Supplemental Digital Content
1.
CPT and ICD-9 codes used in study
2.
Hierarchical model development and calculation of reliability
3.
Table of fixed effect odds ratios and between-hospital variance for each model
1
Supplemental Digital Content 1 - CPT and ICD-9 codes used in study
Colorectal procedures were identified using the following CPT codes:
44140, 44141, 44143, 44144, 44145, 44146, 44147, 44150, 44151, 44155, 44156, 44157, 44158, 44160,
44204, 44205, 44206, 44207, 44208, 44210, 44211, 44212, 45110, 45111, 45112, 45113, 45114, 45116,
45119, 45120, 45121, 45123, 45126, 45130, 45135, 45160, 45395, 45397, 45402, 45550
Postoperative diagnosis groups included the following ICD-9 codes:
Diagnosis group
ICD-9 codes
Diverticulitis
562.11, 562.13, 562.01, 562.03
Diverticulosis
562.10, 562.12, 562.1, 562, 562.00, 562.02
Fistula
596.1, 569.81, 619.1, 998.6, 565.1, 537.4, 619,
599.1, 619.8
Hemorrhage
578.9, 578.1, 569.85, 569.3, 578, 532.40, 534.40,
569.86
Infectious enteritis/colitis/peritonitis
003.0, 008.4, 008.45, 009.0, 009.1, 569.5, 540.1,
567.22, 540.0, 540.9, 567.9, 567.21, 567.29, 540,
542, 567.89, 541, 567, 567.31, 569.61
Inflammatory bowel disease (Ulcerative colitis and
555, 555.0, 555.1, 555.2, 555.9, 556, 556.0, 556.1,
Crohn’s disease)
556.2, 556.3, 556.4, 556.5, 556.6, 556.8, 556.9, 558,
558.1, 558.2, 558.3, 558.9, 567.82
Benign neoplasm
211.3, 235.2, 211.4, 230.3, 239.0, 569.0, 230.4,
238.1, 211.2, 239, 209.57, 215.5, 235.5, 229.8,
230.5, 209.52, 209.60, 211.1, 211.8, 227.0, 228.1,
229.9, 235.3, 238.79, 238.8, 239.7, 239.8, 209.50,
209.53, 209.69, 211.5, 211.7, 211.9, 214.2, 215.6,
217, 230, 235.4, 236.3, 238.9, 214.3, 209.51,
209.43, V12.72, 214.8
Malignant neoplasm
154.1, 153.6, 153.3, 153.4, 153.9, 154.0, 153.1,
153.0, 153.2, 153, 153.7, 153.8, 154, 154.8, 197.5,
153.5, 197.6, 209.03, 154.3, 154.2, 152.2, 197.4,
209.11, 158.0, 202.83, 198.89, 183.0, 202.80,
209.12, 152.9, 171.5, 151.8, 157.2, 197.7, 199.0,
199.1, 209.13, 259.2, 158.8, 196.2, 209.16, 151.9,
157.0, 158.9, 195.3, 198.6, 209.17, 152.8, 156.0,
157, 159.0, 171.9, 174.9, 182.0, 195.2, 200.70,
209.00, 209.15, 150.9, 151.2, 151.3, 151.4, 152.0,
156.1, 157.1, 158, 159.9, 170.6, 171.6, 179, 184.4,
185, 188.9, 189.0, 194.0, 197.8, 198.5, 200.10,
202.03, 203.80, 209, 209.10, 209.29, 209.72, 150.2,
151, 151.6, 152, 152.1, 155, 155.0, 157.9, 161.1,
162.3, 162.9, 172.5, 173.9, 174, 182, 188, 188.8,
193, 195.8, 196.5, 198.82, 200.03, 200.2, 200.23,
200.33, 200.43, 200.7, 202.13, 202.8, 202.87,
202.93, 209.0, 209.01, 209.14, 209.27, 209.3,
209.30, 209.79
Obstruction/perforation
560.0, 560.8, 560.81, 560.89, 560.9, 569.83, 560.2,
552.21, 560, 550.10, 552.8, 552.1, 552.2, 550.0,
551.21, 552.29, 532.50, 537.3, 550.00, 550.11,
551.2, 552.00, 552.20, 532.10, 551.1, 551.8, 552.3,
552.9, 532.11
Rectal prolapse
569.1
Vascular insufficiency
557.0, 557.1, 557.9, 557
2
Supplemental Digital Content 2 – Hierarchical model development and calculation of reliability
John L. Adams, Ph.D.
We developed hierarchical multivariate logistic models for superficial SSI, deep/organ-space SSI,
and “any SSI,” with hospital entered as a normally distributed random intercept:
 
 pij 
   0i  1 X ij
ln 
1 p 
ij 


pij is the probability that person j in hospital i will have an infection. X ij is a vector of person level

covariates. 1 is a vector of fixed regression coefficients corresponding to the person level covariates in

X ij (e.g. demographics).  0 i is a hospital level random intercept:
Where
0i ~ Norma l(0 , l2ogodds)
Where
 0 is the mean of the distribution of hospital intercepts and  lo2 go d d sis the hospital-to-hospital
random effect in the log odds scale.
2
 log
 odds
is a quantity of fundamental interest in reliability calculations
The hospital-to-hospital random effect is in the log odds scale. There is a choice to be made
whether to calculate the reliability in the log odds or the probability scale. Both approaches have
advantages. The log odds scale is the natural scale for logistic regression. The probability scale is the scale
where the hospital profiles will most likely be reported. In the delta calculation reported below you can see
that the reliability will be roughly the same if  isn’t so large that it spans substantial non-linearity in the
logistic transform. We pursue reliability in the probability scale here since it is a better fit to the hospital
profiling policy problem.
2
The basic definition of reliability is:
Reliability=
2
 2   i2
 i2 is the hospital specific sampling error variance for the infection rate. The binomial distribution
ˆ i (1 pˆ i )ni where p̂i is
used to represent the number of infections has a mean of p̂i ni and a variance of p
Where
the proportion of cases at hospital i that have an infection. The rate rather than the total number of
infections is the quantity of interest here so we will use the variance of the rate estimate, the squared
standard error of the rate estimate:
ˆi2  pˆi (1 pˆi ) / ni s
Since our estimate is in the log odds scale we need to apply a delta method calculation to transform
2
 log
 odds
to the probability scale. The expit function ( p 
ex
) transforms from the log odds scale to
1 ex
the probability scale. We need the derivative of this function which is p*(1-p). Since this is the multiplier
to transform
 log  odds
we must square it to apply to
2
2
 log
 odds so our estimate of 
  p * (1  p) 
2
2
2
squared will be:
2
l ogodds
Where p is the probability where the transformation occurs. For p we use the infection rate for the whole
dataset. Note that the inverse of this transformation could be applied to the hospital specific sampling
variances to develop a reliability estimate in the log odds scale.
3
Supplemental Digital Content 3:
Table of fixed effect odds ratios and between-hospital variance for each model
Deep/Organ-space SSI
Superficial SSI Model
“Any SSI” Model
Model
Odds
Odds Ratio
p-value
p-value
Odds Ratio
p-value
Ratio
Intercept
0.041
<0.001
0.037
<0.001
0.083
<0.001
Procedure: (vs. Open colectomy)
Ref
Ref
ref
Laparoscopic colectomy
0.582
<0.001
0.613
<0.001
0.589
<0.001
Open proctectomy
1.207
0.059
1.290
0.014
1.265
0.002
Laparoscopic proctectomy
0.639
0.096
0.962
0.868
0.766
0.153
Diagnosis: (vs. Benign Neoplasm)
Ref
Ref
ref
Malignant neoplasm
1.295
0.007
1.321
0.022
1.321
<0.001
Diverticulitis
1.686
<0.001
1.137
0.344
1.467
<0.001
Diverticulosis
1.634
0.003
1.153
0.518
1.462
0.007
Ulcerative colitis/Crohns
1.323
0.042
1.986
<0.001
1.631
<0.001
Obstruction/perforation
1.649
<0.001
1.549
0.003
1.654
<0.001
Vascular insufficiency
0.968
0.887
1.101
0.672
1.037
0.827
Fistula
1.518
0.016
2.018
<0.001
1.756
<0.001
Rectal prolapse
0.157
<0.001
0.599
0.081
0.320
<0.001
Infectious colitis/peritonitis
1.184
0.418
1.338
0.163
1.254
0.141
Hemorrhage
3.000
<0.001
2.059
0.027
2.875
<0.001
Other
1.125
0.380
1.751
<0.001
1.413
0.001
Age: (vs. <55 years)
Ref
Ref
Ref
1.087
0.224
0.759
<0.001
0.933
0.196
55-64
65-74
1.052
0.495
0.639
<0.001
0.834
0.002
75-84
0.916
0.318
0.582
<0.001
0.736
<0.001
0.795
0.075
0.480
<0.001
0.622
<0.001
>84
Male
0.982
0.715
1.201
0.001
1.079
0.051
Race: (vs. White)
Ref
Ref
Ref
Black
0.933
0.439
0.921
0.399
0.924
0.256
Other
1.052
0.570
1.375
<0.001
1.213
0.004
Hispanic (vs. Non-Hispanic)
1.134
0.285
0.928
0.583
1.055
0.568
Admission source (vs. Home)
Ref
Ref
Ref
Acute care hospital
0.783
0.124
0.969
0.829
0.858
0.179
Chronic care facility
1.062
0.751
0.800
0.288
0.942
0.682
Other
1.417
0.245
0.944
0.878
1.286
0.304
BMI (vs. Normal 18.5-24.9)
Ref
Ref
Ref
Underweight (<18.5)
0.883
0.452
1.057
0.699
0.975
0.823
Overweight (25-29.9)
1.429
<0.001
1.017
0.807
1.234
<0.001
Class I obesity (30-34.9)
1.741
<0.001
1.197
0.026
1.509
<0.001
Class II obesity (35-39.9)
2.205
<0.001
1.307
0.013
1.851
<0.001
2.484
<0.001
1.527
<0.001
2.114
<0.001
Class III obesity (40)
Functional status (vs. Independent)
Ref
Ref
Ref
Partially dependent
1.088
0.402
1.370
0.002
1.253
0.003
Totally dependent
0.898
0.555
0.959
0.812
0.947
0.679
Smoker
1.069
0.292
1.143
0.047
1.109
0.035
Alcohol use
1.253
0.061
1.338
0.021
1.313
0.004
Renal Failure
0.687
0.067
1.200
0.278
0.951
0.711
Diabetes (vs. None)
Ref
Ref
Ref
Oral medication
1.081
0.314
0.865
0.134
0.987
0.832
Insulin
1.061
0.581
0.846
0.186
0.945
0.514
Dyspnea (vs. None)
Ref
Ref
Ref
4
Moderate exertion
At rest
COPD
Pneumonia
Steroid Use
Bleeding disorder
Congestive heart failure
Hypertension
Myocardial infarction
Disseminated cancer
Weight loss
Chemotherapy
Radiotherapy
Preop blood transfusion
Preop Sepsis (vs. None/SIRS)
Sepsis
Septic shock
ASA class (vs. I and II)
Class III
Class IV and V
Wound class (vs. II)
Class III
Class IV
Emergency procedure
Between-hospital variance
(probability scale)
Between-hospital variance
(log odds scale)
1.165
1.142
1.163
0.707
0.926
1.008
0.954
1.003
0.791
0.953
0.850
0.733
0.898
0.877
Ref
0.687
0.546
Ref
1.254
1.080
Ref
1.204
1.060
0.818
0.061
0.466
0.129
0.287
0.459
0.939
0.834
0.957
0.403
0.694
0.161
0.140
0.425
0.637
0.003
0.008
<0.001
0.502
0.015
0.521
0.024
1.598 x 10-
1.032
0.974
1.102
0.747
1.198
0.998
0.586
1.086
1.683
1.510
0.986
0.993
1.434
1.354
Ref
1.351
1.201
Ref
1.339
1.115
Ref
1.306
1.420
0.819
0.747
0.884
0.390
0.279
0.062
0.988
0.062
0.195
0.022
<0.001
0.901
0.969
0.005
0.252
0.008
0.336
<0.001
0.374
0.001
<0.001
0.032
1.132
1.024
1.146
0.742
1.075
0.993
0.771
1.033
1.158
1.219
0.914
0.884
1.101
1.097
Ref
1.000
0.852
Ref
1.311
1.084
Ref
1.268
1.221
0.793
3.997 x
10-4
1.943 x 10-
3
0.312
0.128
0.145
5
3
0.060
0.861
0.085
0.165
0.337
0.936
0.156
0.460
0.437
0.025
0.288
0.380
0.332
0.650
0.998
0.294
<0.001
0.364
<0.001
0.004
0.001