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Original Article

Fixed and Variable Relationship Models to Define the Volume-Value Relationship in Spinal Fusion Surgery: A Macroeconomic Analysis Using Evidence-Based Thresholds

Sergio M. Navarro1, William Case Frankel1, Heather S. Haeberle1, Prem N. Ramkumar2orcid
Neurospine 2018;15(3):249-260.
Published online: September 6, 2018

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Corresponding Author Prem N. Ramkumar http://orcid.org/0000-0002-1704-9156 Cleveland Clinic Foundation, 2049 E 100th Street, Cleveland, OH 44195, USA Tel: +1-562-619-6205 Fax: +1-216-445-9754 E-mail: premramkumar@gmail.com
• Received: March 19, 2018   • Revised: June 17, 2018   • Accepted: June 23, 2018

Copyright © 2018 by the Korean Spinal Neurosurgery Society

This is an open access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Fixed and Variable Relationship Models to Define the Volume-Value Relationship in Spinal Fusion Surgery: A Macroeconomic Analysis Using Evidence-Based Thresholds
Neurospine. 2018;15(3):249-260.   Published online September 6, 2018
DOI: https://doi.org/10.14245/ns.1836088.044
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Fixed and Variable Relationship Models to Define the Volume-Value Relationship in Spinal Fusion Surgery: A Macroeconomic Analysis Using Evidence-Based Thresholds
Neurospine. 2018;15(3):249-260.   Published online September 6, 2018
DOI: https://doi.org/10.14245/ns.1836088.044
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Fixed and Variable Relationship Models to Define the Volume-Value Relationship in Spinal Fusion Surgery: A Macroeconomic Analysis Using Evidence-Based Thresholds
Image Image Image Image Image
Fig. 1. (A) Surgeon volume vs. length of stay (LOS) stratum-specific likelihood ratio (SSLR) threshold analysis. (B) Surgeon volume vs. cost SSLR threshold analysis.
Fig. 2. (A) Hospital volume vs. length of stay (LOS) stratum-specific likelihood ratio (SSLR) threshold analysis. (B) Hospital volume vs. cost SSLR threshold analysis.
Fig. 3. Market share of annual spinal fusion cases for surgeons and hospitals.
Fig. 4. Hospital comorbidities. APR, All Patient Refined.
Fig. 5. Surgeon comorbidities.

Fig. 1.

Fig. 2.

Fig. 3.

Fig. 4.

Fig. 5.

Fixed and Variable Relationship Models to Define the Volume-Value Relationship in Spinal Fusion Surgery: A Macroeconomic Analysis Using Evidence-Based Thresholds
Variable No. (%)
Sex
 Female 82,632 (52.4)
 Male 75,156 (47.6)
Age groups (yr)
 18–29 11,152 (7.1)
 30–49 47,719 (30.2)
 50–69 74,387 (47.1)
 ≥ 70 24,530 (15.5)
Race
 Caucasian 115,584 (73.3)
 African-American 17,503 (11.1)
 Other race 24,341 (15.4)
 Multiracial 360 (0.2)
Insurance type
 Medicare 43,747 (27.7)
 Private insurance 35,100 (22.2)
 BC/BC & BS 27,812 (17.6)
 Other types 51,129 (32.4)
Volume Sensitivity 1-Specificity SSLR Category p-value No. Odds ratio
0 1.000 1.000 1.000 Low 0.001 3,381 19.253 (9.062–40.906)
1 0.845 0.757 1.116
2 0.744 0.604 1.231
3 0.707 0.560 1.262
5 0.661 0.513 1.290
10 0.587 0.416 1.411
20 0.492 0.309 1.591
30 0.428 0.226 1.895
40 0.369 0.168 2.199
50 0.311 0.126 2.471
58 0.276 0.091 3.019 Medium 0.015 435 8.718 (3.961–19.186)
60 0.269 0.088 3.051
70 0.228 0.064 3.552
80 0.191 0.041 4.677
91 0.163 0.028 5.864 High 0.004 270 4.365 (1.868–10.203)
100 0.140 0.020 6.844
110 0.119 0.015 8.087
120 0.096 0.008 11.790
125 0.087 0.006 15.228 Very high 282 Reference
150 0.058 0.002 23.775
175 0.034 0.002 20.657
200 0.022 0.001 27.088
Volume Sensitivity 1-Specificity SSLR Category p-value No. Odds ratio
0 1.000 1.000 1.000 Low 0.136 3,381 1.357 (1.185–1.554)
1 0.991 0.988 1.003
2 0.981 0.970 1.012
3 0.975 0.948 1.028
5 0.961 0.932 1.031
10 0.924 0.869 1.063
20 0.864 0.794 1.088
30 0.784 0.710 1.105
40 0.713 0.608 1.174
44 0.697 0.577 1.208 High Reference
50 0.659 0.520 1.268
75 0.554 0.437 1.267
100 0.479 0.380 1.260
126 0.416 0.341 1.222
150 0.363 0.292 1.242
175 0.331 0.276 1.199
200 0.296 0.258 1.147
225 0.266 0.247 1.074
Volume Sensitivity 1-Specificity SSLR Category p-value No. Odds ratio
0 1.000 1.000 1.000 Low 0.008 437 10.548 (4.202–26.478)
1 0.995 0.973 1.023
2 0.990 0.936 1.058
3 0.986 0.897 1.099
5 0.976 0.866 1.127
10 0.941 0.786 1.197
15 0.909 0.740 1.229
20 0.884 0.693 1.275
25 0.857 0.624 1.374
50 0.697 0.327 2.129
75 0.602 0.219 2.748
81 0.583 0.191 3.056 Medium 0.016 333 2.090 (0.794–5.505)
100 0.533 0.149 3.563
126 0.464 0.139 3.337
150 0.399 0.134 2.980
200 0.327 0.134 2.439
258 0.280 0.119 2.358
300 0.253 0.113 2.231
350 0.212 0.077 2.745
400 0.174 0.052 3.372
451 0.146 0.036 4.059
472 0.141 0.026 5.453 High 100 Reference
497 0.115 0.026 4.477
525 0.092 0.021 4.484
564 0.075 0.010 7.318
Volume Sensitivity 1-Specificity SSLR Category p-value No. Odds ratio
0 1.000 1.000 1.000 Low 0.846 468 1.602 (1.120–2.142)
1 0.991 0.988 1.003
2 0.981 0.970 1.012
3 0.975 0.948 1.028
5 0.961 0.932 1.031
10 0.924 0.869 1.063
20 0.864 0.794 1.088
30 0.784 0.710 1.105
40 0.713 0.608 1.174
50 0.659 0.520 1.268
75 0.554 0.437 1.267
95 0.498 0.382 1.305 High 402 Reference
100 0.479 0.380 1.260
126 0.416 0.341 1.222
150 0.363 0.292 1.242
200 0.296 0.258 1.147
250 0.246 0.246 1.000
300 0.223 0.219 1.022
350 0.186 0.174 1.071
400 0.150 0.140 1.071
451 0.129 0.108 1.196
502 0.095 0.086 1.102
Table 1. Demographic data of the cohort studied (n=157,788)

BC, Blue Cross; BS, Blue Shield.

Table 2. Surgeon volume vs. length of stay threshold analysis

SSLR, stratum specific likelihood ratio.

Low: 6.28 days; Medium: 4.57 days; High: 4.02 days; Very high: 3.62 days.

When sampling is low, sensitivity and 1-specificity are low and thus may cause SSLR to decrease within a grouping as observed with certain volumes above.

Table 3. Surgeon volume vs. length of stay threshold analysis

SSLR, stratum specific likelihood ratio.

Low: 6.28 days; Medium: 4.57 days; High: 4.02 days; Very high: 3.62 days.

When sampling is low, sensitivity and 1-specificity are low and thus may cause SSLR to decrease within a grouping as observed with certain volumes above.

Table 4. Hospital volume vs. length of stay threshold analysis

SSLR, stratum specific likelihood ratio.

Low: 6.10 days; Medium: 4.23 days; High: 3.99 days.

When sampling is low, sensitivity and 1-specificity are low and thus may cause SSLR to decrease within a grouping as observed with certain volumes above.

Table 5. Hospital volume vs. cost threshold analysis

SSLR, stratum specific likelihood ratio.

Low: $34,797.15; High: $31,915.50.

When sampling is low, sensitivity and 1-specificity are low and thus may cause SSLR to decrease within a grouping as observed with certain volumes above.

Table 1.

Table 2.

Table 3.

Table 4.

Table 5.

NS : Neurospine
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