Data Analytics for Healthcare decision Making 3

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Getting Started With Assessment #3: Predicting an Outcome Using Regression Models

Lecture: Linear Multiple Regression Analysis

Introduction In this lecture, we cover linear multiple regression analysis, which is essential for predicting hospital inpatient service costs for the upcoming year. In this case, we are using predictive analytics to analyze if the hospital can control inpatient service risk (cost) and thus participate in Medicare’s Value-Based Payment (VBP) program. Using the standard multiple regression formula allows us to predict the dependent variable, in this case hospital costs, based on multiple independent variables. Understanding this type of analysis is crucial for making informed decisions in healthcare management.

What Is Regression Analysis? Regression analysis is a statistical method that examines the relationship between a dependent variable and one or more independent variables. This method is often used for making predictions or assessing the impact of various factors. There are three primary uses for regression analysis: determining the strength of predictors, forecasting an effect, and trend forecasting. For this case, regression analysis is used to predict costs based on risk factors such as age, risk level, and patient satisfaction. Given the complexity of healthcare data, predictions can sometimes be improved by using multiple regression, which incorporates more than one independent variable to predict the dependent variable.

Types of Regression Analysis

For this assessment, we will focus on multiple regression. Multiple regression involves more than one independent variable (e.g., X1, X2, X3) to predict a single dependent variable (Y). This approach provides a comprehensive understanding of how various factors collectively influence the outcome.

Case Scenario The hospital administration must decide on the reimbursement level required to cover expected costs for the upcoming year. They are considering a shift from inpatient prospective payments to value-based reimbursement and need to determine whether to accept a contract based on their projected costs. The key is to evaluate if this strategy is viable and identify necessary actions to implement it effectively. Given that hospitals are reimbursed under Medical Severity Diagnostic Related Groups (MS-DRGs)—a cost- based prospective payment system—they can use these cost projections to determine their revenue requirements and assess the viability of the Value-Based Payment (VBP) system, which puts the hospital at-risk for all costs related to the patient’s inpatient stay.

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Hospitals have limited control over fixed reimbursements under MS-DRGs and APCs but they can manage risk and cost. Based on the regression analysis, determine which variables the facility can control or influence. This information will help decide whether the hospital should participate in the Value-Based Payment (VBP) Program and develop actionable recommendations.

If you have any questions regarding these notes, please feel free to reach out to me by email or phone. My contact info is located in the announcements. You may also reach out to the course Graduate Assistants (tutors) by scheduling a meeting or submitting a question to “Ask the Graduate Assistant” as needed. Thank you.

Assessment Step by Step

• STEP 1. Review Case Scenario: Hospital administration must decide on the level of

reimbursement required to cover expected costs for the upcoming year. The administration is considering a shift from inpatient prospective payments to value- based reimbursement and must determine whether to accept a contract based on their projected costs. The challenge is to evaluate if this strategy is viable and identify necessary actions to implement it effectively. Key case points:

1. Decision Required: The hospital administration needs to determine the amount of reimbursement necessary to cover the projected costs for the next year. Since hospitals are reimbursed under Medical Severity Diagnostic Related Groups (MS-DRGs)—a cost-based prospective payment system—they can use these cost projections to determine their revenue requirements.

2. Value-Based Reimbursement Consideration: Value-Based Reimbursement Consideration: The administration is evaluating the adoption of a value-based reimbursement model under the Alternative Payment Models (APMs) of the Medicare Access and CHIP Reauthorization Act (MACRA) Quality Payment Program. This evaluation specifically focuses on Hospital Value-Based Purchasing and other Hospital Quality Initiatives, which are designed to incorporate elements of value-based care and shared savings for hospitals.

Value-Based Reimbursement Consideration: The administration is evaluating the adoption of a value-based reimbursement model, which is part of the Alternative Payment Models (APMs) under the Medicare Access and CHIP Reauthorization Act (MACRA)(2015) Quality Payment Program. Within this legislative framework, Hospital Value-Based Purchasing and other Hospital Quality Payment Initiatives represent the relevant tracks for hospitals, incorporating elements of value- based care and shared savings (CMS-Innovation, 2024).

3. Contract Evaluation: The administration is contemplating whether to accept a contract that offers value-based reimbursement, contingent on the hospital's anticipated risks and costs.

4. Viability Assessment: Administrators must assess the viability of adopting a value-based reimbursement strategy tailored to the specific needs and

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operational realities of the hospital.

5. Strategy Development: There is a need to identify actions required to make value-based reimbursement a viable financial strategy for the hospital, ensuring that it aligns with regulatory requirements and optimizes financial outcomes.

• STEP 2. Formulate a Case Question: The key question to guide the regression

analysis in evaluating the adoption of a value-based reimbursement system by a hospital administration might be:

"Should this hospital participate in the Value-Based Payment (VBP) Program?"

This central question will direct the formulation of your regression model, with the hospital's costs as the dependent variable, effected by independent variables, which include patient population age, operational and clinical risk, patient satisfaction and utilization. In constructing your regression model, the analysis will factor in historical cost data, demographic shifts, risk management changes, and patient satisfaction effects on cost per discharge.

• STEP 3. Identify the Case Variables: Case Variables. Look at the STRENGTH OF THE

RELATIONSHIPS BETWEEN THE Y (Dependent) AND X VARIABLES (Independent) to make the best management decision and determine which variable the hospital has no risk management control over, which can be control through quality initiatives, and which variable the hospital has influence over:

(Y) cost (hospital cost in dollars). (X1) age (patient age in years). (X2) risk (count of patient risk factors). (X3) satisfaction (patient satisfaction score percentile rank).

• STEP 4. Running Linear Multi-Regression Statistic: You will run only one (1) multiple

regression analysis for all four (4) case variables in MS Excel using the Toolkit, i.e., the dependent variable, or Y-intercept, and your three (3) independent variables are “X1, X2, X3”.

• STEP 5. Interpretating the Results of Regression Output Table

This analysis will help you understand how each factor influences hospital costs and to what extent.

A. Beta Coefficients and Significance: The beta coefficients represent the change in the dependent variable for each unit change in the independent variable. The significance (p-values) indicates whether the relationship is statistically significant. Age has a beta coefficient of and p-value= (significant?) Risk has a beta coefficient of and p-value of (significant?) Satisfaction has a beta coefficient of and p-value of (significant?)

B. Effect Size: Is the independent variable's effect significant on the

dependent variable? If no, run effect size: In business statistics, the relationship between dependent and independent variables may not always manifest through statistical significance. A lack of significant findings in regression models or correlation

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analyses does not imply the absence of significance from the independent variable on the dependent variable, such as cost and satisfaction does not have a relationship or effect. Effect size measures the strength of the relationship between the independent and dependent variables. Even if statistical significance is not met, effect size can indicate practical importance.

The regression's effect size (h) is a way to calculate the strength (magnitude) of the relationship between the coefficients. The (h) identifies the difference between two variables. The effect size is determined by subtracting the mean value of each independent variable from the mean cost per visit and dividing that value by the standard deviation for that independent variable. The effect size may be calculated using the standardized mean difference between two groups; A large effect size means that a product is practical for the case and a small effect size indicates it is not. A small effect size also means that the model has limited practical applications. To interpret the Effect size, statisticians often use Cohen's Effect Size Values (1988) (Lakens, 2013). Use the Cohen’s d effect size calculator (SOC, 2024).

Effect Size Interpretation: Small h = 0.2 • Medium h = 0.5 • Large h = 0.8

Effect Size Calculations To calculate Cohen's d effect size for comparing two means, follow these steps: 1. Subtract the Mean of the Second Group from the Mean of the First Group: This gives

the difference in means between the two groups. 2. Calculate the Pooled Standard Deviation: The pooled standard deviation is a

weighted average of the standard deviations of both groups. To find it: 3. Multiply the standard deviation of the first group by the number of observations in

that group minus one. 4. Multiply the standard deviation of the second group by the number of observations in

that group minus one. 5. Add these two values together. 6. Divide the sum by the total number of observations in both groups minus two. 7. Take the square root of this value to get the pooled standard deviation. 8. Divide the Difference in Means by the Pooled Standard Deviation: This result is the

Cohen's d effect size, which measures the standardized difference between the two means.

Cost/RISK (SOC Statistics, 2021): Cohen's d = ( - ) / = h Cost/AGE (SOC Statistics, 2021): Cohen's d = ( - ) / = h Cost/Satisfaction (SOC Statistics, 2021): Cohen's d = ( _- ) / = h

OR Use the SOC Statistics Effect Size Calculator, which is an accurate tool for calculating Cohen's d, for measuring the effect size by comparing the means of two groups. Run Quantitative statistics using ToolPak for your four variables. To ensure accuracy:

• Mean (M): Input the average value of your data for each group. • Standard Deviation (s): Input the standard deviation, which measures the

amount of variation or dispersion in each group. • Sample Size (n): Input the number of observations in each group.

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Figure. Effect Size Calculator.

Note: High value results, when calculating Cohen’s d, may suggest potential outliers or scale differences between the measures, which might not typically be expected in practical scenarios. However, in this case analysis, you do not need to remove any outliers to calculate effect size.

Effect Size References Lakens D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A

practical primer for t- tests and ANOVAs. Frontiers in Psychology, 4, 863. https://doi.org/10.3389/fpsyg.2013.00863

SOC Statistics. (2024). Effect Size Calculator.

https://www.socscistatistics.com/effectsize/default3.aspx

Sullivan, G. M., & Feinn, R. (2012). Using effect size-Or why the P-Value is not enough. Journal of Graduate Medical Education, 4(3), 279–282. https://doi.org/10.4300/JGME-D-12-00156.1

• STEP 6. Interpret the Goodness of the Fit, or R-squared ? Regression is about the "fit" of the regression model, i.e., how aligned the data points are to the regression line. You will next write about the goodness of the fit and the strength of the relationship. Regression measures the strength of the relationship between the dependent variable (Cost) and the independent variables, age, Risk, and satisfaction. Regression relationships are anything between 0-1 or - 1-0. The closer the relationship is to 1, the stronger the relationship, and the closer it is to 0, the weaker the relationship is. You do not have to have a “great” regression line, to be a good regression model.

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Figure. Goodness of Fit

Note: This image illustrates four scatter plots with linear regression lines, each depicting a different R-squared value (R²), which reflects the proportion of variance in the dependent variable that is predictable from the independent variables in the model. From top left to bottom right: 'Great' shows an R² of 100%, indicating a perfect fit where the model accounts for all the variances; 'Good' has an R² of 80%, where the model explains a significant portion of the variance; 'OK' shows an R² of 40%, indicating a moderate fit; and 'Inconsistent' has an R² of 0%, demonstrating no explanatory power of the model over the variance.

• STEP 7. (Optional) Correlation; strength of the relationships between

variables: This table and accompanying correlation interpretation guide helps us evaluate the strength of relationships between variables such as cost, age, risk, and satisfaction. It is optional if you wish to run a correlation chart for this case assessment.

Cost age risk satisfaction Cost 1 age 1 risk 1 satisfaction 1

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Correlation Interpretation Guide: Exactly –1. A perfect downhill (negative) linear relationship –0.70. A strong downhill (negative) linear relationship –0.50. A moderate downhill (negative) relationship –0.30. A weak downhill (negative) linear relationship Exactly 0. No linear relationship +0.30. A weak uphill (positive) linear relationship +0.50. A moderate uphill (positive) relationship +0.70. A strong uphill (positive) linear relationship Exactly +1. A perfect uphill (positive) linear relationship

• STEP 8. Predict Next Year’s Cost-Budget Variables:

This standard formula is used extensively in healthcare today. The hospital administration can estimate next year's budget by using a predictive regression equation that incorporates the coefficients for age, risk, and satisfaction. These coefficients are adjusted multiplication factors that you will use in the formula. Given that hospitals are reimbursed under the prospective payment systems for inpatient services [Medical Severity Diagnostic Related Groups (MS-DRGs)] and outpatient services [Ambulatory Payment Groups (APGs)], both cost-based systems, accurate cost predictions are vital for determining revenue requirements. In this context, the standard multiple regression equation models the dependent variable, cost (Y), as a function of three independent variables (predictors): X1 (age), X2 (risk), and X3 (satisfaction). To make accurate predictions, it is necessary to input the coefficients derived from empirical data into the formula. Additionally, the independent variables should be risk-adjusted based on this data to predict both the cost per patient and the total annual cost for all patients.

Table. Making your risk adjustment assumptions for the next budget year.

Variables

Coefficient

Current Average Cost per Discharge

Next year’s

Average Cost per

Discharge

Logical Assumptions for Next Year’s Cost-Budget

cost 6652.176 $14,907 $ ? Use the prediction formula shown above to calculate your next- year’s cost budget.

Assumptions

age

107.0359

73

?

The current year average age is 73 years. For next year’s average age, is the population older or younger and why? Consider, hospital's medical service area's population, birth and death rates, pandemics, and population health status. Explain your adjustment.

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risk 153.5571 6 ? The average risk factor to this year is 6, on a scale of 1-10 with 10 being the highest risk. For next year will risk go up or down. What kind of hospital programs are planned to lower risk, or not? Explain your adjustment.

satisfaction

-9.19469

50

?

The average satisfaction rate this year is 50 but based on operational and clinical improvements, this may go up in the next year? Explain your adjustment.

Risk Adjusting the Independent Variables: You will make new independent variable risk assumptions based on internal and external factors. These assumptions must be factual and logical. NOTE: Different analysts will get slightly different answers when they make a prediction using the multiple regression equation prediction because they must make certain assumptions regarding the independent variables used for risk adjustment of the coefficients as shown in the table.

Predict Next Year’s Number of Discharges

Total budget is based on the number of discharges in the year. There are 185 discharges for the current year’s budget. So, to project the annual Cost for next year, project a logical number of discharges for next year's hospital discharges multiplied by the predicted Cost for a single encounter. This will give you the Total Annual Budgeted Expense.

• STEP 9. Predict next year’s Cost-Budget Variables using the “Standard,

Linear, Multiple Regression Equation for Predictive Analysis”

Y= intercept coefficient = +

(X1 = age coefficient = * mean age risk adjusted ) +

(X2 = risk coefficient = * mean risk adjusted ) +

(X3 = satisfaction coefficient = - * mean satisfaction risk adjusted ) +

Hospitals costs per discharge = x # of discharges = $ Total Annual Budgeted Expense

• STEP 10. Narrative Summary and Actionable Recommendations

Hospitals are paid under the Medical Severity Diagnostic Related Groups (MS-DRGs) for inpatients and Ambulatory Payment Classifications (APCs) for outpatients. This is

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fixed reimbursement, and they don't have much control over it. However, they can control risk and cost.

For this exercise, you looked at all of the STRENGTH OF THE RELATIONSHIPS BETWEEN THE Y AND X VARIABLES to make a prediction and the best management decisions:

Y) Cost is dependent (X1) Age, (x2) Risk, and (X3) Satisfaction are independent variables

OF THE THREE INDEPENDENT VARIABLES IN YOUR SUMMARY

• What VARIABLE does the

facility have no control over? • What VARIABLE does the

facility need to "control"? • What VARIABLE does the facility have influence over?

Based on these variables, statistical results, risk management, and your cost prediction should this hospital participate in the Value-Based Payment (VBP) Program? Yes/No, why or why not? What more might be required in order to make a determining and actionable decision and plan?

Assessment Activity Outline

APA formatting with headings, subheadings (required): 1. Introduction-What the paper is about? 2. Data Analysis:

1. Regression Analysis and Significance. 2. Effect Size. 3. R2 interpretation. 4. Generate a prediction with a regression equation.. 5. Copy/Past table results in the body of your MS Word from Excel and

explain and refer to them in your paper. 3. Interpretation of Results-Explanation of statistics in the results tables or charts explained.

1. Regression Analysis and Significance. 2. Effect Size. 3. R2 interpretation. 4. Generate a prediction with a regression equation. 5. Copy/Past table results in the body of your MS Word from Excel and

explain and refer to them in your paper. 4. Recommendations – Narrative and Actionable Recommendations to

Leadership for Management Decision- Making 5. References-minimum three, preferably more. You must support all concepts,

numbers, dates borrowed from an outside source. References must be either evidence-based journal articles, or primary sources (.gov, .org, or .edu).

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References Boston University School of Public Health. (2016). The Multiple Linear

Regression Equation. https://sphweb.bumc.bu.edu/otlt/mph- modules/bs/bs704-p713_multivariablemethods/bs704- ep713_multivariablemethods2.html

Centers for Medicare and Medicaid Services (CMS). (2024). Acute Inpatient Prospective Payment System (IPPS).

https://www.cms.gov/medicare/payment/prospective-payment-systems/acute- inpatient- pps

Centers for Medicare and Medicaid Services (CMS). (2023). The Hospital Outpatient Prospective Payment System (OPPS). https://www.cms.gov/cms- guide-medical-technology-companies-and-other-interested- parties/payment/opps

Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t- tests and ANOVAs. Frontiers in Psychology, 4, 863. https://doi.org/10.3389/fpsyg.2013.00863

SOC Statistics. (2024). Effect Size Calculator. https://www.socscistatistics.com/effectsize/default3.aspx

Sullivan, G. M., & Feinn, R. (2012). Using effect size-Or why the P-Value is not enough. Journal of Graduate Medical Education, 4(3), 279–282. https://doi.org/10.4300/JGME-D-12-00156.1

StatQuest. (n.d.) Video Index. https://statquest.org/video-index/ Wrathall, J., & Belnap, T. (2017). Reducing health care costs through patient

targeting: Risk adjustment modeling to predict patients remaining high cost. The Journal of Electronic Health Data and Methods, 5(2), 4. https://doi.org/10.13063/2327-9214.1279

Jalayer Academy. (2015). Multiple regression in Excel. (2015). YouTube. https://www.youtube.com/watch?v=cXiZ_t2NK1k