應用Rasch連續資料模型分析醫院護病比：機率估計、集群分析與視覺化測量

Applying the Rasch Continuous Data Model to Analyze Hospital Nurse-to-Patient Ratios: Probability Estimation, Cluster Analysis, and Visual Measurement

醫院護病比是醫界關切的課題，健保署逐月公佈各醫院的護病比，只見數字卻未見其分析與比較。本研究示範利用醫院護病比的資料，進行其機率分佈與估計、集群分析與關聯、與挑出關鍵少數的測量，期以能簡化資料的分析：基層的分析人員能輕鬆製作有意義的視覺圖；硏究人員、政策制定者、和民眾，能輕鬆獲得有價值的訊息。建立試題反應理論處理的連續資料數理模式，本研究針對2023年台灣444家醫院（包括331家地區醫院、88家區域醫院、4家專科醫院、與21家醫學中心）的護病比進行可視化分析：包括（1）驗證連續資料模式的合宜、（2）呈現醫院護病比的量尺分數與擬合偏離指標、（3）展示護病比偏高的醫院關聯、（4）挑出護病比趨勢上升與下降的關鍵少數醫院。研究結果顯示，連續變數模型在此議題上的應用具有可行性，並能有效區分出三個層級的醫院表現（分別為平均護病比超出閾值的零家（<9）醫學中心、及10家（≧1l）區域醫院、與19家（≧13）地區醫院的集群關聯）；亦挑選出護病比最高的11家醫院作為關鍵的少數。本文提供一種簡便的資料視覺化方法，僅需複製貼上護病比數據，即可快速生成圖表。期望此研究能促進健保開放資料的應用，鼓勵學界、業界、與民眾更廣泛地參與公共健康議題，並推動以健保資料為基礎的可視化分析與決策測量。

The nurse-to-patient ratio in hospitals is a critical issue in the medical field. While Taiwan's National Health Insurance Administration(NHIA) publishes monthly nurse-to-patient ratios for each hospital, these figures are often presented without in-depth analysis or comparison. To simplify data analysis and enable frontline analysts to easily create meaningful visualizations, this study explores probability estimation through iterative aggregation, cluster analysis of interrelated patterns, and the identification of key outliers in hospital nurse-to-patient ratios. The aim is to provide valuable insights for researchers, policymakers, and the general public. To establish a mathematical model for handling continuous data within the framework of item response theory (IRT), this study conducts a visual analysis of the nurse-to-patient ratios of 444 hospitals in Taiwan in 2023, including 331 district hospitals, 88 regional hospitals, 4 specialized hospitals, and 21 medical centers. The analysis includes: (1) verifying the suitability of the continuous data model, (2) presenting hospital performance scale scores and fit deviation indices for nurse-to-patient ratios, (3) identifying hospital clusters associated with high nurse-to-patient ratios, and (4) highlighting key hospitals with increasing or decreasing trends in nurse-to-patient ratios. The results demonstrate the feasibility of applying a continuous data model to this issue, effectively distinguishing three levels of hospital performance: (1) zero medical centers with an average nurse-to-patient ratio exceeding the threshold (<9), (2) 10 regional hospitals with a ratio of≧11, and (3)19 district hospitals with a ratio of≧13, forming distinct clusters. The study also identifies the five district hospitals with the highest nurse-to-patient ratios as key outliers. This paper introduces a simple data visualization approach, allowing users to generate charts quickly by copying and pasting nurse-to-patient ratio data. It is hoped that this research will promote the application of NHIA open data, encourage broader participation from academia, industry, and the public in healthcare issues, and advance data-driven visualization analysis and decision-making in public health.