Using Case Mix Index within Diagnosis-Related Groups to Evaluate Variation in Hospitalization Costs at a Large Academic Medical Center

Abstract

In analyzing direct hospitalization cost and clinical data from an academic medical center, commonly used metrics such as diagnosis-related group (DRG) weight explain approximately 37% of cost variability, but a substantial amount of variation remains unaccounted for by case mix index (CMI) alone. Using CMI as a benchmark, we isolate and target individual DRGs with higher than expected average costs for specific quality improvement efforts. While DRGs summarize hospitalization care after discharge, a predictive model using only information known before admission explained up to 60% of cost variability for two DRGs with a high excess cost burden. This level of variability likely reflects underlying patient factors that are not modifiable (e.g., age and prior comorbidities) and therefore less useful for health systems to target for intervention. However, the remaining unexplained variation can be inspected in further studies to discover operational factors that health systems can target to improve quality and value for their patients. Since DRG weights represent the expected resource consumption for a specific hospitalization type relative to the average hospitalization, the data-driven approach we demonstrate can be utilized by any health institution to quantify excess costs and potential savings among DRGs.

Introduction

In response to rapid medical inflation since the establishment of Medicare in 1965, Congress introduced an inpatient prospective payment system in 1982, which bundled routine operating costs for specific hospitalization types into a single flat fee reimbursement per case¹. Under this system, institutions began to classify hospitalizations into diagnosis-related groups (DRG) based on primary diagnoses or procedures, secondary diagnoses (including complications and comorbidities), patient age, and patient sex². A flat fee payment per DRG was theorized to benefit cost-efficient hospitals, which could keep the difference between the reimbursement and operating costs, and incentivize less efficient hospitals to lower costs.

Centers for Medicare & Medicaid Services (CMS) assigns relative weights for each Medicare Severity DRG (MS-DRG) as the ratio of resource consumption for the DRG to average overall Medicare inpatient resource consumption³. The DRG payment system formalized the concept of case mix index (CMI), calculated as the average DRG weight of a hospital’s discharges, as a robust measure of resource use linearly proportional to hospitalization costs in a Medicare population². Although CMI originated as a metric to calculate hospital payments, the correlation between resource consumption and disease severity led to the common practice of adjusting hospital utilization for case mix index to account for differences in patient acuity within and between hospitals, even outside of the Medicare population^4–6. Extending this concept to a DRG-specific CMI within a single institution, the objectives of this study are to determine how well hospital DRG weights and CMI explain variation in hospitalization costs at an academic medical center, develop an approach that identifies and ranks DRGs with disproportionate costs given their CMI, and further determine how much cost variation in such cases is explainable based on clinical data available before the first day of hospitalization. Such variation would reflect mostly unmodifiable clinical factors, as opposed to downstream execution, implementation, or process factors that may be more amenable to health system quality improvement and efficiency optimization efforts. This approach provides a quantitative method to prioritize hospitalization types for cost efficiency initiatives in light of pressures to reduce inpatient costs while improving quality of care.

Methods

Data source

De-identified structured electronic health record (EHR) data, DRG weights, and total direct costs were available for 54,316 inpatient admissions among 37,360 unique patients who received treatment at a large academic medical center (Stanford Health Care, Palo Alto, CA) between March 2019 and August 2021. Cost and DRG data under the MS-DRG and All Patients Refined DRG (APR-DRG) classification systems were linked for each patient by DRG weight and dates of admission and discharge. All but two admissions had an associated DRG code for each system. No admission had multiple distinct codes under a single system, consistent with expectations that each admission was assigned a single DRG code for billing and reimbursement.

Total direct costs consisted of expenses incurred by the medical center for a patient’s treatment during a hospitalization. Cost components included blood, imaging, laboratory tests, implants, supplies, operating room, pharmacy, and general accommodations, as well as care in the emergency department, intensive care unit (ICU), intermediate ICU, and cardiac care unit. Because organ acquisition costs are not included in the CMS DRG weight calculation for solid organ transplants⁷, they were removed from total costs for organ transplant-related hospitalizations.

Since costs spanned multiple years, they were standardized for inflation to 2021 rates using the Consumer Price Index (CPI) for medical care, available from the U.S. Bureau of Labor Statistics. The CPI for medical care summarizes price changes in medical goods and services, such as medical equipment, pharmaceuticals, physicians’ services, hospital services, and health insurance⁸. Hospitalization costs were multiplied by the ratio of the 2021 CPI to the CPI for the discharge year, effectively accounting for an inflation rate equal to this ratio minus 100%. The annual average CPI for each year in the data and the corresponding inflation rate to 2021 prices are displayed in Table 1 below.

Table 1:

Annual Consumer Price Index and inflation rates for medical care

Year	CPI for Medical Care9	Inflation rate to 2021 prices
2019	498.413	5.39%
2020	518.876	1.23%
2021	525.276	0.00%

For display purposes, costs were scaled in terms of the average hospitalization cost at the medical center. All analyses henceforth will refer to inflation-adjusted and scaled costs unless otherwise specified.

Statistical analysis

To assess the correlation and variation of resource consumption with DRG weight, we fit a linear model for total cost per hospitalization against DRG weight. Observing that variation in costs increased with DRG weight after plotting the two variables, heteroskedasticity-robust standard errors were calculated using White’s heteroskedasticity consistent estimator and used to calculate 95% confidence intervals (CI) for the parameters. Although the definitions for DRG weight and CMI suggest a directly proportional relationship with resource use, i.e., a null intercept, an intercept was included to allow for more flexibility in the model and to allow for an unbiased estimate of explained variance in costs due to DRG weight.

Given inflation-adjusted costs c_i and corresponding DRG weights w_i of unique observed admissions, we estimated the intercept ${\widehat{\beta }}_0$ and coefficient ${\widehat{\beta }}_1$ relating the two variables using the ordinary least squares objective:

$${\widehat{\beta }}_0,{\widehat{\beta }}_1=\underset{{\beta }_0,{\beta }_1}{\arg \min }{\displaystyle \sum _i{(c_i-{\beta }_0-w_i{\beta }_1)}^2}$$ (1)

Model fit was evaluated with the coefficient of determination (R²), which summarizes the proportion of variance in costs explained by the model. A 95% nonparametric bootstrap CI for the R² value was generated with 1,000 bootstrap samples. Next, the expected cost ${\widehat{c}}_i$ for admission i based on its DRG weight was calculated as:

$${\widehat{c}}_i={\widehat{\beta }}_0+w_i{\widehat{\beta }}_1$$ (2)

For each DRG δ, net excess cost NEC was calculated as the sum of total hospitalization costs less the sum of expected costs given the case mix within the DRG and fitted linear model on all cost data:

$$NE{C}_{\delta }={\displaystyle \sum _{i\epsilon \delta }{c}_i-{\widehat{c}}_i}$$ (3)

Since patient acuity and care intensity naturally vary within a particular DRG, one would expect treatment costs to fluctuate around expectation given DRG weight such that higher- or lower-than-expected costs would balance out overall, leading to a low NEC. However, DRGs with a high NEC would signal a systematically higher cost burden compared to other DRGs after controlling for expected resource consumption. NEC was assessed for DRGs under both the MS-DRG and APR-DRG systems.

For select DRGs with a high NEC, we ran a lasso regression to assess cost variance explained by features known before admission. Patient age, sex, race, ethnicity, Clinical Classifications Software Refined (AHRQ-CCSR) groupings mapped from International Classification of Diseases, 10th Revision, Clinical Modification (ICD-10-CM) codes in the medical record before admission, lab results within 14 days before admission, medication classes ordered within 28 days before admission, surgical procedures within 28 days before admission, and flowsheet values within 3 days before admission were extracted from the clinical record. Continuous variables were binned into five quantiles. Given the high number of extracted features for the sample size of admissions in each DRG, lasso regression of hospitalization costs against extracted features with 10-fold cross validation to tune the L1 hyperparameter allowed for a sparse model. The regressions provided a preliminary estimate of variance in costs explained by features known before admission (R²) and the degree of association between specific features and costs.

Results

The linear regression on DRG weight explained R² = 37.2% (95% bootstrap CI: [35.0%, 39.6%]) of the variance in total hospitalization costs, indicating a 61.0% correlation between the two variables. The intercept ${\widehat{\beta }}_0$ and coefficient ${\widehat{\beta }}_1$ for the linear model relating DRG weight and hospitalization costs scaled by average inpatient cost are reported in Table 2 below.

Table 2:

Linear regression parameters for hospitalization cost versus DRG weight

Parameter	Value	95% CI
${\widehat{\beta }}_0$	0.1328	(0.087, 0.178)
${\widehat{\beta }}_1$	0.3325	(0.312, 0.353)

For example, based on the fitted model, a hospitalization with a DRG weight of 10 would have a predicted cost of ${\widehat{c}}_i$ = 0.1328 + 10 × 0.3325 = 3.458 times the average inpatient admission cost. Although the model includes a nonzero intercept, as DRG weight increases, the intercept’s contribution to the predicted cost becomes negligible (0.1328 ÷ 3.458 = 3.840% of the predicted cost in this example).

Figure 1 plots the observed hospitalization costs against DRG weight along with the predicted cost based on the fitted model. Two DRGs with systematically higher (MS-DRG 003) or lower (MS-DRG 018) costs than predicted given their DRG weights are additionally plotted. Costs are scaled relative to the average inpatient admission cost. To better visualize the distribution of the high density of admissions with a low DRG weight, DRG weight was displayed in log scale.

Figure 1:

Hospitalization costs versus DRG weight with fitted linear model and highlighted DRG examples Abbreviations: CAR = chimeric antigen receptor; ECMO = extracorporeal membrane oxygenation; MS-DRG = Medicare Severity Diagnosis-Related Group; MV = mechanical ventilation; OR = operating room

The MS-DRGs with the highest net excess cost included DRGs related to life support, psychoses, organ and bone marrow transplant, cardiovascular procedures, treatment complications, infection, and leukemia (Table 4). Organ transplants, cardiovascular procedures, and infectious diseases were also flagged as high-excess-cost APR-DRGs, although relative rankings were different due to the systems’ different aggregations of primary diagnoses, severity of illness, and risk of mortality¹⁰ (Table 3).

Table 4:

Cost statistics for MS-DRGs and APR-DRGs with highest net excess cost

Rank	DRG	As % of total hospitalization costs		As proportion of avg. hospitalization cost
		Total cost	Net excess cost	Avg. cost	Avg. excess cost
MS-DRG
1	ECMO or tracheostomy with MV >96 hours or principal diagnosis except face, mouth and neck with major OR procedures	4.078%	1.109%	8.824	2.399
2	Psychoses	1.779%	0.674%	0.869	0.329
3	Autologous bone marrow transplant with CC/MCC	2.281%	0.665%	3.385	0.987
4	Cardiac valve and other major cardiothoracic procedures without cardiac catheterization with MCC	3.144%	0.390%	3.162	0.392
5	Heart transplant or implant of heart assist system with MCC	2.730%	0.370%	10.903	1.479
6	Liver transplant with MCC or intestinal transplant	1.226%	0.339%	4.898	1.353
7	Complications of treatment with MCC	0.646%	0.271%	1.276	0.534
8	Infectious and parasitic diseases with OR procedures with MCC	1.464%	0.269%	2.209	0.406
APR-DRG
1	Liver transplant and/or intestinal transplant	1.520%	0.508%	5.194	1.734
2	Heart and/or lung transplant	3.040%	0.447%	8.381	1.231
3	Implantable heart assist systems	0.836%	0.424%	16.214	8.225
4	Other cardiothoracic and thoracic vascular procedures	2.268%	0.419%	2.725	0.503
5	Septicemia and disseminated infections	4.604%	0.417%	0.911	0.083
6	Infectious and parasitic diseases including HIV with OR procedure	1.655%	0.404%	2.391	0.583
7	Cardiac catheterization for other non-coronary conditions	0.841%	0.354%	1.293	0.545
8	Major hematologic or immunologic diagnoses except sickle cell crisis and coagulation	1.020%	0.351%	0.979	0.337

Abbreviations: AMI = acute myocardial infarction; APR-DRG = All Patients Refined Diagnosis-Related Group; avg. = average; CC = complication or comorbidity; ECMO = extracorporeal membrane oxygenation; HIV = human immunodeficiency virus; MCC = major complication or comorbidity; MS-DRG = Medicare Severity Diagnosis-Related Group; MV = mechanical ventilation; OR = operating room

Table 3:

Characteristics of MS-DRGs and APR-DRGs with highest net excess cost

Rank	DRG	Code	Admissions N	DRG weight Mean (SD)
MS-DRG
1	ECMO or tracheostomy with MV >96 hours or principal diagnosis except face, mouth and neck with major OR procedures	003	251	18.92 (0.16)
2	Psychoses	885	1112	1.22 (0.01)
3	Autologous bone marrow transplant with CC/MCC	016	366	6.81 (0.10)
4	Cardiac valve and other major cardiothoracic procedures without cardiac catheterization with MCC	219	540	7.93 (0.12)
5	Heart transplant or implant of heart assist system with MCC	001	136	27.94 (0.71)
6	Liver transplant with MCC or intestinal transplant	005	136	10.26 (0.04)
7	Complications of treatment with MCC	919	275	1.83 (0.00)
8	Infectious and parasitic diseases with OR procedures with MCC	853	360	5.02 (0.08)
APR-DRG
1	Liver transplant and/or intestinal transplant	001	159	10.01 (2.46)
2	Heart and/or lung transplant	002	197	21.10 (7.92)
3	Implantable heart assist systems	161	28	23.63 (8.48)
4	Other cardiothoracic and thoracic vascular procedures	167	452	6.28 (3.04)
5	Septicemia and disseminated infections	720	2746	2.09 (1.47)
6	Infectious and parasitic diseases including HIV with OR procedure	710	376	5.04 (3.03)
7	Cardiac catheterization for other non-coronary conditions	192	353	1.85 (1.09)
8	Major hematologic or immunologic diagnoses except sickle cell crisis and coagulation	660	566	1.53 (0.46)

Abbreviations: AMI = acute myocardial infarction; APR-DRG = All Patients Refined Diagnosis-Related Group; CC = complication or comorbidity; ECMO = extracorporeal membrane oxygenation; HIV = human immunodeficiency virus; MCC = major complication or comorbidity; MS-DRG = Medicare Severity Diagnosis-Related Group; MV = mechanical ventilation; OR = operating room; SD = standard deviation

A lasso regression with 10-fold cross validation was run for two MS-DRGs (003: extracorporeal membrane oxygenation [ECMO] or tracheostomy with MV >96 hours or principal diagnosis except face, mouth and neck with major OR procedures; 919: complications of treatment with major complication or comorbidity [MCC]) to assess cost variation explained by patient demographic and clinical features known at admission. Patient features before admission explained 39.8% of variation in the ECMO cohort. In this cohort, a prior lab order for parathyroid hormone plus calcium, a lab order for a research lab kit, and a medication order for cough or cold preparations were associated with higher costs. In the treatment complications cohort, prior features explained 59.2% of variation in costs, with higher costs associated with a prior diagnosis of chronic lymphocytic leukemia, a lab order for C. difficile culture with reflect to toxin B, a lab order for a direct Coombs broad spectrum test, a lab order for cytomegalovirus, a medication order for skin preparations, and a lab order for serum magnesium.

Discussion

Consistent with the expected proportional relationship between case mix index and resource consumption, we found a moderate positive correlation of 61.0% between DRG weights and hospitalization expenses incurred by a large academic medical center. The proportion of observed cost variance explained by DRG weight was 37.2%, comparable to an early analysis of Medicare’s CMI, which found that the CMI of a hospital explained about 30% of the variation in the hospital’s Medicare average cost per case². DRGs related to life support, psychoses, certain transplant types, cardiovascular procedures, and infectious diseases were found to have disproportionately high overall costs after adjusting for CMI within the DRG. These ranged from DRGs with a low average cost but high frequency, such as psychoses (MS-DRG 885), to DRGs with high average expenses and low volume, such as implantable heart assist systems (APR-DRG 161).

Identification of DRGs with higher than expected resource consumption after benchmarking with Medicare CMI can inform efforts to improve documentation or standardize processes. For example, some clinical or perioperative pathways have been successful in reducing hospital length of stay and health care resource use^11,12. Furthermore, if higher costs are due to greater patient acuity than the Medicare average, a hospital can achieve more equitable reimbursement by improving documentation to reflect acuity or identifying cost-driving patient characteristics that DRGs or other payment systems do not yet account for. Preliminary regressions showed that for two DRGs with high net excess cost, less than 60% of variation in costs could be explained by patient factors known at admission, warranting future work to investigate factors during the hospitalization that contribute to higher costs, such as complications, medication interactions, or treatment delays.

A previous analysis of the same inpatient population ranked MS-DRGs based on total cost burden, encounter frequency, and a coefficient of variation estimating potentially modifiable costs¹³. The coefficient of variation was calculated as the ratio between the standard deviation and mean of admission costs within a DRG¹³. ECMO, heart transplant with MCC, autologous bone marrow transplant with complication or comorbidity/MCC, and cardiac valve and other major cardiothoracic procedure with MCC were selected as top DRGs in both the current and prior study, reflecting the two methods’ consistencies in detecting DRGs with a high cost burden¹³. However, the prior study also selected allogeneic bone marrow transplant, which had a net negative excess cost in the current study after adjusting for DRG weight. Another difference was the current method’s selection of DRGs such as psychoses and complications of treatment with MCC, which had low variation in DRG weights and costs but higher than expected costs for their case mix index. Both methods have different strengths in identifying DRGs with disproportionate and modifiable cost burden, and future research could refine and combine methods to prioritize DRGs for cost efficiency improvement.

The analysis has several limitations. CMI depends not only on acuity of patient condition but also on documentation and coding practices, which may introduce variation in the DRG and weight assigned to a case extrinsic to clinical characteristics. For instance, an analysis found that public hospitals had systematically lower CMIs than private non-profit or for-profit hospitals after stratifying by teaching status and trauma level, possibly due to fewer financial incentives to document for a higher CMI; however, the analysis also concluded that CMI and patient acuity could still be accurately compared between hospitals of the same type⁴. Although insurers and analyses commonly apply DRG weights to hospitalizations regardless of payer, DRG weights are based on relative resource use in the Medicare population, which may not generalize to other populations, such as commercially insured patients, which are included in the current analysis. Additionally, the current analysis does not account for potential differences in care stemming from potential differences in payment rates between Medicare and private insurers^{14, 15}.

Cost data for individual admissions were mapped to clinical data using anonymized patient identifiers, DRG weights, and admission and discharge dates. While the majority (81.3%) of admissions could be linked with exact admission and discharge dates, 18.7% of admissions were linked with admission dates within 5 days apart, potentially due to variation in the coding of encounter timings in the clinical and cost databases, as well as discrepancies due to anonymization of costs and clinical data to protect patient information. The accuracy of the DRG and cost data depends on accurate coding and processing of the electronic health records.

Hospitalization costs were highly skewed right, with mean approximately twice the median. The maximum cost was over 70 times the mean. As a result, high outlier costs likely had high leverage in the linear model, and outliers could drive the high net excess costs for some DRGs. Such skew could be reduced by analyzing with logarithmic costs, although doing so would violate the assumption of linearity with DRG weight. A large proportion (24%) of patients had multiple admissions, which may have led to correlation in hospitalization costs within DRGs that the linear model did not account for. For example, a patient admitted to the hospital repeatedly for the same condition and therefore under the same DRG would likely have a more severe illness than a patient admitted once, leading to repeated higher costs and thus a higher net excess cost for the DRG. Future work could improve on accounting for outliers and repeat admissions. Given data availability, we could also improve the validity of our excess cost estimates by benchmarking against inpatient expenses incurred at other healthcare systems.

While the focus of the current analysis was on hospitalization types with a high overall cost burden, institutions could also benefit from analyzing DRGs with low resource consumption in two ways. First, future work could learn from hospitalizations with low costs relative to DRG weight. Second, DRGs with low excess costs due to low volume could see productivity gains from scaling up, a phenomenon supported by literature^16,17.

Conclusion

We studied undesirable variability in hospitalization costs by comparing DRG-specific expenses after adjusting for case mix index similarly to how Medicare and other payers compare hospital cost efficiency. This method identified DRGs with high excess costs within a single institution, warranting further analysis on uncontrollable versus potentially modifiable factors contributing to cost differences. For targeted DRGs, regression models of costs versus patient factors at admission can estimate non-modifiable factors associated with higher costs. However, the degree of variability unexplained by such regression models hints at clinical and operational factors during the hospitalization that may influence costs. Other institutions can adopt this workflow to quantify cost inefficiencies within admissions related to specific diagnoses or procedures and prioritize cost reduction efforts by potential impact.

Contributions

SP: study ideation and design, analysis, interpretation of results, manuscript first draft; JM: study ideation and design, operational interpretation; SPM: study ideation and design, clinical interpretation; CKC: developed patient feature extraction pipeline for analysis; AM: study ideation, curated and provided data; JHC: study ideation and design, interpretation of results, manuscript first draft. All authors reviewed and provided feedback on manuscript.