運用Benford定律的智慧型健保費用異常偵測模型之研究

楊喻翔

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運用Benford定律的智慧型健保費用異常偵測模型之研究

An intelligent model of detecting anomalous health-insurance expenses using Benford's Law

楊喻翔 , Ph.D　　Advisor：姜國輝　　

繁體中文

Benford定律；健保費用；申報異常；計算智慧；班福定律

Abstract │ Reference (150) │ Altmetrics

Abstract 〈TOP〉

目前健保局所能查核到的違規案件來源有五項，即民眾檢舉、投保單位經辦人檢舉、審查費用時發現異常而移辦、專案稽查、繳回之健保卡發現異常。但只有審查費用流程應用電腦檔案分析可透過大量的資料分析方法篩選出異常院所。然而，電腦檔案分析只能偵測醫師的服務量是否「偏離常態分配」，亦即只能偵查出某些醫師或院所可能做了過多不必要的服務，而無法偵測出虛報或詐欺等行為。
因而，本研究透過大量詐欺文獻回顧，發現其中Bolton & Hand (2002)指出一個最佳的例子為應用Benford定律的數字分析。Benford定律即是凡符合此法則的資料中，其第一位數的值越小者則出現的頻率就越大，而數值越大者出現的機率就越小。近幾年，Benford定律被應用在不同領域的舞弊或詐欺的審查流程中。
由於目前尚未有專文探討運用Benford定律於臺灣健保醫療費用異常之相關研究。本研究以Benford定律為基礎，利用健保研究資料庫的1999至2003年住院全部及門診抽樣的申報資料進行實證，步驟上有三：一、進行全體住院及門診機構的整體實證，二、檢視單獨以數字分析法是否可以找出異常機構，三、提出一個智慧型費用異常偵測模型並實證其效果。
本研究結論有三：
一、健保特約機構中，住院機構的健保費申請數字符合第一位數的Benford定律，第二、第三及第四位位數不符合。而其中的一般費用部分符合第一、二、三、四位數的Benford定律，論病計酬案件則只有第一位數符合。至於健保費的申請數字之第二、第三及第四位數不符全之原因為論病計酬案件不符合Benford定律，此乃因為論病計酬案件之特殊計價方式所造成。
二、本研究指出單獨應用Benford定律的數字分析方法檢驗的確能找出異常院所，但同時也容易將正常院所誤判為異常，在利用卡方檢定、Cramer’s V統計值判斷法，無論是住院或門診機構，由於鑑別度不高造成整體正確率不佳，由此可推論單純利用數字分析法不足以檢驗出異常院所，因此需要再進一步結合其他工具。
三、本研究所建構的智慧型費用異常偵測模型，是以GHSOM類神經網路進行變數選取工作，找出數個變數群組後，分別利用RBFNN(徑向基類神經網路)、GRNN（通用迴歸類神經網路）及ERNN（Elman反饋式類神經網路）等進行異常院所預判，並以逐步邏輯斯迴歸模型作為Benchmark，結果是以逐步邏輯斯迴歸模型所構建的線性模型得到比較好的效果，本研究推論原因可能為應用Benford定律的衍生指標和異常/正常院所之間就存在線性關係，因此可以利用邏輯斯迴歸模型來預判，並利用類神經網路模型加以佐證之。 
因此，本研究希望利用Benford定律的計算智慧技術能運用於健保資料庫，進行大規模電腦初步審查，找出更多不良醫療院所之異常申報之來源，以提供實地查核進而查到真正違規之醫療院所，如此可遏止醫療院所之犯意，進而節省健保支出，健全其財務收支平衡，為健保永續經營貢獻一份心力。

Parallel Abstract 〈TOP〉

There are five sources of illegal medical cases checked by BNHI (Bureau of National Health Insurance): reported by public, reported by the operator of insured unit, unusual findings while auditing expenses, special case audit, and unusual findings for returned health insurance cards. The abnormal medical institutions can only be found out by analyzing digital data in the source of auditing expenses. However, the digital data can only detect whether the physicians’ service deviates from the normal distribution (excessive unnecessary service offered by some physicians or hospitals), instead of the false claim of medical expenses and fraud behavior. 
Thus, by reviewing a lot of fraud literature, this study finds the best example in Bolton & Hand (2002) is digit analysis of Benford's Law. Benford's Law points that the smaller the first digit is, the more frequent the digit shows, vice versa. In recent years, Benford's law has been applied in fraud review process in different fields.
So far no specific article has applied Benford's Law in the research related to the BNHI medical expenses, so we did a study using inpatient (total) and outpatient (sampling) data from 1999 to 2003. There are three steps in this study: 1. Overall empirical study of all inpatient and outpatient medical institutions. 2. Try to find out the unusual medical institutions only using digit analysis. 3. Find out a smart anomaly detection model and verify its effectiveness. 
There are three conclusions of the study:
1. For the health insurance expenses applied by the BNHI-contracted inpatient institutions, the frequency of the first digit accords with Benford's Law, while the second, third, and fourth digits does not accord with Benford's Law. For the general health insurance expense, the frequencies of the first, second, third, and fourth digit accord with Benford's Law. While only the first digit meets Benford's Law for cases paid by disease, as its special pricing method causes the different frequencies of the second, third, and fourth digits of health insurance expenses. 
2. This study shows that the digit analysis of Benford's Law does contribute to find out the abnormal institutions, but also pay the price of misidentify the normal institutions. By using chi-square test and Cramer's V statistics method, the low discrimination rates of both inpatient and outpatient hospitals leads to poor overall accuracy. It suggests that the simple method of digit analysis is insufficient to test the abnormal institutes, and further investigation with other tools is requested.
3. This study establishes a smart anomaly detection model of health insurance expense, which is based on variable selection with GHSOM neural networks to identify the optimal model, and then uses RBFNN (radial basis function neural network), GRNN (general regression neural network), and ERNN (Elman recurrent neural network) to predict the abnormal institutions. Comparing RBFNN, GRNN and ERNN with the stepwise logistic regression model as the Benchmark, the study concludes that the linear relationship between derived indicator of Benford's Law and abnormal/normal institutions exits. Therefore, we can predict by logistic regression model and verify by neural network model.
The study intends to apply the smart technology of Benford's Law to the large-scale preliminary review of the National Health Insurance database, which can help to identify the sources of the anomaly expenses of medical institutions and find out the fraud ones. Therefore, the decreasing fraud of medical institutions will cut down the health insurance expense for financial break-even. We hope we can contribute to the sustainable development of health insurance.。

Reference ( 150 ) 〈TOP〉

Berger, A., & Hill, T. P. "A basic theory of Benford's Law," Probability Surveys (8) 2011, pp 1-126.
連結：
Bhattacharya, S., Xu, D. M., & Kumar, K. "An ANN-based auditor decision support system using Benford's law," Decision Support Systems (50:3), Feb 2011, pp 576-584.
連結：
Bolton, R. J., & Hand, D. J. "Statistical fraud detection: A review," Statistical Science) 2002, pp 235-249.
連結：
Breiman, L. "Heuristics of instability and stabilization in model selection," The annals of statistics (24:6) 1996, pp 2350-2383.
連結：
Busta, B., & Weinberg, R. "Using Benford’s law and neural networks as a review procedure," Managerial Auditing Journal (13:6) 1998, pp 356-366.
連結：

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