Development of a methodology for the detection of hospital financial outliers using information systems

Authors


SUMMARY

Comparison of financial indices helps to illustrate differences in operations and efficiency among similar hospitals. Outlier data tend to influence statistical indices, and so detection of outliers is desirable. Development of a methodology for financial outlier detection using information systems will help to reduce the time and effort required, eliminate the subjective elements in detection of outlier data, and improve the efficiency and quality of analysis. The purpose of this research was to develop such a methodology.

Financial outliers were defined based on a case model. An outlier-detection method using the distances between cases in multi-dimensional space is proposed. Experiments using three diagnosis groups indicated successful detection of cases for which the profitability and income structure differed from other cases.

Therefore, the method proposed here can be used to detect outliers. Copyright © 2013 John Wiley & Sons, Ltd.

INTRODUCTION

Current environment

In recent years, hospitals have been expected to improve their financial efficiency. A WHO report in 2007 stated that “not enough resources are being spent on healthcare” (World Health Organization, 2007: 65) and “the complaint from comparatively well-funded systems, as well as from systems that receive only a small fraction of what is required in their health systems, is that more needs to be spent” (World Health Organization, 2007: 65). The report cites Japan as one example of a well-funded system, but more than 70% of all hospitals in Japan reported that total expenses exceeded income during the 2006 fiscal year (Japan Hospital Federation, 2007). It is essential for hospitals to improve their financial efficiency and to secure the profitability necessary to survive in such an environment.

Hospitals are licensed establishments primarily engaged in providing medical, diagnostic, and treatment services and the necessary specialized accommodations to inpatients; they may also provide outpatient services as a secondary activity (OECD, 2012). In fact, hospitals earn the majority of their income through inpatient care. For example, in Japan, the proportion of total income in 2006 attributable to inpatient care was >60%, whereas that from outpatient care was ~30% (Japan Hospital Federation, 2007). Additionally, the majority of a hospital's costs are related to inpatient care. Therefore, it is important for hospitals to assess the proper functioning of inpatient care to improve efficiency.

Effect of benchmarking analysis

Benchmarking is a process by which a company measures its products, services, and practices against those of its competitors or companies recognized as leaders in its industry. Benchmarking can measure a company's functional performance and financial efficiency; it is expected to provide clues about the internal weaknesses of a company and its position in the market (Gale Virtual Reference Library, 2009).

In the field of hospital management, benchmarking is generally considered to involve comparing indices among several hospitals with similar features (Hata, 2010), such as location, size, and clinical specialty portfolio. Some performance indices, such as length of stay (LOS) and income per patient for each disease, are widely accepted because they are closely related to financial indices.

Necessity for outlier elimination

In practical comparisons, average values are widely used as descriptive statistics, but they are likely to be affected by a few outlying cases (outliers), that is, cases that are markedly different from others. Because descriptive statistics are used to summarize the characteristics of sample data, such outliers must be determined and eliminated from analyses.

Benefits of a descriptive analysis including outliers

Detailed analysis and notation of outliers is informative. Hawkins defined an outlier as “an observation that deviates so much from other observations as to arouse suspicion that it is generated by a different mechanism” (Hawkins, 1980: 1). Thus, outliers must be associated with one or more factors that are responsible for this differentiation. Comparisons and analyses of normal cases and outliers will identify these factors. This may facilitate reduction of variation or may be a model for other cases to follow if outliers are the result of a new treatment.

Comparison of the distribution of outliers versus normal cases provides additional information regarding the outliers, such as the outlying degree, which may allow better separation in the region or reduce the variability.

Research on methods of outlier detection

Several Japanese studies have included cases in which the LOS and income exceeded predefined threshold values and were therefore regarded as outliers. These studies focused on groups of cases pertaining to identical disease categories, and the reasons for the outliers were investigated by using medical records (Hashimoto and Sekimoto, 2005; Sato et al., 2006). In these studies, the criteria for outliers were based on predefined indices, and the predefined thresholds were based on external assumptions. Only one category was analyzed.

Several considerations are necessary to ensure successful detection of outliers in massive data sets. First, the method of selecting indices to evaluate the appropriateness of outlier analysis (i.e., indices to serve as axes for analysis) must be considered. Second, the method used to set the threshold based on the distribution should be taken into account. For objective and reproducible analyses, axis selection and threshold setting independent of external data and assumptions, such as national averages, are preferable.

Third, the number of combined indices and disease categories reflects an operational difficulty. Although one patient may have multiple diseases or diagnoses, it is common to select one main disease per case. Outlier detection is usually conducted by using a group of cases belonging to the same disease category, which groups similar diseases. Despite such grouping, which is intended to reduce the number to be analyzed, a large number of categories may be seen within one hospital because many patients are treated in a single institution. For example, more than 1000 categories are used in one year in Kyoto University Hospital.

Thus, a great deal of time and effort is required to detect outliers in all categories by using all selected indices and appropriate thresholds fixed according to the distribution. The use of information systems will likely reduce the time and effort required for this process and increase the quantity of information obtained.

Automated indicator selection and threshold setting eliminates external assumptions and will enhance benchmarking efficacy in analyses without outliers. This will facilitate discovery of internal weaknesses and clarify the institution's organizational position in the market. This, in turn, may lead to improved process efficiency in the hospital and the establishment of its position in the region, so that each hospital can focus on its specialty area.

OBJECTIVE

The purpose of this research was to propose a methodology for detecting outliers from hospital care data and reimbursement data, with the aim of reducing the time and effort required to complete such analyses and eliminate subjective decisions regarding the criteria for elimination indices and thresholds.

METHODS

Case model

To clearly define outliers, we constructed a case model from both the clinical and financial points of view.

In this model, we used only inpatients, as described in BACKGROUND. One case was defined as the period from patient admission to discharge. As shown in Figure 18, each patient may have one or more diseases. Each disease is treated with medical interventions, including surgical procedures, prescription and administration of drugs, and so on.

Figure 18.

Case model

Medical treatment can be described in terms of a number of properties, such as the date of treatment, name of the doctor who placed the order, clinic the doctor belongs to, and so on. Each case is classified into one disease category in this model. To conduct medical treatments, resources must be devoted, and thus expenses incurred.

Cost, that is, the total expenditure of the healthcare organization during a period of hospitalization, is the summation of the cost of all medical treatments during this period.

Income payment systems vary among countries according to their healthcare insurance system. These include blanket payment systems, such as flat fee per case systems, represented by the diagnosis-related group (DRG) of the US, the flat fee per day system used in Japan (Okamura et al., 2005; Wang et al., 2010), and fee for service (FFS), which involves a fee for each medical treatment performed, and so on.

Income in the case of FFS is the sum of the income from all medical treatments during the period. Income in the case of flat-fee payment is based on the disease(s) or LOS, depending on the local insurance system.

Outlier definition

Because outliers are defined as highly deviant cases (Hawkins, 1980), a clinical outlier can be defined as a case that is highly deviant compared with other cases in the same disease category. Similarly, by using financial indices calculated for each case, financial outliers can be regarded as cases for which the index value differs greatly from that of other cases in the same disease category.

For hospitals to survive, they must generate fair profits, even if they are not-for-profit organizations. Profit, profit rate, profit-per-day, and the like can be considered financial indices that demonstrate profitability and profit efficiency and that can be calculated for each case. Therefore, finding outliers and the causes thereof may facilitate increased profitability.

As defined earlier, outliers are cases that deviate greatly from the norm. Referring to the model (Figure 18) proposed in the Case model section'Case model', cases become outliers because of relationships between pairs of the four factors represented by blue arrows and black lines: (i) case and disease; (ii) disease and treatment; (iii) treatment and cost; and (iv) disease category and hospital income. So, all outliers can be classified into one of the following four types (Figure 2):

  • Type A: Cases in which the combination of diseases is totally different from other cases in the same category.
  • Type B: Cases in which the medical treatments for the same disease are totally different from other cases.
  • Type C: Cases in which the costs are totally different for identical medical treatments.
  • Type D: Cases in which the hospital incomes are totally different among cases in the same category.
  • Some outliers can be classified as multiple types simultaneously, for example types A and B; that is, a patient with more diseases receives more medical treatments than other patients do.
Figure 2.

Outlier types

Of the aforementioned four types, types A, C, and D are detectable. That is, Type A can be detected by comparing the category and list of diseases from patient records. Type C can be detected by comparing the costs for each medical treatment. Type D can be detected by using macro-financial indices such as profit rate.

Detection of Type B outliers is problematic because there is no link between hospital information systems, such as those for medical accounting and medical treatment, to show for which disease the treatment was actually conducted. We expect that cases that are highly discrepant from others in the same category in terms of medical treatments conducted will likely have similarities with those classified as Type B. Unlike Type B, outliers of the disease category and treatment sort can be detected because only one category is assigned to each case.

Medical treatment coding systems add further complexity. A number of codes are involved in each procedure classification. For instance, there are 14 codes for wound treatments based on wound size and depth and patient age. Moreover, different codes may be used for the same treatment depending on the specific insurance policy involved. For example, codes for basic admission vary depending on LOS: the shorter the stay, the higher the charge per day. So for hospitals, shorter stays lead to greater income efficiency (in other words, more income per day), which is an incentive for hospitals to shorten the LOS. As a result, more than ten million codes are registered in procedure master files, including drugs and materials. Additionally, many medical treatments may be performed during a period of hospitalization. For example, although the average is 25 codes, a maximum of more than 100 treatment codes per day are recorded in the medical accounting system of Kyoto University Hospital. The average LOS is approximately 17 days, so more than 400 codes are typically recorded during hospitalization. Thus, detection of cases that are outliers in terms of medical treatments requires advanced data-mining techniques.

To summarize such complexity, we adopted a summary division system in this study. Medical services are classified into several divisions, such as consultation, surgery, and injection, in the Japanese National Health Insurance System. Similar summarizing occurs in other insurance systems. Statistical processing can be performed by swapping medical treatment codes for a numeric value that represents the associated income.

Hereafter, we define income structure as the pattern of medical treatments indicated by income, subtotaled by division. Outliers with an income structure that deviate greatly from others in the same disease category are termed micro-financial outliers. To avoid confusion, the previously defined outliers associated with profitability are termed macro-financial outliers.

Although most cases can fall into any outlier type, some are neither a micro-financial outlier (different income structure) nor a macro-financial outlier (different profitability). For instance, some cases may include more diseases, but their profitability and income structure are not different from those of most cases. Such cases, however, are not the target of this research because from the management viewpoint, they are not outliers, regardless of whether a macroscopic or microscopic standpoint is taken.

Due to these healthcare business and business process considerations, it can be said that two types of outliers should be detected from a financial point of view: macro-financial outliers (associated with profitability) and micro-financial outliers (associated with patterns of medical treatment, i.e., income structure).

Outlier-detection algorithm

Hodge and Austin identified three fundamental approaches to outlier detection (Hodge and Austin, 2004).

  • Type 1: Learning approach, similar to unsupervised clustering.
  • Type 2: Similar to supervised classification.
  • Type 3: Similar to semi-supervised recognition.

Supervised data appear to indicate ideal medical treatment patterns. However, data preparation requires enormous time and effort because of the characteristics of the data (i.e., cases are clinically scattered due to patient factors, variation in standard treatment among institutions, and the multitude of disease categories).

A normal distribution cannot be assumed because clinical homogeneity is not assured. Furthermore, the distribution cannot be predicted in a group of clinical data in the same disease category.

Additional data characteristics:

  1. Data are static, and real-time processing is unnecessary.
  2. Few data will be processed simultaneously (a few hundred cases maximum).
  3. The ratio of outliers to the total number of cases is unknown.

Thus, Type 1 is the most appropriate algorithm and was used in this study.

According to Hodge and Austin, proximity based and self-organizing map (SOM) (Kohonen et al., 1997) techniques can be used in a Type 1 approach (Hodge and Austin, 2004).

However, in an SOM, a neural network that requires an unsupervised learning algorithm, distances on the map are not calculated by using the Euclidean distance, which means the similarity of two adjacent points is not the same as that of other adjacent points. Additionally, the same data might lead to a different result because initial values are random. Thus, an SOM is not appropriate for this research.

In contrast, proximity-based techniques are simple to implement and make no prior assumptions regarding the data-distribution model. Nevertheless, they suffer from exponential computational growth because they are founded on the calculation of the distances between all records (Hodge and Austin, 2004). The computational complexity is directly proportional to both the dimensionality of the data and the number of records (Hodge and Austin, 2004).

Knorr and Ng adopted the notion of distance-based (DB) outliers and proposed an algorithm that increased calculation speed and reduced memory usage (Knorr and Ng, 1998). DB outliers are defined as follows: an object O in a dataset T is a DB (p, D) outlier if at least fraction p of the objects in T lies at a distance from O that is greater than D. In Figure 3, 100 objects are located in a circle with radius = 1.0 and center = (0, 0) while an object O is located at (2, 2). In this case, because these 100 objects lie more than 1.8 from O, O is a DB (0.99, 1.8) outlier.

Figure 3.

DB (p, D) outlier

In this study, computation time and memory usage were not problematic, as shown by preliminary work using a simple algorithm. However, in this algorithm, users must set two parameters, and results vary depending on those settings.

Breunig et al. defined a quantitative outlier, based on the local outlier factor (LOF) using the k-nearest neighbor (Breunig et al., 2000). In this algorithm, when the k variable of the k-nearest neighbors, that is, the number that indicates how many points are treated as nearest neighbors in the calculation, is well-selected, outliers can be detected visually by drawing a line or bar graph of LOF values sorted in ascending order. The line exhibits a sudden change in slope, that is, a change point, so objects with an LOF value above the change point represent outliers. However, selecting the optimum k is difficult.

Byers and Raftery determined the optimum k by estimating the change in entropy caused by a change in k (Byers and Raftery, 1998). However, this method requires labeling normal data in advance.

As described previously, in this study, neither supervised data nor prior labeling was available. To reduce the number of parameters, users need to decide to employ this technique, and based on the DB outlier-detection method, we used the detection algorithm described below.

Figure 4 shows a normally distributed cluster of size N, where N is the number of points. The distribution of distances between any two points extracted from all N points plotted in the form of a histogram is considered a heap with a long tail on the right side (Figure 5). The total number of distances is NC2 = N × (N − 1)/2 because it is a combination of two elements from among N elements. Then, a point that deviates greatly from the cluster, PN + 1, is added (Figure 6); it is assumed that N is sufficiently greater than one. In this case, the distance between two arbitrary points extracted from (N + 1) points is illustrated (Figure 7). The heap on the left of the graph indicates the distances between any two points extracted from N points within the cluster, whereas the heap on the right shows the distance between the point PN + 1 and a single arbitrary point extracted from N points within the cluster. The change point in the histogram is shown as Dth, which can be used as the distance, D, in DB (p, D) outlier mentioned earlier (“th” indicates threshold).

Figure 4.

A cluster with N points following normal distribution

Figure 5.

Histogram of distances between each point in Figure 4

Figure 6.

A cluster with N points and a point apart from the cluster

Figure 7.

Histogram of distances between each point in Figure 6

Next, concerning (N + 1) points, we counted the number of points to which the distance from the point is equal to or longer than the distance Dth. In terms of N points within the cluster, the point PN + 1 is the only one with a distance exceeding Dth. That is, the result is one. In terms of point PN + 1, the result is N because all points in the cluster are applied. As N is sufficiently greater than one, the point PN + 1 can be distinguished from others within the cluster. That is, PN + 1 is a DB (p, Dth) outlier where p = (N − 1)/N.

Although a normal distribution is assumed in the previous argument, this outlier-detection algorithm can be applied to other distributions when points in a cluster are distributed densely enough, even if the distribution is non-normal.

Additionally, even in cases where multiple outliers exist, this method can be applied when outliers deviate greatly from the cluster and when the number of outliers is sufficiently smaller than the size of the cluster. In this case, one minus the ratio of outliers corresponds to p in the DB (p, D) outlier definition.

Various distance functions are available, such as Euclidean distance and Manhattan distance. In this study, Mahalanobis distance (MD) (De Maesschalck et al., 2000) was used to calculate the distance between points. MD is a standardized form of Euclidean distance where data are standardized by scaling responses in terms of standard deviations, and adjustments are made for intercorrelations between variables (Judson, 2005).

When X is a data matrix containing n objects in the rows measured for p variables, and Cx is the variance–covariance matrix, the MD for each object xi is calculated using the formula (De Maesschalck et al., 2000):

display math

In this study, the variables do not always have the same unit or scale (discussed in the Parameter Selection section'Parameter selection'). For example, it is possible to select a time period, such as LOS, for the first parameter, and an amount of money, such as total income during hospitalization, as the second. It is also possible to select total income during hospitalization for the first and cost per day for the second. Thus, each variable may have a different unit and scale. To adjust for differences between variables, it is appropriate to select MD for the distance function.

One-dimensional change-point detection is conducted by visual examination of graphs. To automatically detect change points, the fitted regression line may be useful, as it is commonly used to detect change points in longitudinal data.

Disease-classification system

The disease-classification system used in this study has two requirements:

  1. Cases belonging to the same category must have strong clinical similarities.
  2. Each case must belong to a single category.

Several classification systems, such as the International Statistical Classification of Diseases and Related Health Problems (ICD) and Diagnosis-Related Groups (DRGs) are used in a number of nations. Any of these can be adopted for this method of outlier detection so long as it satisfies the two requirements stated at the beginning of this section.

In this study, the Diagnosis Procedure Combination (DPC) was adopted as the disease-classification system. DPC is currently used for medical claims in Japan.

In Japan before 2003, medical payments were calculated under the total FFS system, in which the payment for one case was the sum of the fees for all treatments. Since 2003, when the new case-mix payment system was introduced, the payment has been divided into a blanket component and an FFS component. The blanket component is a per diem prospective payment of the hospital fee, and the amount of payment per day is fixed for each DPC. The FFS component for the doctor's fee is based on the national fee schedule and corresponds to charges for surgical procedures (Okamura et al., 2005; Wang et al., 2010).

DPC was selected for two reasons; first, it allows collection of similar cases from both the clinical and financial points of view because it is coded based on the disease that was most resource consuming and its severity, as well as the method of treatment. Second, no additional coding is required because codes are already assigned in the claims data.

DPC adoption may influence interpretation of the output and use to which detected outliers might be put.

Parameter selection

Parameters that indicate profitability

A number of financial indices indicate profitability, and profit is one of the most fundamental indices in these institutions. Hospital profits can be described by the following formula:

display math

Total_LOS is the sum of the LOS of all cases during a certain period, which is likely to be determined by the number of beds. The number of beds is regulated by regional health planning in each medical care area. Thus, a hospital cannot use its discretion to increase the number of beds. Therefore, improving Profit_per_day is thought to be an effective means of increasing the profit of the entire organization.

Profit_per_day for each case is expressed by the following formula, where LOS is the period of hospitalization for one case, Income is the total income during a period of hospitalization, and Cost is the total costs:

display math

The most appropriate way to break down Income depends on the healthcare insurance system.

The relevant parameters are defined as follows (all variables are totals during hospitalization):

  • Income_BL: the amount of payment in the blanket component, depending on disease category (DPC in this case) and LOS (BL, blanket).
  • Income_FFS: the amount of payment in the FFS component.
  • IncomeSup: the supposed income calculated under the FFS system for all treatments during hospitalization. This indicates the actual volume of treatments conducted (Sup, supposed).

By using these, Profit_per_day for each case can be converted into the following equations:

display math

Therefore, the following three parameters appear to be appropriate:

  • FFS income per day: Income_FFS/LOS
  • Cost divided by IncomeSup: Cost/IncomeSup
  • Income divided by IncomeSup: Income/IncomeSup

For “Income divided by IncomeSup,” the inverse “IncomeSup divided by Income” can be adopted instead. We adopted the former because it is more popular in the current analysis situation, and its use will thus assist readers' understanding of the results.

Income_BL was omitted from the selection because it is pre-decided by the government according to disease category and LOS.

We used these parameters in this study because they indicate profitability.

Income-structure parameters

In the Outlier definition section'Outlier definition', income structure was defined based on subtotal income by division.

In the medical payment system in Japan, the income calculated under the FFS system can be divided into two divisions, A and B. Division A comprises procedure, drugs, and materials, and Division B includes 10 categories such as consultation, surgery, and hospitalization fees. Table 1 lists the categories of Division A and B. For example, drugs used during surgery are included in the cell “drug” (Division A) and category 5 (surgery), while drugs for daily use are included in the cell drug and category 2 (prescription). Thus, the combinations of the two divisions can involve up to 30 parameters.

Table 1. Income divisions for FFS system
Division BDivision A
ProcedureMaterialDrug
0Own expense   
1Consultation   
2Prescription   
3Injection   
4Treatment   
5Surgery   
6Examination   
7Imaging   
8Rehabilitation   
9Hospitalization   

Because all medical treatments conducted are recorded in the medical accounting system, we can calculate the FFS income even if the actual incomes were paid under the flat-fee payment system. Thus, subtotal income by division is computable in all cases.

However, in the DB outlier-detection method, calculation of the distances between any two points extracted from among all points becomes increasingly complex as the data become multi-dimensional. In this study, principal component analysis (PCA) was conducted after standardization of the values for 30 types of subtotal income by division to reduce the number of indices. PCA is an ordination technique used primarily to display patterns in multivariate data. Its purpose is to display the relative positions of data points in fewer dimensions, while retaining as much information as possible, and thereby exploring the relationships among dependent variables (Syms, 2008). The statistical software “r” version 2.9.0 (R Foundation, Vienna, Austria). was used to conduct the PCA.

With regard to the principal component, one commonly used approach is to select conditions with an eigenvalue of 1 or greater, a cumulative contribution ratio of 80% or higher, and/or conditions in which the contribution ratio was markedly larger than that of the next principal component. In this study, however, we used a cumulative contribution ratio of 60% or lower, based on our preliminary work.

Verification

A prototype system was constructed by using the methods explained earlier. The system was developed by the authors using Java version 1.6.0 (Sun Microsystems, Santa Clara, CA, USA). The three DPC categories (Table 2) were selected because medical treatments are determined by disease severity and are therefore more likely to be less scattered in these categories. All data were obtained from the Kyoto University Hospital cost-accounting system for fiscal year 2011.

Table 2. DPC categories used in the experiment
NoCodeDiagnosisSurgery 1Surgery 2ComplicationsNo. of cases
1060035XX0100XXColectomy of large intestineNoNo50
2010060X09912XXCerebral infarction (under JCS 30)NoYesNo56
3040080XX99X00XPneumoniaNoNoNo99

Selection of parameters that indicate income structure

Income-structure parameters were selected based on the principal component analysis.

  1. DPC No. 1 Colon cancer

Table 3 indicates the contribution ratio for each principal component. The first two principal components (PC1 and PC2) were adopted according to the rule that principal components be adopted until the cumulative contribution ratio reaches 60%.

Table 3. DPC No. 1 micro outlier contribution ratio and cumulative contribution ratios for principal component
 Contribution ratioCumulative contribution ratio
  • *

    The number of points is 50.

PC10.4350.435
PC20.1110.547
PC30.0900.637
PC40.0690.707
PC50.0590.766

Table 4 shows the eigenvectors for PC1 and PC2. The PC1 eigenvector is comparatively high at elements for which the coefficient of determination (R2) with LOS is higher. For example, R2 with LOS was 0.90 at X91, 0.85 at X31, and 0.75 at X72. This indicates that PC1 is associated with LOS, and PC2 is associated with examination (category 6) and rehabilitation (category 8).

Table 4. DPC No. 1 micro outlier eigenvector for PC1 and PC2Thumbnail image of
  • *

    Services not covered by insurance, such as private room and documentation fees, are included in “0, Own expense” in Division B.

  • **

    Blank cells with no value indicate that the subtotal income by division was 0.

  • ***

    Cells in which the absolute value is larger than 0.20 are highlighted.

  • ****

    The number of points is 50.

  • Examination and rehabilitation, however, were not performed in the majority of cases (29 of 50 cases had zero for X62, 49 cases for X63, and 44 cases for X81). The data used in this study had the characteristic that the scale varied depending on the variables. For example, most of the values in X91 (Admission Fee, Procedure) are above ¥10 000 (about 100 US dollars) per day, and the values in X51 (Operation, Procedure) may be very large. In fact, the data of DPC No. 1 for fiscal year 2011 reveal that values were between a minimum of ¥400 000 (about 400 US dollars) and a maximum of more than ¥1 500 000 (about 1500 US dollars). To adjust for these differences among variables, data standardization was conducted at PCA. This operation may have resulted in the phenomena that variables such as X63 and X81, which did not apply to the majority of cases, had a disproportionate effect, even if their actual values were much smaller compared with other variables.

    • b.DPC No. 2 Cerebral infarction

    The first four principal components (PC1, PC2, PC3, and PC4) were adopted. PC1 was considered to be associated with LOS, PC2 with rehabilitation (category 7), and PC3 with injection (category 3) and treatment (category 4), although the values were small. The maximum value of X33 was 220, and that of X43 was 3300, while that of X72 was over 160 000. X72 was the dominant variable for PC2. PC4 was associated with operation (category 5), but 53 cases of 55 had zero for X51, and 54 cases for X52, so a similar explanation as DPC No. 1 could be adopted.

    • c.DPC No. 3 Pneumonia

    The first principal components (PC1) were adopted. PC1 was associated with LOS.

    Outlier detection

    Financial outliers were detected using the algorithm proposed in the Outlier detection algorithm section'Outlier-detection algorithm'. In this algorithm, the parameters previously mentioned were used, that is, the three parameters indicating profitability derived in the Parameters that indicate profitability subsection for macro-financial outliers and the parameter indicating income structure calculated in the Selection of parameters that indicate income structure subsection for micro-financial outliers.

    1. DPC No. 1 Colon cancer
    Micro-financial outliers

    Figure 8 shows the distances between any two points extracted from all points. The distribution changes at around step 13 to step 15 on the x-axis. Step 13 indicates distances between 2.55 and 2.77.

    Figure 8.

    Histogram of distances between points for DPC No. 1 micro financial outlier

    Suppose we choose step 13 as the change point. The maximum value at step 13, 2.77, was regarded as the threshold value, Dth. The number of points to which the distance D from the point is 2.77 or longer were counted and sorted in ascending order (Figure 9). It is obvious that the last three bars deviate greatly from the other 47. Thus, the three cases represented by these bars can be regarded as micro-financial outliers. These are DB (0.94, 2.77) outliers; that is, at least 94% (47/50) of all cases lie at a distance from them greater than Dth = 2.77.

    Figure 9.

    Number of points where D is 2.77 or larger (sorted in ascending order)

    The 50 cases in DPC No. 1 were plotted with the PC1 value on the x-axis and the PC2 value on the y-axis (Figure 10). The 47 normal cases are plotted as blue dots, and the three outliers (Nos. 7, 8, and 34) in red. The numbers plotted next to some points are the identification number of each case. All three outliers deviated from the normal cases.

    Figure 10.

    DPC No. 1 micro financial outlier (red) versus normal case (blue) (X, PC1; Y, PC2)

    If step 14 or 15, instead of step 13, is selected as the first step, the same three cases are detected as outliers; so all are DB (0.94, 3.19) outliers (3.19 is the maximum distance at step 15).

    Macro-financial outliers

    In the distance histogram, a single DB (0.98, 4.85) outlier (No. 34) was detected. Figure 11 shows a plot with FFS income per day on the x-axis and cost divided by IncomeSup on the y. Figure 12 shows a scatter plot with FFS income per day on the x-axis and Income divided by IncomeSup on the y. The 49 points representing normal cases are shown in blue, and the single outlier in red. The outlier differs from the standard cases; this case, No. 34, was also detected as a micro-financial outlier.

    Figure 11.

    DPC No. 1 macro outlier (X, Income_FFS/LOS; Y, Cost/IncomeSup)

    Figure 12.

    DPC No. 1 macro outlier (X, Income_FFS/LOS; Y, Income/IncomeSup)

    In Figure 11, the x-axis represents the FFS component in income per day, and higher x-values originate from a higher proportion of paid treatment and/or shorter LOS. Similarly, for the y-axis (Cost/IncomeSup), as IncomeSup represents all the treatments conducted (paid or included in blanket), lower y-values indicate that cost performance is better because the same treatments represented by IncomeSup can be conducted at lower cost.

    So, points with high x-values and low y-values might indicate financially ideal cases, due to their higher earnings and lower costs.

    In Figure 12, the y-axis represents Income/IncomeSup and the index means the ratio of actual income (Income) and all the treatments conducted (IncomeSup), regardless of whether they are paid. So, lower y-values may originate from income loss, because of uncharged treatments or for other reasons, although no y-axis outlier was detected here. Cases with high x-values and y-values represent financially ideal cases.

    Table 5 shows the detection ratio, that is, the percentage of cases, LOS and income, as the DPC01 micro-outlier and macro-outlier detection results.

    • b.DPC No. 2 Cerebral infarction
    Table 5. DPC No. 1 outlier detection results, percentage of number of cases; LOS; and income.
      Number of cases [%]LOS [%]Income [%]
    1. Total number of cases is 50.

    (i) Micro outlierDB (0.94, 3.19) outlier6.011.012.9
    (ii) Macro outlierDB (0.98, 4.85) outlier2.06.28.5
    Micro-financial outliers

    Three cases (Nos. 1, 4, and 38) were detected as micro-financial outliers. According to Figures 13 and 14, all three deviated from other cases.

    Figure 13.

    DPC No. 2 micro outlier (X, PC1; Y,PC2)

    Figure 14.

    DPC No. 2 micro outlier (X, PC3; Y, PC4)

    Macro-financial outliers

    Figure 15 shows a histogram of distances between two arbitrary points extracted from among all points. This plot comprises one distribution, and thus no change-point is detected. Figures 16 and 17 show scatter graphs of three parameters that indicate profitability. There are no outliers because the cases are distributed widely.

    Figure 15.

    Histogram of distances between two arbitrary points for DPC No. 2 macro outlier

    Figure 16.

    Scattered graph for DPC No. 2 macro outlier (X, Income_FFS/LOS; Y, Cost/IncomeSup)

    Figure 17.

    Scattered graph for DPC No. 2 macro outlier (X, Income_FFS/LOS; Y, Income/IncomeSup)

    Table 6 shows the percentage of cases, LOS and income as the DPC02 micro-outlier detection result.

    • cv.DPC No. 3 Pneumonia
    Table 6. DPC No. 2 outlier detection results, percentage of number of cases; LOS; and income.
      Number of cases [%]LOS [%]Income [%]
    1. Total number of cases is 56.

    (i) Micro outlierDB (0.95, 4.40) outlier5.48.47.4
    (ii) Macro outlierno outlier detected
    Micro-financial outliers

    Two cases (Nos. 3 and 67) were detected as outliers. Figure 18 shows a scatter plot with PC1 on the x-axis and PC2 on the y, although only PC1 was used for outlier detection from the results of PCA in Selection of parameters that indicate income structure section. According to the plot, both differed from other cases.

    Figure 18.

    DPC No. 3 micro outlier (X, PC1; Y, PC2)

    Macro-financial outliers

    Two cases (Nos. 3 and 91) were detected as outliers (Figures 19 and 20). One case (No. 3) was both a macro-financial and a micro-financial outlier.

    Figure 19.

    DPC No. 3 macro outlier (X, Income_FFS/LOS; Y, Cost/IncomeSup)

    Figure 20.

    DPC No. 3 macro outlier (X, Income_FFS/LOS; Y Income/IncomeSup)

    In Figures 19 and 20, the two outliers on the right have higher x-values (Income_FFS/LOS), which suggests a higher income efficiency (more paid treatment and/or shorter LOS). In contrast, the outlier with a higher y-value (Income/IncomeSup) in Figure 20 indicates a higher Income (i.e., actual income) or a lower IncomeSup (i.e., all the treatments conducted) versus other cases. It is possible that some procedures were not recorded in the accounting systems or they were not conducted for some reason; more detailed analysis of medical records would be required to clarify this issue.

    Table 7 shows the detection ratio, that is, the percentage of cases, LOS and income as the DPC03 micro-outlier and macro-outlier detection results. All detected outliers were highly deviated from other cases.

    Table 7. DPC No. 3 outlier detection result, percentage of number of cases; LOS; and income.
      Number of cases [%]LOS [%]Income [%]
    1. Total number of cases is 99.

    (i) Micro outlierDB (0.98, 2.18) outlier2.012.916.7
    (ii) Macro outlierDB (0.98, 5.02) outlier2.06.511.0

    Thus, financial outliers can be detected by this method using information systems.

    DISCUSSION

    The purpose of this study was to propose a methodology for detection of outliers from hospital care and reimbursement data with the aim of reducing the time and effort required for detection of outliers and eliminating the need for subjective decisions regarding elimination criteria indices and thresholds.

    Comparison with previous research

    Previous researchers have conducted studies to detect and analyze outliers (Hashimoto and Sekimoto, 2005; Sagae et al., 2006; Sato et al., 2006). They defined outliers as cases in which the LOS is longer than a predefined threshold or the Income/IncomeSup is less than 1.0. Because these variables are fixed in advance and only one-dimensional detection is performed, it is possible that important variables and outliers are missed. Additionally, as the threshold value is obtained by the government from the national statistics data in the case of LOS, it may not represent the actual distribution.

    In contrast, the method we propose detects outliers by using multiple variables selected from candidates in multi-dimensional space, and the threshold is set according to the distribution, facilitating detection of outliers that differ more from other cases. This approach results in provision of more appropriate information when benchmarking or outlier analyses are performed.

    One Australian study investigated suspicious medical treatments using detailed claims data provided by the health insurance union (Yamanishi et al., 2004). While the outliers detected differed from the other cases in some respects, this approach could not explain the underlying causes. Moreover, this method requires massive amounts of data, although the quantity of data stored in a single hospital is necessarily limited.

    In contrast, in the present study, the outliers clearly differed in terms of the variables used in the analysis, and analysis of the underlying causes was possible. The method proposed here requires less data and so can be applied to smaller hospitals and/or shorter periods.

    Limitations

    We propose a method for detection of financial outliers by selecting axes for analysis, expressing outliers quantitatively by adopting the notion of DB (p, D) outliers and setting threshold values. We extracted outliers that deviated greatly in the verification experiments. These findings provide information that will facilitate increases in profitability and satisfy all requirements.

    The definition of an outlier is subjective, and the border between an outlier and a normal case is ill defined. The threshold-setting method used in this paper is based on two assumptions: the number of outliers is sufficiently small for the size of the main cluster, and outliers deviate greatly from the main cluster. As a result, we successfully extracted outliers that were markedly different from the main cluster.

    However, some cases that are only slightly different from the main cluster can also be useful for increasing profitability when the medical treatments are analyzed closely.

    Thus, there is room to consider the method of setting threshold values.

    These methods target outlier detection by using profitability and medical treatment patterns, represented by income structure; that is, the outcomes of patient conditions were not analyzed. Therefore, an optimal result, in terms of the best outcome, may not be obtained. To address this issue, additional data and/or information on outcomes should be obtained from hospital information systems, such as electronic medical records, and analyzed as objective functions. However, this does not guarantee that the same results will always be obtained, as the results vary according to health condition, even if identical medical treatments are conducted. Therefore, optimizing patients' health outcomes is problematic.

    Future possibilities

    In this study, methods for detection of outliers were developed to increase profitability. To make use of these methods to improve profit, factor analyses of the outliers detected are required.

    Table 8 shows the four types of outliers described in the Outlier definition section'Outlier definition' and the main clinical and financial factors that cause cases to be outliers. Clinical factors are more uncontrollable, such as disease severity and co-existing diseases. Financial factors, meanwhile, tend to be more controllable, such as miscoding of disease category and unnecessary medical treatments. Therefore, analysis of financial factors is more likely to result in increased profitability. Thus, determination of financial factors is critical. However, it should be noted that even though disease severity seems to be totally uncontrollable, it may be controlled in the long run when combined with, for example, a marketing strategy to recruit more patients.

    Table 8. Outlier types and major factors
    Outlier typeRelation betweenClinical factorFinancial factor
    ADisease category and diseaseCoexisting diseaseMalcoding
    BDisease and treatmentSeverityUnnecessary medical treatment
    Difference in operative proceduresInadequate treatment
    CTreatment and costConsultation (surgery) hoursLoss of materials
    Arrangement of personnelInappropriate cost-distribution rules
    DDisease category and incomeAdministrative mistakes

    To determine to which factor the outliers detected belong, more detailed treatment data must be analyzed. We will obtain and analyze such data in a future research project.

    CONCLUSIONS

    The purpose of this research was to propose a methodology for detection of outliers from hospital care and reimbursement data with the aim of reducing the time and effort required for detection of outliers and eliminating the need for subjective decisions regarding elimination criteria indices and thresholds.

    In our clinical and financial case model, financial outliers are defined as cases in which profitability and income structure differ from those of the majority in the group of cases in the same disease category. Next, a method for outlier detection using distances between cases in multi-dimensional space was proposed. Then, experiments using three diagnosis groups successfully detected cases with a profitability and income structure that differ from those of others.

    The method proposed here can be used to detect outliers.

    ACKNOWLEDGEMENTS

    This work was partially supported by the research fund for joint studies with NTT DATA Corporation. The authors declare no conflict of interest with the content of this manuscript.

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