The Distribution of Risk Across Healthcare Providers and Reducing Misclassification

William Thomas Cecil

doi:doi:10.11648/j.ajtas.20241302.11

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The Distribution of Risk Across Healthcare Providers and Reducing Misclassification

William Thomas Cecil^*

Published in American Journal of Theoretical and Applied Statistics (Volume 13, Issue 2)

Received: 22 March 2024 Accepted: 7 April 2024 Published: 29 April 2024

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Abstract

Four linear multilevel mixed-risk models were compared using model assumption tests and predictions. Models varied by the number of random intercepts from 1 to 4, producing 2-level through 5-level models of the same measure, operative time. Normality of the dependent variable and residuals, variance homoscedasticity, level-1, and level-2 exogeneity were tested using the robust test of the level-1 residuals variance by surgeon, estimates of density, skew, and the Hausman test. Measure (operative time by hospital and surgeon) aberrancy and risk classification were evaluated using traditional methods and used to assess distribution measures. The dependent variable and the level-1 residuals required transformation for linearity and variance stabilization, respectively. Normality criteria were met for both level-1 and level-2 residuals and standardized residuals. The likelihood ratio comparing the four models was significantly larger for the 5-level (1016.1; P<0.00005) model than the likelihood ratio for the four-level and other models. Shrinkage was greatest for the 2-level model (0.039; P<0.00005) and least for the 5-level model (0.028; P<0.00005). Level-1 variance homoscedasticity was confirmed by the robust variance test across all models (P>F=1). Aberrant value detection did not require the exclusion of any observations, while prediction intervals revealed low or high risk for 54.2% of surgeons for the 2-level model and 8.6% for the 5-level model. The traditional (c2 = -11.01; P=1) and instrumental variable (c2 = 21.06; P=1) Hausman tests show that the null hypothesis cannot be rejected for level-1 or level-2 exogeneity. Once level-1 and level-2 exogeneity was confirmed, and since deconfounding was a model consideration, causal inferential capacity was assumed. The likelihood ratio, residual variance, shrinkage, and predictions show that the 5-level model is preferred to the other models.

Published in	American Journal of Theoretical and Applied Statistics (Volume 13, Issue 2)
DOI	10.11648/j.ajtas.20241302.11
Page(s)	29-38
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Misclassification, Assumption/Specification Tests, Multi-level Mixed Effects Model, Random Intercept, Confounding, Causal

References

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[3]	Cecil W. T., Selection of Reliable and Valid Surgeon Performance Measures, American Journal of Management Science and Engineering. Volume 5, Issue 5, September 2020, pp. 62-69. https://doi.org/10.11648/j.ajmse.20200505.12
[4]	Hannan, Ph. D., E. L., Kilburn, Jr, MA, H., O'Donnell, MA, MS, J. F., Lukacik, MA, G., & Shields, E. (1990). Adult Open Heart Surgery in New York State: An Analysis of Risk Factors and Hospital Mortality Rates. JAMA, 2768 - 2774.
[5]	David M. Shahian, Sharon-Lise Normand, David F. Torchiana, Stanley M. Lewis, John O. Pastore, Richard E. Kuntz, Paul I. Dreyer, Cardiac surgery report cards: comprehensive review and statistical critique. This review is an abridged version of a report submitted by the Massachusetts Cardiac Care Quality Commission to the Massachusetts Legislature, May 2001., The Annals of Thoracic Surgery, Volume 72, Issue 6, 2001, Pages 2155-2168, ISSN 0003-4975, https://doi.org/10.1016/S0003-4975(01)03222-2
[6]	Daley BJ, Cecil W, Clarke PC, Cofer JB, Guillamondegui OD. How slow is too slow? Correlation of operative time to complications: an analysis from the Tennessee Surgical Quality Collaborative. J Am Coll Surg. 2015 Apr; 220(4): 550-8. https://doi.org/10.1016/j.jamcollsurg.2014.12.040.
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[15]	Clayton, D. G., and M. Hills. 1993. Statistical Models in Epidemiology. Oxford: Oxford University Press.
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Cecil, W. T. (2024). The Distribution of Risk Across Healthcare Providers and Reducing Misclassification. American Journal of Theoretical and Applied Statistics, 13(2), 29-38. https://doi.org/10.11648/j.ajtas.20241302.11

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Cecil, W. T. The Distribution of Risk Across Healthcare Providers and Reducing Misclassification. Am. J. Theor. Appl. Stat. 2024, 13(2), 29-38. doi: 10.11648/j.ajtas.20241302.11

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AMA Style

Cecil WT. The Distribution of Risk Across Healthcare Providers and Reducing Misclassification. Am J Theor Appl Stat. 2024;13(2):29-38. doi: 10.11648/j.ajtas.20241302.11

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@article{10.11648/j.ajtas.20241302.11,
  author = {William Thomas Cecil},
  title = {The Distribution of Risk Across Healthcare Providers and Reducing Misclassification
},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {13},
  number = {2},
  pages = {29-38},
  doi = {10.11648/j.ajtas.20241302.11},
  url = {https://doi.org/10.11648/j.ajtas.20241302.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20241302.11},
  abstract = {Four linear multilevel mixed-risk models were compared using model assumption tests and predictions. Models varied by the number of random intercepts from 1 to 4, producing 2-level through 5-level models of the same measure, operative time. Normality of the dependent variable and residuals, variance homoscedasticity, level-1, and level-2 exogeneity were tested using the robust test of the level-1 residuals variance by surgeon, estimates of density, skew, and the Hausman test. Measure (operative time by hospital and surgeon) aberrancy and risk classification were evaluated using traditional methods and used to assess distribution measures. The dependent variable and the level-1 residuals required transformation for linearity and variance stabilization, respectively. Normality criteria were met for both level-1 and level-2 residuals and standardized residuals. The likelihood ratio comparing the four models was significantly larger for the 5-level (1016.1; PF=1). Aberrant value detection did not require the exclusion of any observations, while prediction intervals revealed low or high risk for 54.2% of surgeons for the 2-level model and 8.6% for the 5-level model. The traditional (c2 = -11.01; P=1) and instrumental variable (c2 = 21.06; P=1) Hausman tests show that the null hypothesis cannot be rejected for level-1 or level-2 exogeneity. Once level-1 and level-2 exogeneity was confirmed, and since deconfounding was a model consideration, causal inferential capacity was assumed. The likelihood ratio, residual variance, shrinkage, and predictions show that the 5-level model is preferred to the other models.
},
 year = {2024}
}

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TY  - JOUR
T1  - The Distribution of Risk Across Healthcare Providers and Reducing Misclassification

AU  - William Thomas Cecil
Y1  - 2024/04/29
PY  - 2024
N1  - https://doi.org/10.11648/j.ajtas.20241302.11
DO  - 10.11648/j.ajtas.20241302.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 29
EP  - 38
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20241302.11
AB  - Four linear multilevel mixed-risk models were compared using model assumption tests and predictions. Models varied by the number of random intercepts from 1 to 4, producing 2-level through 5-level models of the same measure, operative time. Normality of the dependent variable and residuals, variance homoscedasticity, level-1, and level-2 exogeneity were tested using the robust test of the level-1 residuals variance by surgeon, estimates of density, skew, and the Hausman test. Measure (operative time by hospital and surgeon) aberrancy and risk classification were evaluated using traditional methods and used to assess distribution measures. The dependent variable and the level-1 residuals required transformation for linearity and variance stabilization, respectively. Normality criteria were met for both level-1 and level-2 residuals and standardized residuals. The likelihood ratio comparing the four models was significantly larger for the 5-level (1016.1; PF=1). Aberrant value detection did not require the exclusion of any observations, while prediction intervals revealed low or high risk for 54.2% of surgeons for the 2-level model and 8.6% for the 5-level model. The traditional (c2 = -11.01; P=1) and instrumental variable (c2 = 21.06; P=1) Hausman tests show that the null hypothesis cannot be rejected for level-1 or level-2 exogeneity. Once level-1 and level-2 exogeneity was confirmed, and since deconfounding was a model consideration, causal inferential capacity was assumed. The likelihood ratio, residual variance, shrinkage, and predictions show that the 5-level model is preferred to the other models.

VL  - 13
IS  - 2
ER  -

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Author Information

William Thomas Cecil

Independent Consultant, Knoxville, United States

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Plain Text BibTeX RIS

APA Style

Cecil, W. T. (2024). The Distribution of Risk Across Healthcare Providers and Reducing Misclassification. American Journal of Theoretical and Applied Statistics, 13(2), 29-38. https://doi.org/10.11648/j.ajtas.20241302.11

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ACS Style

Cecil, W. T. The Distribution of Risk Across Healthcare Providers and Reducing Misclassification. Am. J. Theor. Appl. Stat. 2024, 13(2), 29-38. doi: 10.11648/j.ajtas.20241302.11

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AMA Style

Cecil WT. The Distribution of Risk Across Healthcare Providers and Reducing Misclassification. Am J Theor Appl Stat. 2024;13(2):29-38. doi: 10.11648/j.ajtas.20241302.11

Copy | Download

@article{10.11648/j.ajtas.20241302.11,
  author = {William Thomas Cecil},
  title = {The Distribution of Risk Across Healthcare Providers and Reducing Misclassification
},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {13},
  number = {2},
  pages = {29-38},
  doi = {10.11648/j.ajtas.20241302.11},
  url = {https://doi.org/10.11648/j.ajtas.20241302.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20241302.11},
  abstract = {Four linear multilevel mixed-risk models were compared using model assumption tests and predictions. Models varied by the number of random intercepts from 1 to 4, producing 2-level through 5-level models of the same measure, operative time. Normality of the dependent variable and residuals, variance homoscedasticity, level-1, and level-2 exogeneity were tested using the robust test of the level-1 residuals variance by surgeon, estimates of density, skew, and the Hausman test. Measure (operative time by hospital and surgeon) aberrancy and risk classification were evaluated using traditional methods and used to assess distribution measures. The dependent variable and the level-1 residuals required transformation for linearity and variance stabilization, respectively. Normality criteria were met for both level-1 and level-2 residuals and standardized residuals. The likelihood ratio comparing the four models was significantly larger for the 5-level (1016.1; PF=1). Aberrant value detection did not require the exclusion of any observations, while prediction intervals revealed low or high risk for 54.2% of surgeons for the 2-level model and 8.6% for the 5-level model. The traditional (c2 = -11.01; P=1) and instrumental variable (c2 = 21.06; P=1) Hausman tests show that the null hypothesis cannot be rejected for level-1 or level-2 exogeneity. Once level-1 and level-2 exogeneity was confirmed, and since deconfounding was a model consideration, causal inferential capacity was assumed. The likelihood ratio, residual variance, shrinkage, and predictions show that the 5-level model is preferred to the other models.
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - The Distribution of Risk Across Healthcare Providers and Reducing Misclassification

AU  - William Thomas Cecil
Y1  - 2024/04/29
PY  - 2024
N1  - https://doi.org/10.11648/j.ajtas.20241302.11
DO  - 10.11648/j.ajtas.20241302.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 29
EP  - 38
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20241302.11
AB  - Four linear multilevel mixed-risk models were compared using model assumption tests and predictions. Models varied by the number of random intercepts from 1 to 4, producing 2-level through 5-level models of the same measure, operative time. Normality of the dependent variable and residuals, variance homoscedasticity, level-1, and level-2 exogeneity were tested using the robust test of the level-1 residuals variance by surgeon, estimates of density, skew, and the Hausman test. Measure (operative time by hospital and surgeon) aberrancy and risk classification were evaluated using traditional methods and used to assess distribution measures. The dependent variable and the level-1 residuals required transformation for linearity and variance stabilization, respectively. Normality criteria were met for both level-1 and level-2 residuals and standardized residuals. The likelihood ratio comparing the four models was significantly larger for the 5-level (1016.1; PF=1). Aberrant value detection did not require the exclusion of any observations, while prediction intervals revealed low or high risk for 54.2% of surgeons for the 2-level model and 8.6% for the 5-level model. The traditional (c2 = -11.01; P=1) and instrumental variable (c2 = 21.06; P=1) Hausman tests show that the null hypothesis cannot be rejected for level-1 or level-2 exogeneity. Once level-1 and level-2 exogeneity was confirmed, and since deconfounding was a model consideration, causal inferential capacity was assumed. The likelihood ratio, residual variance, shrinkage, and predictions show that the 5-level model is preferred to the other models.

VL  - 13
IS  - 2
ER  -

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