Modeling the Length of Stay in the Intensive Care Unit by Using Mixture Distribution

Year 2024, , 427 - 436, 11.07.2024

Selin Saraç Güleryüz

https://doi.org/10.21605/cukurovaumfd.1514433

Abstract

Intensive care units play a central role in the healthcare system, and the length of stay in hospitals serves as a significant indicator of hospital management quality. Statistical characterization of patient lengths of stay is essential in areas such as simulation, scheduling, and planning. However, these data are often highly skewed, making statistical modeling a challenging task. Mixture distribution models are capable of overcoming this challenge. In this study, a mixture distribution approach was employed to model the highly skewed patient length of stay data observed in two different intensive care units (general surgery, coronary). Four different distributions (normal, Weibull, gamma, lognormal) were used to develop mixture distribution models. The optimal number of components for the mixture distribution was determined using the Bayesian information criterion value, and distribution parameters were estimated using the expectation-maximization algorithm. The validity of the mixture distribution was evaluated using mean absolute percentage error and R-squared value, demonstrating its ability to represent real datasets with high accuracy.

Keywords

Length of stay, Performance metrics, Mixture distribution, Prediction, Intensive care unit

Yoğun Bakım Ünitesinde Hasta Kalış Süresinin Karma Dağılım ile Modellenmesi

Abstract

Yoğun bakım üniteleri sağlık sisteminde merkezi bir rol oynamaktadır. Hastanede kalış süresi, hastane yönetimi kalitesinin önemli bir göstergesidir. Simülasyon, çizelgeleme, planlama gibi alanlarda hasta kalış sürelerinin istatistiksel olarak tanımlanması gerekir. Ancak bu veriler oldukça çarpıktı ve bu nedenle istatistiksel modelleme zorlu bir iş olabilir. Karma dağılım modelleri, bu zorluğun üstesinden gelebilecek kabiliyete sahip modellerdir. Bu çalışmada, iki farklı yoğun bakım ünitesinde (genel cerrahi, koroner) gözlemlenen oldukça çarpık hasta kalış süresi verilerinin modellenmesi için karma dağılım yaklaşımı kullanılmıştır. Karma dağılım modellerini geliştirmek için dört farklı dağılım (normal, Weibull, gamma, lognormal) kullanılmıştır. Karma dağılımının optimal bileşen sayısı Bayes bilgi kriteri değeri yardımıyla belirlenmiş ve dağılım parametreleri beklenti-maksimizasyon algoritması kullanılarak tahmin edilmiştir. Bileşen ve parametre tahmini yapılan karma dağılımın model geçerliliği, ortalama mutlak yüzde hata ve R2 değeri kullanılarak değerlendirilmiş ve gerçek veri setlerini oldukça yüksek doğrulukla temsil ettiği görülmüştür.

Keywords

Kalış süresi, Performans metrikleri, Karma dağılım, Tahmin, Yoğun bakım ünitesi

References

• 1. Burchardi, H., Moerer, O., 2001. Twenty-four Hour Presence of Physicians in the ICU. Critical Care, 5(3), 131-137.
• 2. Mekhaldi, R.N., Caulier, P., Chaabane, S., Chraibi, A., Piechowiak, S., 2020. Using Machine Learning Models to Predict the Length of Stay in a Hospital Setting. Trends and Innovations in Information Systems and Technologies, 202-211.
• 3. Arkin, N., Zhao, T., Wang, L., 2024. Development and Validation of a Novel Risk Classification Tool for Predicting Long Length of Stay in NICU Blood Transfusion Infants. Scientific Reports, 4, 6877.
• 4. Lequertier, V., Wang, T., Fondrevelle, J., Augusto, V., Polazzi, S., Duclos, A., 2024. Length of Stay Prediction with Standardized Hospital Data from Acute and Emergency Care using a Deep Neural Network. Medical Care 62(4), 225-234.
• 5. Vasilakis, C., Marshall, A.H., 2005. Modelling Nationwide Hospital Length of Stay: Opening the Black Box. Journal of the Operational Research Society, 56(7), 862-869.
• 6. Johnson, K., Orfanos, A., Chen, E., Cohen, E., 2024. Machine Learning to Predict Length of Stay Following Revision Hip Arthroplasty. Journal of Hip Surgery.
• 7. Abd-Elrazek, M.A., Eltahawi, A.A., Abd Elaziz, M.H., Abd-Elwhab, M.N., 2021. Predicting Length of Stay in Hospitals Intensive Care Unit using General Admission Features. Ain Shams Engineering Journal, 12(4), 3691- 3702.
• 8. Bahalkeh, E., Hasan, I., Yuehwern, Y., 2022. The Relationship between Intensive Care Unit Length of Stay information and its Operational Performance. Healthcare Analytics (2).
• 9. Meyer, A., Zverinski, D., Pfahringer, B., Kempfert, J., Kuehne, T., Sündermann, S., Eickhoff, C., 2018. Machine Learning for Real-Time Prediction of Complications in Critical Care: A Retrospective Study. Lancet Respiratory Medicine, 6(12), 905-914.
• 10. Marlene Gyldmark, C., 1995. A Review of Cost Studies of Intensive Care Units: Problems with the Cost Concept. Critical Care Medicine, 23(5), 964-972.
• 11. Shea, S., Sideli, R.V., Dumouchel, W., Pulver, G., Arons, R.R., Clayton, P.D., 1995. Computer-Generated Informational Messages Directed to Physicians: Effect on Length of Hospital Stay. Journal of the American Medical Informatics Association, 2(1), 58-64.
• 12. Quarmalah, N.M., Einbeck, J., Coolen, F.P., 2017. Mixture Models for Prediction Form Time Series with Application to Energy Use Data. Archives of Data Science. Series A, 2(1), 1-15.
• 13. Xiao, J., Lee, A., Vemuri, S., 1999. Mixture Distribution Analysis of Length of Hospital Stay for Efficient Funding. Socio-Economic Planning Sciences, 33(1), 39-59.
• 14. Wu, J., Lin, Y., Li, P., Hu, Y., Zhang, L., Kong, G., 2021. Predicting Prolonged Length of ICU Stay through Machine Learning. Diagnostics, 11(12), 2242.
• 15. Maharlou, H., Niakan Kalhori, S., Shahbazi, S., Ravangard, R., 2018. Predicting Length of Stay in Intensive Care Units after Cardiac Surgery: Comparison of Artificial Neural Networks and Adaptive Neuro-fuzzy System. Healthcare Informatics Research, 24(2), 109-117.
• 16. Çiftçi, S., Batur Sir, G.D., 2023. Acil Servise Başvuru Sayısının Zaman Serisi Analiz ve Makine Öğrenmesi Yöntemleri ile Tahmin Edilmesine Yönelik Bir Uygulama. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 29(7), 667-679.
• 17. Papi, M., Pontecorvi, L., 2015. Hospital Resource Consumption Modelling. Research in Business and Management, 1(1), 105-122.
• 18. Frühwirth-Schnatter, S., 2011. Markov Chain Monte Carlo Estimation of Classical and Dynamic Switching and Mixture Models. Journal of the American Statistical Association, 96(453), 194-204.
• 19. Ng, S.K., Xiang, L., Yau, K.K., 2019. Mixture Modelling for Medical and Health Sciences. CRC Press, Boca Raton, 314.
• 20. Millard, P., 1988. Geriatric Medicine: A New Method of Measuring Bed Usage a Theory for Planning. Yüksek Lisans Tezi. Londra Üniversitesi.
• 21. Lee, A., Xiao, J., Codde, J., Ng, A., 2002. Public Versus Private Hospital Maternity Length of Stay: A Gamma Mixture Modelling Approach. Health Services Management Research, 15(1), 46-54.
• 22. Deb, P., Trivedi, P., 1998. Demand for Medical Care by the Elderly: A Finite Mixture Approach. Journal of Applied Econometrics, 12(3), 313-336.
• 23. Cleary, P.G., 1991. Variations in Length of Stay and Outcomes for Six Medical and Surgical Conditions in Massachusetts and California. JAMA, 266(1), 73-79.
• 24. McClean, S., Millard, P., 1993. Patterns of Length of Stay after Admission in Geriatric Medicine: An Event History Approach. Statistician, 42(3), 263-274.
• 25. Quantin, C., Entezam, F., Brunet-Lecomte, P., Lepage, E., Guy, H., Duserre, L., 1999. High Cost Factors for Leukaemia and Lymphoma Patients: A New Analysis of Costs within these Diagnosis Related Groups. Journal of Epidemiology and Community Health, 53(1), 24-31.
• 26. Wang, K., Yau, K., Lee, A., 2002. A Hierarchical Poisson Mixture Regression Model to Analyse Maternity Length of Hospital Stay. Statistics in Medicine, 21(23), 3639-3654.
• 27. Atienza, N., Garcia-Heras, J., Munoz-Pichardo, J., Villa, R., 2008. An Application of Mixture Distributions in Modelization of Length of Hospital Stay. Statistics in Medicine, 27(9), 1403-1420.
• 28. Garg, L., McClean, S., Meenan, B., El-Darzi, E., Millard, P., 2009. Clustering Patient Length of Stay using Mixtures of Gaussian Models and Phase Type Distributions. 22nd IEEE International Symposium on Computer-Based Medical Systems, 1-7.
• 29. Singh, C., Ladusingh, L., 2010. Inpatient Length of Stay: A Finite Mixture Modeling Analysis. The European Journal of Health Economics, 11(2), 119-126.
• 30. Titterington, D., Smith, A., Makov, U., 1985. Statistical Analysis of Finite Mixture Distributions. Wiley, New York, 243.
• 31. Fraley, C., Raftery, A.E., 1998. How Many Clusters? Which Clustering Method?-Answers via Model-Based Cluster Analysis. The Computer Journal, 41(8), 578-588.
• 32. Sin, C.Y., White, H., 1996. Information Criteria for Selecting Possibly Misspecified Parametric Models. Journal of Econometrics, 71(1-2), 207-225.
• 33. Akaike, H., 1974. A New Look at the Statistical Model Identification. IEEE Transactions on Automatic Control, 19(6), 716-723.
• 34. Schwarz, G., 1978. Estimating the Dimension of a Model. Annals of Statistics, 6(2), 461-464.
• 35. Dempster, A., Laird, N., Rubin, D., 1977. Maximum Likelihood from Incomplete Data via the EM Algorithm (with Discussion). Journal of the Royal Statistical Society Series B (Methodological) 39(1), 1-38.
• 36. McLachlan, G., Peel, D., 2000. Finite Mixture Models. John Wiley & Sons, Inc, New York, 464.
• 37. Lewis, C.D., 1982. Industrial and Business Forecasting Methods. Butterworths, Londra, 40.
• 38. Steel, R.G, Torrie, J.H., 1960. Principles and Procedures of Statistics with Special Reference to the Biological Sciences. McGraw Hill, New York, 481.
• 39. Nas, S., Koyuncu, M., 2019. Emergency Department Capacity Planning: A Recurrent Neural Network and Simulation Approach. Computational and Mathematical Methods in Medicine.
• 40. Antmen, F.Z., Oğulata, S.N., 2013. The Capacity Planning of Intensive Care Units via Simulation: A Case Study in University Hospital. International Journal of Applied Mathematics and Statistics, 51(21), 214-235.
• 41. Snedecor, G.W., Cochran, W.G., 1991. Statistical Methods, 8th Edition. Iowa State University Press, Ames, 524.
• 42. Keribin, C., 2000. Consistent Estimation of the Order of Mixture Models. The Indian Journal of Statistics, Series A, 62(1), 49-66.