Surgery volume and operative mortality:
A re-examination using fixed-effects regression
Amresh Hanchate, PhD
Section of General Internal Medicine
Boston University School of Medicine
AcademyHealth
Annual Research Meetings 2006
June 26, 2006
Funding: AHRQ
Acknowledgements
• Arlene Ash, Ph.D (Boston University)
• John Birkmeyer, MD (University of Michigan)
• Therese Stukel, PhD (Institute for Clinical
Evaluative Sciences, Toronto)
• AHRQ Grant
2
Provider Volume & Operative Mortality:
Background
• Most studies indicate that hospitals and surgeons with
higher volumes have significantly lower operative
mortality
• True for a variety of complex, high-risk surgeries
• Volume – proxy for “volume process effect”
3
Patient profiles across hospitals and surgeons
• Studies are based on observational data -- administrative or clinical
chart databases
• We may not observe significant
– process of care details
– patient characteristics (severity)
• Patient profiles may vary systematically across hospitals and surgeons
(Dranove, Kessler, et al, JPE, 2003)
• Which patient goes to which provider?
– physician referral (technology, expertise)
– patient choice (experience, recommendations, report cards)
– provider choice (report cards)
• To estimate “volume process effect”, need to adjust for patient profiles
at provider level
– Fixed effects: allows cluster effects to be correlated with covariates
– Random effects: assumes cluster effects to be uncorrelated with covariates
4
Objective
To compare the estimates of the association of hospital and
surgeon volumes with operative mortality for CABG using
(a) fixed effects (FE) regression
(b) random effects (RE) regression.
5
Data:
Birkmeyer, Stukel et al (NEJM, 2003)
Source: All CABGs during 1998 & 1999 from Medicare Fee for
Service Inpatient Files
N
Patients
Mean volume
/ year
220,592
Hospitals
958
297
Surgeons
2,772
85
All surgeries at one hospital (%)
56%
77
All surgeries at 2+ hospitals (%)
44%
97
Clustering:
• Patients clustered among surgeons and hospitals
• Surgeons not nested in hospitals
6
Variables
• Outcome: Operative mortality (1/0) within 30-day or before
discharge
• Patient characteristics
–
–
–
–
Age, gender and race
Charlson score
Elective / Non-elective admission
Area (zip code) income indicator
• Surgeon
– Volume per year (at all hospitals)
• Hospital
–
–
–
–
Volume per year
Teaching status
Ownership (not-for-profit, government, for-profit)
Urban / Non-urban
7
Regression Methodology
• Linear probability model
• Fixed Effects Regression
– “within cluster”
– Outcome and covariates are transformed by differencing out the cluster
mean
– To estimate surgeon volume effect
• Hospital as fixed cluster – surgeons within same hospital compared
• Within Hospital Cohort – Patients in hospitals with at least two surgeons (1%
patients excluded)
– To estimate hospital volume effect
• Surgeon as fixed cluster
• Within Surgeon Cohort – Patients whose surgeons operated at two or more
hospitals (49% patients, 44% surgeons and 21% hospitals excluded)
• Random Effects Regression – 3-tiered hierarchical
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Comparison of the two cohorts
# patients
# surgeons
# hospitals
Operative mortality rate (per 1,000)
Provider volume
% patients with high volume surgeons
% patients in high volume hospitals
Patient characteristics (%)
Age 75 or older
Female
Black
Charlson score 3 or higher
Nonelective admission
Resident zip code mean Social Security
income below $2,500
Within
Hospital
cohort
217,790
2,744
898
50
Within
Surgeon
cohort
112,143
1,216
755
52
34%
34%
36%
28%
40%
35%
3.7%
9.7%
57%
40%
35%
3.8%
9.5%
56%
66%
67%
• Operative mortality & patient characteristics alike
• Relatively fewer high volume hospital patients in Within Surgeon Cohort
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Estimates of Volume Effects
# Excess Operative Deaths per 1,000 CABG surgeries
FE
Mean
Surgeon volume
Lowest tertile (<101)
Middle tertile (101 - 162)
Highest tertile (>162)
Hospital volume
Lowest tertile (<314)
Middle tertile (314 - 628)
Highest tertile (>628)
95% CI
RE-1
RE-2
(Within Hospital Cohort) (Within Hospital Cohort)
Mean
95% CI
Mean
95% CI
15.6
[6.7, 24.6]
-1
[-10.3, 8.2]
Reference
14.1
2.4
[10.8, 17.3]
[-0.7, 5.6]
Reference
13.6
[3.4, 23.7]
8
[-2.4, 18.4]
Reference
5.3
4.7
[0.9, 9.6]
[0.2, 9.2]
Reference
14.8
[9.8, 19.9]
2.7
[-2.2, 7.5]
Reference
2.3
2.8
[-3.7, 8.2]
[-2.6, 8.2]
Reference
• Surgeon volume effects: FE and RE are similar
• Hospital volume effect: FE > RE
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Adjusted Operative Mortality
(Operative Deaths Per 1,000 CABG surgeries)
Surgeon volume
Lowest tertile (<101)
Middle tertile (101 - 162)
Highest tertile (>162)
Hospital volume
Lowest tertile (<314)
Middle tertile (314 - 628)
Highest tertile (>628)
RE-1
FE
59
48
45
64
47
48
53
52
47
59
52
43
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Volume Effect Decomposition
(Operative Deaths Per 1,000 CABG surgeries)
Surgeon volume
Lowest tertile (<101)
Middle tertile (101 - 162)
Highest tertile (>162)
Hospital volume
Lowest tertile (<314)
Middle tertile (314 - 628)
Highest tertile (>628)
RE-1
FE
(covariate
effect)
"Observed"
59
48
45
64
47
48
53
52
47
59
52
43
FE - Mean
Total FE
Hospital
(Observed +
Residual
Unobserved)
"Unobserved"
-6.3
-1.1
3.0
53
51
46
• “Unobserved” – Operative mortality effect of unobserved factors at
hospital level
• Low volume hospitals have protective factors not being captured in our
data
• High volume hospitals may have sicker patient profile than low volume
hospitals
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Conclusions
• The FE approach decomposes volume effect into Observed
and Unobserved component effects.
• The RE estimate may be viewed as the net of Observed and
Unobserved effects from FE regression.
• The sizable Unobserved effect indicates that for CABG
patients in high volume hospitals are different from those in
low volume hospitals – they may be sicker.
• Question: To what extent can the Observed component (FE)
be seen as the “volume process effect”?
• Limitations
– Poor measure of illness severity (Charlson Scores)
– Other unobserved phenomena
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