% CI)Average mortality in populationAdjusted mortality if volume ≥ VARL
(95% CI)
Population-based risk difference (95% CI)PIN Population impact number (95% CI)
Simple modelFull model
βpβp
Common emergency conditions
 Acute myocardial infarction−0.0003<0.001−0.0003<0.001309 (288 to 330)9.8%9.1% (9.0 to 9.2)0.7% (0.7 to 0.8)137 (127 to 149)
 Heart failure−0.00010.0010.00000.3588.9%
 Ischaemic stroke−0.00020.0000.00000.0256.9%
 Pneumonia0.00000.0030.0000<0.00111.6%
 Chronic obstructive pulmonary disease−0.00030.039−0.00020.026271 (240 to 301)4.2%3.6% (3.5 to 3.6)0.6% (0.5 to 0.6)170 (158 to 185)
 Hip fracture0.00000.1380.00000.8285.5%
Elective heart and thoracic surgery
 Isolated surgical aortic valve replacement−0.00140.001−0.00100.039147 (111 to 182)2.6%2.4% (2.2 to 2.6)0.2% (0.0 to 0.3)516 (288 to 2589)
 Transcatheter aortic valve replacement−0.0024<0.001−0.0017<0.001157 (142 to 171)6.6%5.8% (5.5 to 6.2)0.8% (0.5 to 1.0)133 (101 to 193)
 Isolated coronary artery bypass graft−0.0007<0.001−0.00030.024475 (430 to 521)2.1%2.0% (1.9 to 2.1)0.2% (0.1 to 0.2)658 (445 to 1271)
 Partial lung resection for carcinoma−0.0034<0.001−0.0025<0.001108 (95 to 120)2.9%2.3% (2.1 to 2.5)0.6% (0.5 to 0.7)168 (137 to 217)
Elective major visceral surgery
 Colorectal resection for carcinoma−0.0023<0.001−0.0014<0.00182 (76 to 88)6.0%5.4% (5.3 to 5.5)0.5% (0.4 to 0.6)197 (167 to 241)
 Colorectal resection for diverticulosis−0.0049<0.001−0.00250.00344 (38 to 49)3.5%3.2% (3.1 to 3.4)0.3% (0.2 to 0.4)364 (269 to 564)
 Total nephrectomy for carcinoma−0.00320.012−0.00290.04740 (24 to 56)2.1%1.9% (1.7 to 2.0)0.2% (0.1 to 0.3)459 (295 to 1056)
 Cystectomy for carcinoma−0.0054<0.001−0.0055<0.00131 (23 to 39)4.7%4.3% (4.0 to 4.6)0.4% (0.2 to 0.7)227 (150 to 480)
 Complex oesophageal surgery for carcinoma−0.0105<0.001−0.0111<0.00122 (17 to 28)8.5%6.3% (5.7 to 6.9)2.1% (1.6 to 2.6)47 (38 to 62)
 Pancreatic resection for carcinoma−0.0049<0.001−0.00450.00129 (21 to 37)8.8%6.6% (6.2 to 7.2)2.2% (1.7 to 2.6)46 (39 to 58)
Elective vascular surgery
 Surgical lower extremity revascularisation for atherosclerosis−0.0011<0.001−0.0007<0.001123 (102 to 144)3.0%2.8% (2.7 to 2.9)0.2% (0.1 to 0.3)561 (387 to 1024)
 Open repair of abdominal aortic aneurysm−0.0129<0.001−0.0112<0.00118 (14 to 23)6.0%5.0% (4.6 to 5.5)1.0% (0.6 to 1.3)104 (76 to 166)
 Endovascular repair of abdominal aortic aneurysm−0.00310.014−0.00280.0691.7%
 Carotid endarterectomy−0.0021<0.001−0.0014<0.00193 (69 to 116)0.87%0.81% (0.74 to 0.88)0.06% (0.01 to 0.11)1646 (886 to 12661)
Elective low-risk surgery
 Cholecystectomy for cholelithiasis−0.00030.008−0.00010.4250.43%
 Inguinal or femoral hernia repair−0.00190.009−0.00070.2120.09%
 Primary hip replacement for arthrosis or arthritis−0.0020<0.001−0.0013<0.001252 (227 to 278)0.17%0.13% (0.12 to 0.14)0.04% (0.03 to 0.05)2747 (2186 to 3701)
 Primary knee replacement for arthrosis or arthritis−0.0020<0.001−0.0016<0.001228 (190 to 265)0.10%0.07% (0.07 to 0.08)0.02% (0.01 to 0.03)4729 (3513 to 7269)
 Transurethral resection of prostate−0.00030.130−0.00010.7400.36%
  • Logistic regression coefficients of hospital volume relate to an increment of 1 case per year.

  • VARL, value of acceptable risk limit,27 calculated from the logistic regression coefficient of the simple model. It estimates a minimum volume threshold to achieve a risk of inhospital mortality which is lower than a predefined acceptable risk. The acceptable risk for each treatment was set to the average mortality in the respective patient population during the observation period. The population impact number PIN is the reciprocal of the difference between the average mortality in the patient population and the adjusted mortality in those patients treated by hospitals with volumes above the threshold (population-based risk difference). It can be interpreted as average number of the entire patient population among whom one death is attributable to treatment by a below-threshold volume hospital. Covariates used for risk adjustment are displayed in the online supplementary table 3.