1 of 18

The Predictive Factors of Hospital Bankruptcy: �A Longitudinal Analysis

Brad Beauvais (1), Zo Ramamonjiarivelo (1), C. Scott Kruse (1), Ramalingam Shanmugam (1), Larry Fulton (2), Aleksandar Tomic (2), Arvind Sharma (2)

Texas State University, School of Health Administration (1)

Boston College, Woods College of Advancing Studies (2)

2 of 18

Motivation

In recent years, the operational viability of numerous hospitals across the United States has faced challenges

Intricate landscape of regulatory, reimbursement, and workforce issues affecting revenue cycles

This has resulted in a significant upswing in healthcare-related bankruptcies

Polsinelli Financial Distress Index reveals a 305% increase since 2010

With the closure of a hospital comes the increased societal cost of not just lost jobs, but also poorer access to care, and other supportive clinical services

Earlier attempts by researchers to propose explanatory methods for predicting bankruptcy have not undergone extensive testing in the health care industry

We develop an explanatory and predictive logistic model for hospital bankruptcy

Utilizing only 8 financial and hospital-level variables
Outcomes showcase superior performance on 5 out of 7 commonly used metrics in the confusion matrix
Presents practitioners with a robust tool for both assessing and predicting financial distress in the healthcare sector before it is “too late”

Abstract

In recent years, the operational viability of numerous hospitals across the United States has faced challenges due to the intricate landscape of regulatory, reimbursement, and workforce issues. This has resulted in a significant upswing in healthcare-related bankruptcies, as emphasized by the Polsinelli Financial Distress Index, revealing a 305% increase since 2010. Despite earlier attempts by researchers to propose explanatory methods for predicting bankruptcy, such as the Altman's discriminant multivariate analysis, the Ohlson's "O-Score" nine-factor linear factor model, and the Zmijewski’s reduced factor model, none of these models have undergone extensive testing in the health care industry. Addressing this gap, this study develops an explanatory and predictive logistic model for hospital bankruptcy, utilizing only 8 financial and hospital-level variables and drawing on data from 3,091 hospitals spanning the period from 2008 to 2021. The outcomes showcase superior performance on 5 out of 7 commonly used metrics in the confusion matrix, as well as presenting practitioners with a robust tool for both assessing and predicting financial distress in the healthcare sector.

Conclusion

Bankruptcy is the unfortunate result of many businesses throughout the US economy. Businesses start and fail daily in our country. Any time a ‘regular’ business closes, there is a resulting cost to the local market of limited supply of products, services, and labor market opportunities. However, in recent years, there has been an increased number of hospitals in the United States that have met this problematic ending.

With the closure of a hospital comes the increased societal cost of not just lost jobs, but also poorer access to care, and other supportive clinical services. A hospital closure means patients and families must travel further for definitive care – with an implied cost of time, money, and, in the case of emergency situations, the loss of human life. It is these implications that provided the impetus for our research into gaining a deeper understanding of what contributes to hospital bankruptcy. As our population grows, and ages, our healthcare delivery facilities must remain financially viable to continue to provide care for and treat the patients and families they serve.

�

3 of 18

Bankruptcy Definition

There are three types of bankruptcy

Drawn from different “chapters” in the U.S. Bankruptcy Code

Chapter 13 - sole proprietorships can reorganize assets and liabilities

Chapter 7 - ceases operations of the business/partnership
Chapter 11 - reorganization and allows the business to continue to operate

4 of 18

Literature Review

Bankruptcy studies often focused on non-healthcare service organizations or manufacturing industries

Early studies of bankruptcy and financial distress in hospitals suggested both non-financial and financial factors should be considered [McCue (1991); Bazzoli & Cleverley (1994); Bazzoli and Andes (1995)]

Financial factors : Low or declining liquidity, negative equity, inability to make profit, high long-term debt, insolvency, rising costs, low outpatient revenue, low cash flows, financial ratios …
Non-Financial factors : Smaller hospital size in terms of number of beds, low occupancy rate, poor payer mix in terms of a high percentage of Medicare and Medicaid patients, aging facilities, poor management, demographic changes, quality issues, physician malpractice insurance, …
Notably, none of these models include time-lagged variables for prediction - they seek to explain

Some earlier researchers have applied predictive models like Financial Strength Index, the Altman Z-score model, the Ohlson O Score, and the Zmijewski score to assess the likelihood of bankruptcy of hospitals

These have not been tested, nor the financial and non-financial ratios were significantly associated with for-profit hospital financial solvency [Corbett and Gosset (2017)]
Most studies of bankruptcy have relied solely on financial data to derive their models

Existing models lack predictive capability as they apply to the hospital setting

Potential to create better model and test their predictions

5 of 18

Table of Content

Motivation
Literature Review

Bankruptcy Models

Altman Model
Ohlson Model
Zmijewski Model

Data
BRKFSST Model

Summary Statistics
Results
Comparison with other bankruptcy models

Summary

6 of 18

Predicting Bankruptcy: Altman Model

Z = 0.012×X1 + 0.014×X2 + 0.033×X3 + 0.006×X4 + 0.999×X5

(1)

It is comprised of the combination of five weighted ratios from five areas of organizational financial performance: profitability, leverage, liquidity, solvency, and activity.

X1 = working capital/total assets: NET LIQUID ASSETS OF THE FIRM

Measure of liquidity. It indicates the proportion of a company's total assets that are financed by its working capital, which is the difference between current assets and current liabilities. Higher values of X1 suggest better liquidity.

X2 = retained earnings/total assets: CUMULATIVE PROFITABILITY OVER TIME

Measure of profitability and financial performance. Retained earnings are the accumulated profits of a company that have not been distributed to shareholders as dividends. Dividing it by total assets provides a measure of how efficiently assets are being utilized to generate profits.

X3 = earnings before interest and taxes/total assets: TRUE PRODUCTIVITY OF ASSETS

Measure of profitability. It shows the company's ability to generate earnings from its total assets before considering the impact of interest and taxes.

X4 = market value of equity/total liabilities: MARKET VALUE DIMENSION - NEW VARIABLE

Measure of solvency and leverage. It compares the market value of a company's equity to its total liabilities. Higher values indicate that the market value of equity is relatively high compared to total liabilities, which suggests lower financial risk.

X5 = net sales/total assets: MANAGEMENT ABILITY

Measure of activity or asset turnover. It assesses how efficiently a company is using its assets to generate sales. Higher values imply better asset utilization and sales generation efficiency.

The Z′-score was developed specifically for private manufacturing companies, while the Z″-score was created for non-manufacturing firms, which might include organizations in the service sector such as hospitals and other healthcare organizations. This revised model is shown below:

7 of 18

Altman Model: Discriminant multivariate analysis

A discriminant score, in the context of discriminant analysis, refers to a numerical value obtained for each observation that indicates the likelihood or probability of that observation belonging to a particular group or category.

When you perform discriminant analysis, you develop a discriminant function based on the predictor variables. This function is essentially a mathematical formula that combines the values of the predictor variables to classify observations into different groups. When you apply this function to new observations, it generates a discriminant score for each observation for each group.

The discriminant score indicates how well the observation fits into each group. A higher discriminant score for a particular group suggests a higher likelihood of the observation belonging to that group, while a lower score suggests a lower likelihood.

In practical terms, when using discriminant analysis for classification tasks, you typically assign each observation to the group with the highest discriminant score. This allows you to classify new observations based on their predictor variables.

�

Discriminant analysis and clustering are two distinct statistical techniques, although they both involve analyzing data to identify patterns or groupings.

In discriminant analysis, the goal is to classify observations into predefined groups based on predictor variables. This is typically done by creating a discriminant function that maximizes the differences between groups while minimizing the differences within groups. The discriminant function is then used to assign new observations to one of the predefined groups.

On the other hand, clustering is a technique used to group similar observations together based on their characteristics, without any predefined groups. Clustering algorithms partition the data into clusters such that observations within the same cluster are more similar to each other than to those in other clusters. Common clustering algorithms include k-means clustering, hierarchical clustering, and DBSCAN.

While both discriminant analysis and clustering aim to uncover patterns or groupings within data, they differ in their objectives and methodologies. Discriminant analysis is supervised learning, meaning it requires labeled data with predefined groups, while clustering is unsupervised learning and does not require labeled data. Additionally, discriminant analysis aims to classify observations into predefined groups, whereas clustering aims to discover inherent groupings within the data itself.

8 of 18

Altman Model for non-manufacturing firms

Z = 0.012×X1 + 0.014×X2 + 0.033×X3 + 0.006×X4 + 0.999×X5

(1)

It is comprised of the combination of five weighted ratios from five areas of organizational financial performance: profitability, leverage, liquidity, solvency, and activity.

X1 = working capital/total assets: NET LIQUID ASSETS OF THE FIRM

Measure of liquidity. It indicates the proportion of a company's total assets that are financed by its working capital, which is the difference between current assets and current liabilities. Higher values of X1 suggest better liquidity.

X2 = retained earnings/total assets: CUMULATIVE PROFITABILITY OVER TIME

Measure of profitability and financial performance. Retained earnings are the accumulated profits of a company that have not been distributed to shareholders as dividends. Dividing it by total assets provides a measure of how efficiently assets are being utilized to generate profits.

X3 = earnings before interest and taxes/total assets: TRUE PRODUCTIVITY OF ASSETS

Measure of profitability. It shows the company's ability to generate earnings from its total assets before considering the impact of interest and taxes.

X4 = market value of equity/total liabilities: MARKET VALUE DIMENSION - NEW VARIABLE

Measure of solvency and leverage. It compares the market value of a company's equity to its total liabilities. Higher values indicate that the market value of equity is relatively high compared to total liabilities, which suggests lower financial risk.

X5 = net sales/total assets: MANAGEMENT ABILITY

Measure of activity or asset turnover. It assesses how efficiently a company is using its assets to generate sales. Higher values imply better asset utilization and sales generation efficiency.

The Z′-score was developed specifically for private manufacturing companies, while the Z″-score was created for non-manufacturing firms, which might include organizations in the service sector such as hospitals and other healthcare organizations. This revised model is shown below:

9 of 18

Predicting Bankruptcy: Ohlson Model

The Ohlson's model for predicting bankruptcy is based on a combination of financial ratios and indicator variables. Here's an explanation of the logic behind each variable:

O: This is the predicted probability of bankruptcy. The model predicts the probability of a firm going bankrupt based on the values of the variables.
O_1: This variable represents the leverage of the firm, calculated as the ratio of total assets (TA) to gross national product (GNP) price-level index. It indicates the extent to which the firm is financed by external sources relative to the overall economic conditions.
O_2: Total liabilities (TL) to total assets (TA) ratio. It measures the proportion of the firm's assets that are financed by creditors.
O_3: Working capital (WC) to total assets (TA) ratio. It shows the proportion of the firm's assets that are financed by its operational capital.
O_4: Current liabilities (CL) to current assets (CA) ratio. It assesses the firm's short-term liquidity position by comparing its short-term obligations to its short-term assets.
O_5: An indicator variable that equals 1 if total liabilities (TL) are greater than total assets (TA), indicating financial distress.
O_6: Net income (NI) to total assets (TA) ratio. It measures the firm's profitability relative to its size.
O_7: Operating funds to total liabilities (TL) ratio. It assesses the firm's ability to cover its liabilities with its operational funds.
O_8: An indicator variable that equals 1 if the firm has experienced two consecutive years of negative net income, indicating a sustained period of financial distress.
O_9: The change in net income (NI) relative to the absolute values of NI in the previous two years. It captures the trend in the firm's profitability over time.

The coefficients (6.72, 1.05, 6.5, 3.26) attached to each variable in the model indicate the relative importance of each variable in predicting bankruptcy. Positive coefficients indicate that an increase in the value of the variable increases the likelihood of bankruptcy, while negative coefficients indicate the opposite. The constant term (-1.32) represents the base probability of bankruptcy when all other variables are zero.

In summary, the Ohlson's bankruptcy prediction model combines financial ratios and indicator variables to assess a firm's financial health and predict the likelihood of bankruptcy.

10 of 18

Predicting Bankruptcy: Zmijewski Model

11 of 18

Data: Sample Construction

Data was acquired by custom query from Definitive Healthcare for the years 2008 through 2021

It was joined by hospital identifier with the Centers for Medicare and Medicaid (CMS) Hospital Compare data
Most of the financial data are available through CMS Hospital Provider Cost Reports

Initial sample size was 47,136 hospital-year observations

Removed observations with missing data exceeding 25% or more in columns and rows, the final sample size was 46,855 hospital-year observations, which equated to 3,196 hospitals
Of these 3,196 hospitals

Some hospitals did not have observations for all years due to closure, bankruptcy, opening, or other factors
71 had declared bankruptcy one or more times during the period

Eliminating hospitals with fewer than three years of consecutive observations
Kept facilities located in U.S. territories only
The set reduced to 3,091 hospitals with 65 unique bankruptcies

For these 3,091 hospitals, three consecutive years of observations were included

For those facilities entering bankruptcy in year y, data from years y-1 and y-2 served as potential predictors
For non-bankrupt hospitals, the starting year of observations was selected via random sampling. Then the two previous years of information were gathered to be used as potential predictors

Data were acquired by custom query from Definitive Healthcare for the years 2008 through 2021 [29]. These data were joined by hospital identifier with the Centers for Medicare and Medicaid (CMS) Hospital Compare data [30]. Most of the financial data are available through CMS Hospital Provider Cost Reports [31], although Definitive uses a parochial estimation model for facilities not reporting to CMS. The initial sample size was 47,136 hospital-year observations. After removing observations with missing columns and rows of 25% or more, the final sample size was 46,855 hospital-year observations, which equated to 3,196 hospitals. Of these hospitals, 71 had declared bankruptcy one or more times during the period. Some hospitals did not have observations for all years due to closure, bankruptcy, opening, or other factors. After eliminating those facilities with greater than 20% missing columnar data, hospitals with fewer than three years of consecutive observations, and facilities located in U.S. territories, the set reduced to 3,091 hospitals with 65 unique bankruptcies.

Vital to note in this study is that unlike most studies, all unknowable, random predictors were lagged. No information for year y was used to predict year y (time t). Only information from year y-1 and y-2 were used to predict time t. This statement holds true for the model comparisons that follow (e.g., Altman). For example, Altman did not use lagged variables in the initial model estimation; however, we used lagged variables to evaluate fairly the Z’’ predictive capacity (both with the original coefficients and re-estimated coefficients). In doing so, the model truly investigates predictive capability, not posterior explanatory information.

For these 3,091 hospitals, three consecutive years of observations were included. For non-bankrupt hospitals, the starting year of observations was selected via random sampling. Then the two previous years of information were gathered to be used as potential predictors. Thus, the entire population of hospitals given the inclusion criteria were represented in the analysis. For those facilities entering bankruptcy in year y, data from years y-1 and y-2 served as potential predictors. Thus, bankrupt status at year y was modeled as a function of data gathered from year y-1 and year y-2.

12 of 18

Only 65 of the 3,091 hospitals in the dataset (2.1%) experienced bankruptcy

13 of 18

Methodology: Logistic Regression

Our team developed an alternative model, titled based on the first letters of the last name of the study authors, with both explanatory and predictive capabilities. For this to be possible, data used to estimate bankruptcy must derive from (1) fixed variables that have known values, (2) forecasted values, making error estimation problematic, or (3) past data. For this analysis, the team chose to use past financial ratio data and an indicator variable for hospital quality. Equation 5 depicts the equation we estimated to both explain and predict bankruptcy

Variable X1 and X2 pertain to management of accounts receivable (AR), which is known to be an important factor in the successful management of any business, but an extraordinarily troublesome issue in the healthcare industry, as reimbursement relies on a third party in the form of insurance companies of varying type, size, and funding source. Each has its own set of requirements to fulfill for health care entities and providers to be fully reimbursed for goods and services provided. As a result, acute care hospitals, on average, experience AR days that can range between 37 – 60 days based on a recent survey [36]. In our study, accounts receivable divided by operating income measures the magnitude of AR compared to organizational income and has proven to be an important indicator of hospital bankruptcy in cross-sectional studies [25]. This measure is included as X1 (lagged at y-1) and X2 (lagged at y-2).

Variable X3, the current ratio (also known as the liquidity ratio and defined as CA/CL), is a well-known variable associated with bankruptcy [11]. The inverse of that variable has also been identified as a predictor as in the case of Ohlson’s O-4 [10] and is included as variable X4.

Variable X5 relates to the cost of labor. For hospitals, increases in labor compensation rates are an indicator of financial distress [25]. We hypothesized that positive changes in labor compensation rates would accelerate organizations towards bankruptcy given the significance of labor costs (possibly the biggest outlay for institutions, e.g. [37]), so we included a change variable (X5) to estimate the percent increase (or decrease) in these rates from y-2 to y-1.

Variable X6 is included in our model as the percent change in CL/CA. This variable measures the change in Ohlson’s X4 (the inverse of the current ratio) to provide directionality for the forecast. We hypothesize that higher percent increases in the change of CL/CA from y-2 to y-1 would be associated with higher risk of bankruptcy.

Variable X7 is adjusted patient days which is also shown to be associated with bankruptcy [10]). By including a workload measure, we evaluate the potential ability to produce revenue. We hypothesized that increases in workload would reduce the risk of bankruptcy. Adjusted patient days are calculated to adjust facility workload to ‘standard workload’ (i.e., case-mix index or CMI of 1.0) and to account for the outpatient workload by estimating its contribution to revenue. The formula for adjusted patient days is Equation 6. [35]

CMI∗ (Total Patient Days/(1−(Gross Outpatient Revenue/Gross Patient Revenue)))

(6)

In Equation 6, facilities with higher patient severity indicated by CMI>1.0 would have their patient days adjusted for that severity. Further, the denominator (which cannot exceed 1.0) adjusts the facilities’ workload by the percentage of inpatient revenue contributions to account for outpatient workload.

The final variable in the model is X8 which factors in the recent quality performance of the hospital. Quality assessments of hospitals have also been associated with bankruptcy [25], so the previous year’s Hospital Compare rating from the Centers for Medicaid and Medicare Services (CMS) were included as a dichotomous variable with low or average quality equal to zero and above average quality equal to one [30]. This variable, X8, measures quality and is a known factor in hospital performance [25].

14 of 18

Data: Summary Statistics

15 of 18

BRKFSST Model

16 of 18

Model Comparison

All models were built on the augmented training set.
These models were then used to forecast the test set. Typical classification performance metrics including accuracy, precision, recall, specificity, and the F1-score were used to compare models

The F1 score is a metric used to evaluate the performance of a classification model, particularly when dealing with imbalanced classes. It combines both precision and recall into a single value, providing a balance between these two metrics.

Precision (also called positive predictive value) measures the accuracy of positive predictions made by the model. It is calculated as the ratio of true positive predictions to the sum of true positive and false positive predictions:

Precision=True PositivesTrue Positives+False PositivesPrecision=True Positives+False PositivesTrue Positives

Recall (also called sensitivity or true positive rate) measures the ability of the model to identify all relevant instances, or in other words, it measures the fraction of actual positives that were correctly identified by the model. It is calculated as the ratio of true positive predictions to the sum of true positive and false negative predictions:

Recall=True PositivesTrue Positives+False NegativesRecall=True Positives+False NegativesTrue Positives

The F1 score is the harmonic mean of precision and recall, and it is calculated as follows:

�1=2×Precision×RecallPrecision+RecallF1=2×Precision+RecallPrecision×Recall

The harmonic mean gives more weight to lower values. As a result, the F1 score will be high only if both precision and recall are high, making it a useful metric for evaluating the balance between precision and recall in classification tasks.

17 of 18

BRKFSST Model Performance

All models were built on the augmented training set.
These models were then used to forecast the test set. Typical classification performance metrics including accuracy, precision, recall, specificity, and the F1-score were used to compare models

The BRKFSST model achieved an F1-score of 0.136 when predicting the test set and a recall of 0.758

While the model performed better than any of the other models, the precision remains relatively low, which is not unexpected given the generally idiosyncratic nature of bankruptcy decisions. While the recall was 0.758, the precision was 0.074, but still the best of the models estimated.