Beyond volume: Does hospital complexity matter? An analysis of inpatient surgical mortality in
the United States
Appendix Contents:

Detailed statistical methodology

Appendix Table 1: International Classification of Disease, 9th Revision, Clinical
Modification (ICD-9) Codes

Appendix Table 2: Multivariable GEE model

Appendix Table 3: Analysis adjusting for hospital procedural volume

Appendix Table 4: Multivariable model: Mortality Rate Ratio among Hospitals of
Different Complexity with Quintiles Defined by Total Number of Discharges

Appendix Table 5. Complete multivariable model rate ratios for individual
procedures

Appendix Table 6. Effect of increasing hospital complexity on mortality rates at low
and high-volume hospitals

Appendix Table 7. Percent variability in aggregate mortality rate
Detailed Statistical Methodology
Indirect Standardization: To generate the indirectly-standardized mortality rate, we first calculated each
hospital’s ratio of observed to expected deaths. The numerator of the ratio is the sum of the actual deaths
for each procedure at that hospital, and the denominator is the sum of the individual risk probabilities
generated by the patient-level logistic regression model for each procedure (the “expected” deaths). This
ratio is also referred to as the “Standardized Mortality Ratio”. To get the indirectly standardized mortality
rate, we then multiplied this ratio by the crude (unadjusted) population mortality rate (total number of
deaths divided by the total number of admissions for the procedures included in the composite). Using
this method, procedures that are performed more frequently in one hospital contribute more data to that
hospital’s indirect standardized mortality rate than a procedure for which the hospital might have only a
small number of cases. In this way, the indirect standardization model accounts for differences in volume
of each condition across hospitals.
Partial-R2: The total R-square is the proportion of variation in the outcome jointly explained by all
variables in the model. The partial R-square is the proportion of variation explained by one variable when
all others are included in the model. If all covariates were uncorrelated, then the partial R-squares would
add up to the total R-squares. However since the variables are correlated, when looking at one covariate
after adjusting for all other variables, the other variables will be explaining some of the effect of that
covariate, so the sum of the partial R-squares will have to be less than the total R-square.
Appendix Table 1: International Classification of Disease, 9th Revision, Clinical Modification (ICD-9)
Codes
Procedure
ICD-9 Procedure Code
Coronary artery bypass graft
3610 – 3617, 3619
Abdominal aortic aneurysm repair
3864, 3834, 3844
Above knee amputation
8417
Colon resection
1731-1736, 1739, 4503, 4526, 4541, 4549, 4552,
4549, 4571-4576, 4579, 4581-4583
Small bowel resection
4531, 4532, 4533, 4534, 4551, 4561, 4562, 4563,
4591, 4602
Appendix Table 2: Multivariable model
Estimate
95% Confidence Interval
p-value
Lowest complexity quintile
0.23
0.15 – 0.32
<0.001
Quintile 2
0.19
0.14 – 0.25
<0.001
Quintile 3
0.09
0.04 – 0.14
<0.001
Quintile 4
0.03
-0.02 – 0.07
0.25
-0.04
-0.05 – -0.02
<0.001
-0.10
-0.21 – 0.02
0.10
-0.04
-0.09 – -0.003
0.03
South
0.05
0.02 – 0.09
0.01
West
-0.04
-0.09 – 0.01
0.14
0.01
-0.03 – 0.06
0.56
-0.01
-0.05 – 0.04
0.78
Complexity
Highest complexity quintile
Number of discharges
reference
(5,000 discharge increment)
Urban
Geographic Region
Northeast
Midwest
reference
Ownership
Investor-owned
Government-owned
Non-profit
reference
Teaching status
-0.03
-0.07 – 0.02
0.22
Percentage Medicare
0.007
-0.002 – 0.02
0.14
0.02
0.01 – 0.02
<0.001
-0.01
0.01 – 0.02
<0.001
(5% increment)
Disproportionate share index
(5% increment)
County Household Income
($10,000 increment)
Appendix Table 3: Analysis adjusting for hospital procedural volume
30-day
Complete model rate
Complete model rate ratio
standardized
ratio using hospital
using procedural volume
mortality rate, % discharges
(95% CI)
(95% CI)
Lowest
12.3
complexity
(11.5 – 13.1)
Quintile 2
11.4
(10.9 – 11.9)
Quintile 3
9.8
(9.5 – 10.1)
Quintile 4
8.9
(8.7 – 9.2)
Highest
8.1
complexity
(7.9 – 8.2)
1.27 (1.17 – 1.37)
1.25 (1.16 – 1.35)
1.22 (1.15 – 1.29)
1.20 (1.13 – 1.27)
1.10 (1.04 – 1.15)
1.08 (1.03 – 1.14)
1.03 (0.98 – 1.07)
1.02 (0.98– 1.06)
1.0
1.0
Appendix Table 4. Multivariable model: Mortality Rate Ratio among Hospitals of Different Complexity
with Quintiles Defined by Total Number of Discharges
Model 1
30-day
Unadjusted Model
standardized
mortality rate, %
Lowest complexity
Rate Ratio
Model 2
Model 3
Model 1 plus
Model 2 plus
Hospital and
Hospital
Population
Volume*±
(95% CI)
Demographics*
1.43 (1.36 – 1.49)
1.37 (1.31 0 1.44)
1.25 (1.16 – 1.35)
1.24 (1.18 – 1.30)
1.20 (1.14 – 1.26)
1.11 (1.03 – 1.19)
1.15 (1.10 – 1.21)
1.12 (1.07 - 1.18)
1.05 (0.99 – 1.12)
1.07 (1.02 – 1.12)
1.06 (1.01 – 1.10)
1.01 (0.96 – 1.07)
1.0
1.0
1.0
11.5
(11.1 – 11.9)
Quintile 2
9.4
(9.1 – 9.7)
Quintile 3
8.7
(8.5 – 9.0)
Quintile 4
8.1
(7.9 – 8.4)
Highest
complexity
7.6
(7.3 – 7.9)
Abbreviations: CI, confidence interval
*Adjusted for hospital region, urban location, ownership, teaching status, percentage of patients insured
by Medicare, Disproportionate Share Index and median county household income
± Adjusted for total number of discharges 2008-2009
Appendix Table 5. Complete multivariable model rate ratios for individual procedures
AAA Repair
Above Knee
Coronary Artery
Colon Resection
Small Bowel Resection
Amputation
Bypass Graft
*
1.52 (1.12 – 2.07)
*
1.04 (0.93 – 1.15)
0.90 (0.70 – 1.15)
Quintile 2
*
1.16 (0.95 – 1.42)
1.28 (1.04 – 1.59)
1.02 (0.94 – 1.11)
1.02 (0.90 – 1.15)
Quintile 3
1.28 (0.83 – 1.97) 1.15 (1.00 – 1.32)
1.06 (0.92 – 1.22)
1.00 (0.93 – 1.08)
1.02 (0.94 – 1.12)
Quintile 4
1.09 (0.88 – 1.36) 1.13 (1.01 – 1.26)
1.06 (0.96 – 1.17)
0.97 (0.91 – 1.03)
1.01 (0.94 – 1.09)
1.0
1.0
1.0
1.0
Lowest
complexity
Highest
complexity
1.0
Appendix Table 6. Effect of increasing hospital complexity on mortality rates at low and high-volume
hospitals
Complexity Quintile
Low
Volume
Quintile 1
Quintile 2
Quintile 3
Quintile 4
Quintile 5
11.67 (11.04 –
11.01 (10.02 –
10.10 (9.09 –
10.20 (9.27 –
8.85 (8.52 –
12.30)
11.99)
11.12)
11.13)
9.19)
9.18 (4.57 –
8.43 (6.60 –
7.83 (7.29 –
8.24 (8.08 –
13.79)
10.26)
8.37)
8.41)
High
*
Volume
* insufficient data for high volume hospitals in lowest complexity quintile
Appendix Table 7. Percent variability in aggregate mortality rate*
Partial-R2
Hospital Complexity
3.72
Number of discharges
1.49
Urban location
0.16
Northeast region
0.27
South region
0.43
West region
0.13
Investor-owned
0.02
Government-owned
0.005
Teaching status
0.09
Percentage Medicare
0.13
Disproportionate Share Index
1.58
County Income
0.64
Complete Model Total R2
21.34
*Due to adjustment for interdependence of variables, the sum of the individual Partial-R2s will be less
than the Total R2 for the entire model. See Appendix: Detailed Statistical Methodology for additional
explanation.