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Ensemble of trees approaches to risk adjustment for evaluating a hospital’s performance

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Abstract

A commonly used method for evaluating a hospital’s performance on an outcome is to compare the hospital’s observed outcome rate to the hospital’s expected outcome rate given its patient (case) mix and service. The process of calculating the hospital’s expected outcome rate given its patient mix and service is called risk adjustment (Iezzoni 1997). Risk adjustment is critical for accurately evaluating and comparing hospitals’ performances since we would not want to unfairly penalize a hospital just because it treats sicker patients. The key to risk adjustment is accurately estimating the probability of an Outcome given patient characteristics. For cases with binary outcomes, the method that is commonly used in risk adjustment is logistic regression. In this paper, we consider ensemble of trees methods as alternatives for risk adjustment, including random forests and Bayesian additive regression trees (BART). Both random forests and BART are modern machine learning methods that have been shown recently to have excellent performance for prediction of outcomes in many settings. We apply these methods to carry out risk adjustment for the performance of neonatal intensive care units (NICU). We show that these ensemble of trees methods outperform logistic regression in predicting mortality among babies treated in NICU, and provide a superior method of risk adjustment compared to logistic regression.

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References

  1. Normand S-LT, Shahian DM (2007) Statistical and clinical aspects of hospital outcomes profiling. Institute of Mathematical Statistics. Stat Sci 22(2):206–226

    Article  Google Scholar 

  2. Austin PC (2008) Bayes rules for optimally using Bayesian hierarchical regression models in provider profiling to identify high-mortality hospitals. BMC Med Res Methodol 8(1):30. BioMed Central Ltd

    Article  Google Scholar 

  3. Berta P, Seghieri C, Vittadini G (2013) Comparing health outcomes among hospitals: the experience of the Lombardy Region. Health Care Manag Sci 16(3):245–257. Springer, US. doi:10.1007/s10729-013-9227-1

    Article  Google Scholar 

  4. Farrell PJ, Groshen S,MacGibbon B, Tomberlin TJ (2010) Outlier detection for a hierarchical Bayes model in a study of hospital variation in surgical procedures. SAGE Publications. StatMethods Med Res 19(6):601–619

    Article  Google Scholar 

  5. He Y, Selck F, Normand S-LT (2013) On the accuracy of classifying hospitals on their performance measures. Stat Med. doi:10.1002/sim.6012

  6. Ieva F, Paganoni A (2014) Detecting and visualizing outliers in provider profiling via funnel plots and mixed effect models. Health Care Manag Sci. Springer, US. doi:10.1007/s10729-013-9264-9

  7. Kalbfleisch JD, Wolfe RA (2013) On monitoring outcomes of medical providers. Stat Biosci 5(2):286–302. Springer US

    Article  Google Scholar 

  8. Mohammed MA, Manktelow BN, Hofer TP (2012) Comparison of four methods for deriving hospital standardised mortality ratios from a single hierarchical logistic regression model. Stat Methods Med Res. doi:10.1177/0962280212465165

  9. Paddock SM, Louis TA (2011) Percentile-based empirical distribution function estimates for performance evaluation of healthcare providers. J R Stat Soc Ser C Appl Stat 60(4):575–589. Wiley Online Library

    Article  Google Scholar 

  10. Phibbs CS, Bronstein JM, Buxton E, Phibbs RH (1996) The effects of patient volume and level of care at the hospital of birth on neonatal mortality. J Am Med Assoc 276(13):1054–1059

    Article  Google Scholar 

  11. Phibbs CS, Baker LC, Caughey AB, Danielsen B, Schmitt SK, Phibbs RH (2007) Level and volume of neonatal intensive care and mortality in very-low-birth-weight infants. N Engl J Med. Mass Med Soc 356(21):2165–2175

    Google Scholar 

  12. Racz MJ, Sedransk J (2010) Bayesian and frequentist methods for provider profiling using risk-adjusted assessments of medicaloutcomes. J Am Stat Assoc 105(489):48–58

    Article  Google Scholar 

  13. Lorch SA, Baiocchi M, Ahlberg CE, Small DS (2012) The differential impact of delivery hospital on the outcomes of premature infants. Am Acad Pediatr 130(2):270–278

    Google Scholar 

  14. Breiman L, Friedman JH, Olshen RA, Stone CJ (1984) Classification and regression trees. Wadsworth & Brooks, Monterey

    Google Scholar 

  15. Quinlan JR (1986) Induction of decision trees. Mach Learn 1(1):81–106

    Google Scholar 

  16. Dietterich TG (2000) Ensemble methods in machine learning. In: Multiple classifier systems. Springer, pp 1–15

  17. Breiman L (1996) Bagging predictors.Mach Learn 24(2):123–140

    Google Scholar 

  18. Freund Y, Schapire RE et al (1996) Experiments with a new boosting algorithm. In: ICML, vol 96, pp 148–156

  19. Bernardo JM, Smith AFM (2009) Bayesian theory, vol 405.Wiley, Hoboken

  20. Breiman L (2001) Random forests. Mach Learn 45(1):5–32

    Article  Google Scholar 

  21. Cutler DR, Edwards TC Jr, Beard KH, Cutler A, Hess KT, Gibson J, Lawler JJ (2007) Random forests for classification in ecology. Ecol Eco Soc Am 88(11):2783–2792

    Google Scholar 

  22. Riddick G, Song H, Ahn S,Walling J, Borges-Rivera D, ZhangW, Fine HA (2011) Predicting in vitro drug sensitivity using Random Forests. Bioinformatics 27(2):220–224. Oxford Univ Press

    Article  Google Scholar 

  23. Svetnik V, Liaw A, Tong C, Culberson JC, Sheridan RP, Feuston BP (2003) Random forest: a classification and regression tool for compound classification and QSAR modeling. J Chem Inform Comput Sci 43(6):1947–1958. ACS Publications

    Article  Google Scholar 

  24. Chipman HA, George EI, McCulloch RE (2010) BART: Bayesian additive regression trees. Ann Appl Stat 4(1):266–298. Institute of Mathematical Statistics

    Article  Google Scholar 

  25. Díaz-Uriarte R, De Andres SA (2006) Gene selection and classification of microarray data using random forest. BMC bioinforma 7(1):3. BioMed Central Ltd

    Article  Google Scholar 

  26. Pasta DJ (2009) Learning when to be discrete: continuous vs. categorical predictors. SAS Global Forum, Washington, DC

    Google Scholar 

  27. Malley JD, Kruppa J, Dasgupta A, Malley KG, Ziegler A (2012) Probability machines: consistent probability estimation using non-parametric learning machines. Methods Inf Med 51(1):74

    Article  Google Scholar 

  28. Little RJA, Rubin DB (2002) Statistical analysis with missing data. Wiley, Hoboken

  29. Bostrom H (2007) Estimating class probabilities in random forests In: 6th international conference on machine learning and applications, 2007. ICMLA 2007. IEEE, pp 211–216

  30. Provost F, Domingos P (2000) Well-trained PETs: improving probability estimation trees. Citeseer

  31. Devroye L (1996) A probabilistic theory of pattern recognition, vol 31. Springer

  32. Rosenbaum PR, Rubin DB (1983) The central role of the propensity score in observational studies for causal effects. Biometrika 70(1):41–55

    Article  Google Scholar 

  33. Stuart EA (2010) Matching methods for causal inference: a review and a look forward. Stat Sci Rev J Inst Math Stat 25(1):1. NIH Public Access

    Google Scholar 

  34. Silber JH, Rosenbaum PR, Ross RN, Ludwig JM, Wang W, Niknam BA, Mukherjee N, Saynisch PA, Even-Shoshan O, Kelz RR, Fleisher LA (2013) Template matching for auditing hospital cost and quality. Health Services Research, in press. doi: 10.1111/1475-6773.12156

  35. Iezzoni LI (1997) Risk adjustment for measuring health care outcomes. Health Administration Press, Chicago

    Google Scholar 

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Liu, Y., Traskin, M., Lorch, S.A. et al. Ensemble of trees approaches to risk adjustment for evaluating a hospital’s performance. Health Care Manag Sci 18, 58–66 (2015). https://doi.org/10.1007/s10729-014-9272-4

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  • DOI: https://doi.org/10.1007/s10729-014-9272-4

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