Average Length of Stay, Average Preventable Readmission Rates, and Average Total Cost of Care: Is there a Relationship?

Average Length of Stay (ALOS), Average Preventable Readmission Rates (APRRs), and Average Total Cost of Care (ATCc) were examined to see if any relationship exists among the variables. Secondary data from the Texas hospital data collection database was used for the study. Out 379 acute care hospitals in Texas, 65 hospitals were selected for analysis using a G*Power analysis. Demographic analysis, Spearman’s Rank correlation, and Regression Analyses were conducted to explore the relationship. The results of the Spearman’s Rho correlation showed a significant negative relationship between ALOS and ATCc [ALOS – ATCc (rs = - .271, p = .016)], and for APRRs and ATCc, there was no statistically significant relationship [APRRs – ATCc (rs = .065, p = .564)]. The multiple regression analysis showed there was no statistically significant relationship between the variables [ALOS – ARRs – ATCc (F (2,62) = 1.584, p = .211)]. The results showed that ALOS and APRRs do not necessarily predict ATCc. Consequently, based on the study results ATCc is not solely determined by ALOS and APRRs. The absence of a significant relationship between ALOS, APRRs, and ATCc does not necessarily indicate inefficiency in practice or lack of effectiveness. The results showed that there are other mediating factors impacting care there were not assessed in the study that needs to be examined carefully which may have implications for practice, research, and methodology. Future research should be considered to determine these moderating factors to better understand the complex relationship between ALOS, APRRs, and ATCc. An understanding of this complex dynamics may inform managerial strategies and help with critical clinical and fiscal decisions in a healthcare setting.


I. INTRODUCTION
Over the last several decades, the cost of health care services in the United Stated (U.S.) rose gradually becoming a burden to patients and third-party payers.Health policy makers have focused on cost containment for several decades, to deal with the rapid rise in healthcare costs.Different measures have been introduced but virtually all of them have failed to achieve cost containment (Goyen, 2010).Despite being among the most developed nations in the world, healthcare outcomes in the U.S. lagged compared to nations with the highest healthcare cost par capital (Organization for Economic Cooperation and Development (OECD, 2023).The OECD estimated that the U.S. spent about $10,586 per person in 2019, the highest globally and 42 percent higher than Switzerland (Kamal, Ramirez, Cox, 2020).Unfortunately, despite spending the most on healthcare, health outcomes in the United States were not better than other countries.Many people find it challenging to meet the cost of their medical care as bills pile up, driving many patients to financial hardship and bankruptcy.Social programs like Medicaid have also seen a dramatic rise in healthcare spending.The National Health Expenditure (NHE) showed tremendous increases over the years.For example, the Center for Medicare and Medicaid (CMS) (2020) reported that healthcare grew to about $11,582 per person, and accounted for 17.7% of Gross Domestic Product (GDP); Medicare, Medicaid, private health insurance grew by 6.7%, 2.9%, and 3.7% respectively in 2019 (CMS, 2021).These statistics were among significant increases in healthcare expenditures, and the projection shows continued increases in the coming years.
Several strategies have been employed by government agencies and third-party payers to reduce length of stay (LOS), preventable readmission rates (PRR), pay-forperformance, and other cost saving measures.Yet, the U.S. global health metrics only showed signs of improvement but no significant cost reduction.Reducing the length of stay (LOS) improves financial, operational, and clinical outcomes (Hussey, Wertheimer, Mehrotra, 2013;CMS, 2021).The CMS and other third-party payers have attached quality metrics to reimbursements to encourage providers to reduce cost of care but no interference with the quality care.
However, the cost of care continues to increase and any effort to save cost tends to interfere with quality of care and patient outcomes.For example, the Center for Medicare and Medicaid (CMS) considers LOS and PRR quality measures and has tied these two metrics to reimbursement rates.Likewise, the Organization for Economic Cooperation and Development (OECD, 2023) now considers the average length of hospital stay (ALOS) as an efficiency indicator, defining it as the average number of days that patients spend in hospital.It is generally measured by dividing the total number of days stayed by all inpatients during a year by the number of admissions or discharges.The OECD has resolved that a shorter stay reduces inpatient care costs in a hospital setting, while a prolonged LOS may increase costs.Similarly, a reduced PRR saves costs, while an increased PRR results in a higher total care cost (C) for the patient and the third-party payers (OECD, 2023).Luhby (2021) reported that the Biden administration had taken dramatic steps to reduce healthcare costs in effect in early 2022.Luhby said that the "No Surprises Act," which banned unexpected medical charges from out-of-network providers, just went into effect on January 1, 2022.The law impacted over 10 million surprise bills annually, and it was one of the prominent consumer protection laws enacted in healthcare (Luhby, 2021).
The rate of 30-day readmissions and how long patients stay in the hospital (Length of Stay or LOS) are two things hospitals often check to see how well they are doing.The Centers for Medicare and Medicaid Services (CMS) warns public about 30-day readmissions for all patients at a hospital.There is a CMS program called the Hospital Readmissions Reduction Program (HRRP) that is part of Medicare (CMS, 2021).This program takes away some money from hospitals if they have too many patients coming back within 30 days.The amount of money a hospital gets is also linked to how well it meets quality standards set by CMS.The Kaiser Foundation (2023) reported that the CMS under the Affordable Care Act cuts payments to hospitals that have high rates of readmissions and those with the highest numbers of infections and patient injuries.For the readmission penalties, Medicare cuts as much as 3 percent for each patient, although the average is generally much lower.Hospitals also monitor patients stay in the hospital because they get a fixed payment for treatments, no matter how many days someone stays.CMS and private payers use this payment model, so hospitals try to make the stay shorter.The cost of unplanned readmissions is 15 to 20 billion dollars annually (CMS, 2023).Preventing avoidable readmissions has the potential to profoundly improve both the quality of life for patients and the financial wellbeing of health care systems (Jencks, et al., 2009).Studies show that the reduction in LOS reduces health costs and minimizes rates of mortality and morbidity as well as hospital readmissions due to complications (Gabutti, Mascia & Cicchetti, 2017).
Hospital managers try different ways to make sure fewer patients come back within 30 days and to make the hospital stay shorter.But, making changes to help with one thing might make the other thing worse.Some studies focused on patients with a specific problem found a link between how long a patient stays and the chance of coming back to the hospital.Other studies looked at certain illnesses, like heart failure, and found that either a shorter or longer stay could make the chance of coming back higher.So, hospitals must be careful with the strategies they use because it can affect both readmission rates and how long patients stay in the hospital.This study examined average length of stay (ALOS), average preventable readmission rates (APRRs), and the average total cost of care (ATCc).Previous studies have shown that reduced LOS and increased RR were directly related to poor quality of care and patient outcomes (Christensen, Grapetine, Pomputius, Spaulding, 2019;Swelling, 2020).The National Academy of Medicine (NAM), previously the Institute of Medicine (IOM) outlined six goals for improving healthcare including, timeliness, safety, effectiveness, efficiency, equitability, and patient-centeredness.Despite these recommendations, the healthcare industry continuously faces challenges in meeting these overarching quality goals, resulting in a more financial burden for providers, patients, and third-party payers.To meet these quality goals and unwanted outcomes, some providers sometimes turn to defensive medicine (Schneider, 2019).Defensive medicine has not only prolonged LOS and increased RRs but also induced financial burdens (Vento, Cainelli, & Vallone, 2018).The practice of defensive medicine may include the ordering of excessive medical tests and procedures, prolonged LOS, and increased RR.However, it was also important to note that some providers may want to observe patients a little longer, especially in teaching hospitals, for research purposes and to ensure better outcomes.

Problem Statement
The escalating cost inflation in healthcare reimbursements has imposed a considerable financial strain on patients and third-party payers.Substantial transformations in the structure of CMS and third-party payment systems for hospitals' medical services have occurred, notably shifting from open-ended payment systems to controlled ones that limit service volumes.The Medicare prospective payment system, a product of these changes, has influenced providers' behavior, prompting a surge in interest to study provider, patient, and third-party payer responses.The prolonged financial burden on third-party payers, patients, and providers due to increased readmissions and extended lengths of stay has been a persistent issue.Despite efforts to establish consistent reimbursement metrics, studies reveal mixed results (Upadhyay, Stephenson, & Smith, 2019), prompting the need for further investigation into the association between length of stay, readmission rates, and cost of care.Investigations of this nature are needed to build a knowledge base for informed clinical decision-making in the face of these complex healthcare challenges.

Purpose of the Study
The purpose of this descriptive correlational study is to investigate the relationship between ALOS, and APRRs, and C of care, in order to provide a basis for making reliable fiscal and clinical decisions.Researchers have investigated the relationship between LOS and RRs with conflicting results.As cost remains one of the single main concern for all healthcare stakeholders, the need to examine these triadic elements is further supported.In addition, further research has validated the complex interactions that occur among these three elements.For example, Upadhyay et al. (2019) recommended further studies be done to examine the relationship between LOS, RR, and C, to help provide more insight into the literature.

Research Questions
The following research questions guided the study: RQ 1: What is the relationship between Average Length of Stay (ALOS) and Average Total Cost of care (ATCc)?H1o: There is no statistical significance between ALOS and ATCc.H1a: There is statistical significance between ALOS and ATCC.
RQ 2: What is the relationship between Average Preventable Readmission Rates (APRRs) and Average Total Cost of care (ATCc)?H2o: There is no statistical significance between APRRs and ATCc.H2a: There is statistical significance between APRRs and ATCC.

A. Conceptual Framework
The Donabedian model, proposed by Avedis Donabedian (1988), is a widely used framework for assessing and improving the quality of healthcare provide the conceptual framework for this study.The model consists of three key components: structure, process, and outcomes.These components are interrelated and provide a comprehensive approach to understanding and enhancing the quality of patient care in healthcare organizations.Since ALOS and APRRs are associated with the quality of care provided in hospitals, the Donabedian model is best fit to asses these variables.
Structure refers to the organizational and environmental factors that shape the context within which care is provided (Donabedian, 2003).This includes the physical facilities, human resources, equipment, policies, and other elements that influence the delivery of healthcare services.The quality of the healthcare infrastructure, availability of skilled staff, and access to necessary resources all impact patient care.Adequate staffing levels, well-maintained facilities, and appropriate technology contribute to a positive patient experience and effective care delivery.The structure component may influence ALOS by affecting the efficiency of care delivery, availability of beds, and the overall capacity of the healthcare organization.
Process refers to the activities and interactions that occur during the delivery of healthcare services (Donabedian, 2003)

Review of Related Literature
Various studies have been conducted investigating the three variables and their interactions in varying situations.

Average Length of Stay (ALOS).
Hospital inpatient length of stay has severe financial implications for stakeholders and the entire healthcare industry (Rachoin et al., 2020).The Health Catalyst (n.d.) reported that systematic data-driven approaches reduce length of stay and improves care delivery.
Improving and reducing length of stay (LOS) improves financial, operational, and clinical outcomes by decreasing the costs of care for a patient.It can also improve outcomes by minimizing the risk of hospitalacquired conditions.Citing one prominent hospital as an example, the authors noted that Memorial's commitment to a datadriven, multi-pronged approach to reducing LOS has produced the desired results in one year, including $2 million in cost savings.This result was achieved by decreasing LOS and utilization of supplies and medications, and improved care coordination and physician engagement.The data on these variables were crucial for addressing research questions, offering data points for both dependent and independent variables.From a total of 517 hospitals of which 379 are acute, serving nearly 29,000,000 people in Texas, 120 were targeted, focusing on 65 randomly selected accredited hospitals.

Sampling and Sampling Procedures Sample and Effect Size
G*Power and sample size analyses was conducted using SPSS 28 software to achieve the recommended level of confidence (Faul et al., 2014).Cohen's (1992) recommendation was used by setting the power to .80 and alpha to .05 to mitigate risk and balance the instances of Type I or II errors.Using a moderate effect size (Cohen, 1992) Variables: Three variables were under investigation namely: Total Cost of Carewas the dependent variable (DV) expressed in the average cost in [dollarscontinuous data] for surgical procedures in the same DRGs in acute.The cost of care for specific procedures was matched with the average ALOS and APRRs in these hospitals to establish the relationship between these variables.
Average Length of Staywas the independent variable (IV) [continuous data] was measured by the amount of time spent in the hospital from admission to discharge (LOS = day of dischargeday of admission).ALOS was converted to categorical data to facilitate further analysis, such as ANOVA and prediction analysis.
Average Preventable Readmission Rateswas also the independent variable.The average preventable readmission rates represent 30-day readmission rates [ratio data] evaluates what happens to patients once they leave the hospital after receiving care for certain conditions.The readmission rates focus on whether patients were admitted again at the hospital 30 days after being initially discharged.

Data Analysis
The statistical software SPSS 28 was used for analysis.The following analyses were done including descriptive statistics, Spearman's Rank Correlation, and multiple regression.

i) Demographic Analysis
To ascertain the optimal sample size for the data analysis process, a G* Power analysis was undertaken, emphasizing the significance of determining power in research to minimize the risk of Type 2 errors when assessing population effects.I estimated the required sample size for testing the R-square at an alpha level of .The hospitals were categorized into metro and non-metro hospitals and were all licensed.The findings show that most hospitals in Texas (78.5%) were in metro regions, while fewer (21.5%) of the hospitals were in non-metro regions (See Table 2).In addition, all the hospitals included in the dataset were acute license-type hospitals (Table 2).Furthermore, I evaluated the procedural groups for which data about the length of stay, readmission rate, and cost of care were considered in this research.There were eight procedure groups investigated, including abdominal paracentesis (41.5%), alcohol and drug rehabilitation (18.5%), amputation of the lower extremity (4.6%), arthroplasty knee (18.5%), blood transfusion (10.8%), cancer chemotherapy (1.5%), cesarean section (3.1%), and other vascular catheterization (not heart) (1.5%) (See Table 3).I also evaluated the individual patient status regarding transfer to another type of health care institution not defined elsewhere in the code list, discharged to home or self-care routine, or transferred to home under the care of an organized home health service organization.The findings show that 1.5% of the patients were transferred to another type of health care institution not defined elsewhere in the code list, 95.4% were discharged to home or self-care, and 3.1% were transferred to home under the care of an organized home health service organization (See Table 4).ii) Hypotheses Testing Before conducting any hypothesis testing, an exploratory data analysis was performed, assessing the normality distribution of variables through the Kolmogorov-Smirnov (K-S) test.The obtained p-value (> .05)indicated non-normal distribution of the variables.Consequently, a Spearman Rank Correlation was employed to explore potential relationships between the variables.Addressing research question 1 regarding the association between ALOS and ATCc, a Spearman rank correlation was utilized.The statistical analysis revealed that the mean average length of stay was 4.81 days (SD = 2.87 days), and the mean average total charges were $60,347 (SD = $70,637).Notably, a significant negative relationship emerged between average length of stay and average total charges or Cost of care [ALOS -ATCc (rs = -.271,p = .016]at the .05alpha level, as detailed in Table 5.

To answer research question 2: What is the relationship between APRR and ATCc?
A Spearman Rank Correlation test was conducted for APRR and ATCc.Again, the Spearman correlation analysis evaluated the relationship.The descriptive statistics showed that the mean total charges were $60,347 (SD = $70,637).On the other hand, the average readmission rate was 29.95 days (SD = 53.119days).The analysis findings show no statistically significant relationship between the average total charges (cost) and the average preventable readmission rate, Spearman's rho, r = .065,p = .564(See Table 6, correlations).

Multiple Regression Analysis for ALOS, APRR, and ATCc
A multiple regression analysis was conducted to examine the relationship between ALOS, APRR, and ATCc.The regression model summary indicated an adjusted R-Square of .018,representing the effect size.This implies that the two predictors could only account for 1.8% of the variation in the dependent variable.The ANOVA model results revealed that the regression model was not statistically significant, [F (2,62) = 1.584, p = .211].The study found that ALOS and APRR were unable to predict the Cost of Care.

Average Length of Stay
The relationship between the average length of stay, average preventable readmission rates, and average total cost of care in healthcare systems in general can be complex and multifaceted.Hospitals aim to reduce ALOS while maintaining quality care.A longer ALOS increases costs, as it requires more resources and hospital bed utilization as indicated by Rachoin et al. (2020).However, in this study, the ALOS was negatively correlated to the ATCc.A negative correlation between ALOS and ATCc in a healthcare setting typically means that as the ALOS decreases, the ATCc tends to increase, and vice versa.This finding was contrary to that of Rachoin et al. (2020).
Several factors can contribute to this negative correlation including the lengthier the hospital stay, the higher the cost of care.However, there are specific situations where an extended stay may be correlated with potentially lower overall costs for the patient.Several examples illustrate these circumstances: Firstly, in instances where complications are paramount, an extended hospital stay may be necessary for continuous monitoring and management.This proactive approach allows for early detection and intervention, averting the development of severe health issues that could require expensive treatments in the future.Secondly, postoperative care, especially following complex or major surgeries, may necessitate a more prolonged hospital stay for close monitoring, effective pain management, and rehabilitation.This extended care period contributes to improved recovery outcomes, potentially reducing the likelihood of complications that might lead to additional costs.In cases requiring rehabilitation services, a longer hospital stay can facilitate a more comprehensive and effective rehabilitation program, leading to better functional outcomes and a reduced need for additional rehabilitation services or readmission after discharge.For patients with chronic conditions, an extended hospital stay may be beneficial for intensive education, counseling, and management strategies.This approach can result in better self-management, adherence to treatment plans, and reduced reliance on emergency services over time.
Additionally, in situations where a patient's condition is unstable or requires significant stabilization, a longer hospital stay may be necessary to ensure the patient is in a controlled and manageable state before transitioning to outpatient care.This finding is consistent with the recommendation of Haque et al. (2020) who recommended providers take all necessary measure to care for patients in critical conditions including monitoring and surveillance measures couple with quality treatment.This preventive measure can help avoid readmissions and emergency visits.It's crucial to note that these examples are context-dependent, and the relationship between length of stay and overall cost can vary based on the specific medical condition, treatment protocols, and the healthcare system.Advances in healthcare delivery and a focus on value-based care aim to optimize patient outcomes while minimizing unnecessary costs, including prolonged hospital stays.

Average Preventable Readmission Rates
The study's findings highlighted a lack of significant correlation between APRR and ATCc in a healthcare setting.This absence of a strong correlation may be influenced by various factors.Firstly, the provision of high-quality care in hospitals may result in lower readmission rates, as patients are less likely to experience complications.However, the cost of delivering high-quality care, involving investments in technology, staffing, and specialized services, may contribute to an increased ATCc.This disparity in cost and quality could diminish the correlation between readmission rates and costs.Secondly, the effectiveness of post-discharge care and follow-up plays a crucial role in reducing readmissions.Healthcare facilities investing in comprehensive post-discharge care, including home health services, outpatient follow-up appointments, and patient education, may achieve lower readmission rates.Nevertheless, this approach can elevate the overall cost of care, further diminishing the correlation between readmission rates and costs.Thirdly, the patient mix served by a healthcare facility varies significantly.Hospitals treating a more medically complex or older population may experience higher readmission rates, irrespective of the quality of care provided.This demographic variation could contribute to a weak correlation between readmission rates and costs.
Additionally, healthcare reimbursement models and policies can impact the relationship between readmission rates and costs.Variations in reimbursement structures, such as value-based care models incentivizing reduced readmissions, can affect the correlation, especially when different hospitals operate under diverse reimbursement frameworks.Moreover, geographic and socioeconomic factors, including patients' access to healthcare services, socio-economic status, and the prevalence of chronic diseases, can influence readmission rates.These factors, along with variations in the cost of living and healthcare infrastructure, may not exhibit a strong correlation with each other, further complicating the relationship between readmission rates and costs.
Hospital-specific practices and protocols also contribute to the lack of a strong correlation.Hospitals with more effective care transition processes, better discharge planning, or robust post-discharge follow-up programs may reduce readmissions without significantly affecting costs.Finally, variations in data collection and reporting practices among healthcare facilities can contribute to the absence of a strong correlation.Inaccurate or inconsistent data reporting may obscure any potential relationship between readmission rates and costs.
In conclusion, the absence of a significant correlation between readmission rates and costs does not necessarily indicate a lack of influence between the two.The complex and interacting nature of multiple factors, coupled with diverse strategies employed by healthcare facilities, contributes to the nuanced relationship between these metrics.

ALOS and APRRs as predictor variables for ATCc
In this study, the ALOS and APRR were found to be ineffective predictors of ATCc.

Limitation of the Study
The study is limited to 65 hospital data of the 2018 Texas Hospital Data collection database.In addition, a descriptive correlation approach was used the investigation.I did not consider other mediating factors that impact care such as hospital specific practices, socioeconomic status, post discharge and follow-up policies; to list a few.

Implications for Research
Based on the study's results, several implications for further research merit considerations.

VI. CONCLUSION
It is important to note that the relationship between ALOS and Average Cost of Care is complex and may vary between different healthcare settings and systems.Reducing ALOS while maintaining or improving the quality of care is a goal in many healthcare systems as it can result in cost savings and better patient experiences.However, achieving this balance often requires careful planning, process improvements, and a focus on value-based care.Even though increased average length of stay and preventable readmission rate increases cost of care, providers should know that this is not always the case if quality practices are upheld with the careful planning.
By focusing on each component of the model, healthcare organizations can systematically evaluate and improve the quality of care they provide to patients.
between structure, process, and outcomes is crucial in addressing key indicators such as average length of stay, average preventable readmission rate, and total cost of care.

Table 2 :
Hospital Metro Status and Licensed Type

Table 5 :
Correlation between ALOS and ATCc Correlation

Table 6 :
Correlations between APRR and ATCc