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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

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 Crohn’s disease)

555, 555.0, 555.1, 555.2, 555.9, 556, 556.0, 556.1, 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

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:

ln ( ^{1− p}

^ij

^p

ij

) ^=β

⁰ⁱ

^{+ β}

¹

^{⃗ X}

^ij

Where

p

_ij is the probability that person j in hospital i will have an infection.

X ⃗

_ij is a vector of person level covariates.

β

₁ is a vector of fixed regression coefficients corresponding to the person level covariates in

X ⃗

_ij (e.g. demographics).

β

_0i is a hospital level random intercept:

β

_0i

~ Normal( β

₀

,τ

²_log−odds

)

Where

β

₀ is the mean of the distribution of hospital intercepts and

τ

²_log−odds is the hospital-to- hospital random effect in the log odds scale.

τ

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

τ

² 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.

The basic definition of reliability is:

Reliability=

τ

²

τ

²

+ σ

_i²

Where

σ

_i² is the hospital specific sampling error variance for the infection rate. The binomial distribution used to represent the number of infections has a mean of

^ p

_i

n

_i and a variance of

^ p

_i

( 1− ^ p

_i

) n

_{i where}

^ p

_i is 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:

σ ^

_i²

= ^ p

_i

( 1 − ^ p

_i

) /n

_i

s

Since our estimate is in the log odds scale we need to apply a delta method calculation to transform

τ

²_log−odds to the probability scale. The expit function (

p= e

^x

1 +e

^x ) transforms from the log odds scale to the probability scale. We need the derivative of this function which is p*(1-p). Since this is the multiplier to transform

τ

_log−odds we must square it to apply to

τ

²_log−odds so our estimate of τ² squared will be:

τ

²

= p

²

∗( 1−p )

²

τ

_log−odds²

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.

Supplemental Digital Content 3:

Table of fixed effect odds ratios and between-hospital variance for each model Superficial SSI Model Deep/Organ-space SSI

Model “Any SSI” Model

Odds Ratio p-value Odds

Ratio p-value Odds Ratio p-value

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

55-64 1.087 0.224 0.759 <0.001 0.933 0.196

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

>84 0.795 0.075 0.480 <0.001 0.622 <0.001

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

Class III obesity (40) 2.484 <0.001 1.527 <0.001 2.114 <0.001

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

Moderate exertion 1.165 0.061 1.032 0.747 1.132 0.060

At rest 1.142 0.466 0.974 0.884 1.024 0.861

COPD 1.163 0.129 1.102 0.390 1.146 0.085

Pneumonia 0.707 0.287 0.747 0.279 0.742 0.165

Steroid Use 0.926 0.459 1.198 0.062 1.075 0.337

Bleeding disorder 1.008 0.939 0.998 0.988 0.993 0.936

Congestive heart failure 0.954 0.834 0.586 0.062 0.771 0.156

Hypertension 1.003 0.957 1.086 0.195 1.033 0.460

Myocardial infarction 0.791 0.403 1.683 0.022 1.158 0.437

Disseminated cancer 0.953 0.694 1.510 <0.001 1.219 0.025

Weight loss 0.850 0.161 0.986 0.901 0.914 0.288

Chemotherapy 0.733 0.140 0.993 0.969 0.884 0.380

Radiotherapy 0.898 0.425 1.434 0.005 1.101 0.332

Preop blood transfusion 0.877 0.637 1.354 0.252 1.097 0.650

Preop Sepsis (vs. None/SIRS) Ref Ref Ref

Sepsis 0.687 0.003 1.351 0.008 1.000 0.998

Septic shock 0.546 0.008 1.201 0.336 0.852 0.294

ASA class (vs. I and II) Ref Ref Ref

Class III 1.254 <0.001 1.339 <0.001 1.311 <0.001

Class IV and V 1.080 0.502 1.115 0.374 1.084 0.364

Wound class (vs. II) Ref Ref Ref

Class III 1.204 0.015 1.306 0.001 1.268 <0.001

Class IV 1.060 0.521 1.420 <0.001 1.221 0.004

Emergency procedure 0.818 0.024 0.819 0.032 0.793 0.001

Between-hospital variance

(probability scale) 1.598 x 10^-3 3.997 x

10^-4 1.943 x 10^-3

Between-hospital variance

(log odds scale) 0.312 0.128 0.145