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Predicting an Outcome Using Regression Models

Melissa Croft

Data Analysis for Health Care Decisions

Capella University

September 2022

Introduction

Healthcare leaders use predictive analysis to make critical business decisions. Regression is one of the essential data analysis types (Gallo, 2015). Multiple regression explains the relationship between one dependent variable and two or more independent variables. Using regression analysis, we can predict the amount of reimbursement to cover expected costs for the next year using hospital costs, patient age, risk factors, and patient satisfaction scores.

Statistical Significance and Effect Size of Regression Coefficients

The regression analysis has two uses, prediction, classification, and explanation. The first step in a regression analysis is determining the criterion variable (Palmer & O'Connell, 2009). In this exercise, the criterion variable is cost, and the independent variables used are age, risk, and satisfaction. Statistical significance determines that the difference between the two groups is coincidental. However, statistical significance does not predict effect size. It is important to consider the effect size when you obtain statistically significant results (Ullah, 2019).

The regression coefficient output shows a p-value for the satisfaction of 0.15, which is greater than the alpha level of 0.05, indicating no significance to the data analysis. The beta coefficient is the degree of change in the outcome variable for every 1-unit change in the predictor variable (Statistical Solutions, 2021). The p-value for each independent variable tests the null hypothesis that the variable does not correlate with the dependent variable (Frost, 2022). The p-value for the age of 0.00 and risk of 0.02 is less than the alpha of 0.05.

ANOVA, otherwise known as analysis of variance, uses the F test to determine if there is a statistically significant difference between two or more groups. A higher F value indicates that the variables are significant (Simkus, 2022). The F value in our analysis is 7.69, and the P value is less than 1, indicating we can reject the null hypothesis and accept the alternative that at least one independent variable affects expected costs. ANOVA testing can be suboptimal for testing against a specific hypothesis. It may not yield exact p-values when the observations come from distributions that are heavier in the tails than normal (Good & Lunneborg, 2006).

Fit of Regression Model for Prediction of Data Analysis

The goodness-of-fit in a regression model is measured by R2 and indicates the percentage of the variance in the dependent variable. R2 is also known as the coefficient of determination or the coefficient of multiple determination for multiple regression. The higher the R2, the better the regression model fits the observation (Frost, 2022). Our analysis demonstrates that R2 equals 0.11 and is considered low in value. R2 is not without limitations and bias. It does not indicate if a regression model adequately fits the data. A good model can have a low R2 value. On the other hand, a biased model can have a high R2 value (Minitab Blog, 2013).

Regression Model Statistical Results

The data retrieved from our multiple regression analysis will be used to predict the amount of reimbursement required to cover expected costs for next year. The following equation was used to predict the estimated effect of age, satisfaction, and risk on the next year's expected reimbursement:

Y (cost coefficient) + (age coefficient * age mean) + (risk coefficient * risk mean) + (satisfaction coefficient * satisfaction mean)

Y = 6,652 + (107.35 * 73.25) + (153.56 * 5.69) + (-9.19 * 50.02) = predicted costs

The predicted budgeted costs for the coming year are $14,907. If one is to assume that last year’s costs were less, hospital administration will need to come up with initiatives to drive down expenses. One way to reduce costs is to decrease the average length of stay (ALOS) for inpatients. Reductions in ALOS will reduce costs without compromising patient outcomes (Clark, 1996). Increasing total revenue is another way to offset the increase in predicted costs. Ensuring providers are coding accurately is an opportunity to enhance accounts receivable. Physicians who under document care and services provided represent hospitals' most significant opportunity to increase charge capture, ensure accurate reflection of patient severity level, and provide adequate audit defense (Richter et al., 2007).

Conclusion

Healthcare leaders are always needing to make decisions about the future. Using regression models are ways to successfully plan for changes in the rapidly changing healthcare environment that align to the organizations strategic plan and directional strategies.

References

Clark, A. (1996, June 16).  Home - PMC - NCBI. National Center for Biotechnology Information. from https://www.ncbi.nlm.nih.gov/pmc/

Frey, B. B. (Ed.). (2018).  Descriptive statistics.   The SAGE encyclopedia of educational research, measurement, and evaluation (Vols. 1–4). Sage.

Frost, J. (2022, July 22). How to interpret p-values and coefficients in regression analysis. Statistics By Jim. https://statisticsbyjim.com/regression/interpret-coefficients-p-values-regression/

Frost, J. (2022, July 22).  How to interpret R-squared in regression analysis. Statistics By Jim. from https://statisticsbyjim.com/regression/interpret-r-squared-regression/

Gallo, A. (2015, November 04).  A refresher on regression analysis.  Harvard Business Review Digital Articles, 2–9.

Good, P. I., & Lunneborg, C. E. (2006, May 1).  Limitations of the analysis of variance - Wayne State University. https://digitalcommons.wayne.edu/cgi/viewcontent.cgi?article=1259&context=jmasm

Kim, T. K. (2017, January 26).  Understanding one-way ANOVA using conceptual figures. Korean Journal of Anesthesiology. https://synapse.koreamed.org/articles/1156679

Minitab Blog. (2013, May 13). Regression analysis: How do I interpret R-squared and assess the goodness-of-fit?  https://blog.minitab.com/en/adventures-in-statistics-2/regression-analysis-how-do-i-interpret-r-squared-and-assess-the-goodness-of-fit

Palmer, P. B., & O'Connell, D. G. (2009, September). Regression analysis for prediction: Understanding the process. Cardiopulmonary physical therapy journal. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2845248/#B15

Richter, E., Shelton, A., & Yu, Y. (2007, June). Best practices for improving revenue capture through documentation. Healthcare Financial Management, 61(6), 44+. https://link.gale.com/apps/doc/A165165016/AONE?u=anon~b707cc3c&sid=googleScholar&xid=82919c65

Simkus, J. (2022, Jan 26).  What is ANOVA (Analysis Of Variance). Simply Psychology. www.simplypsychology.org/anova.html

Statistics Solutions. (2021, August 11). Regression. https://www.statisticssolutions.com/free-resources/directory-of-statistical-analyses/regression/

Ullah, M. I. (2019, May 3).  Effect size and statistical significance. Basic Statistics and Data Analysis. https://itfeature.com/testing-of-hypothesis/effect-size-and-statistical-significance