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

Year 2024, Volume: 39 Issue: 2, 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

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