Health Care Management Science

, Volume 14, Issue 2, pp 125–134

Controlling for quality in the hospital cost function


    • VA Center for Health Quality, Outcomes and Economic ResearchBoston University School of Public Health
  • Theodore Stefos
    • VA Office of Productivity, Efficiency and StaffingBoston University School of Public Health

DOI: 10.1007/s10729-010-9142-7

Cite this article as:
Carey, K. & Stefos, T. Health Care Manag Sci (2011) 14: 125. doi:10.1007/s10729-010-9142-7


This paper explores the relationship between the cost and quality of hospital care from the perspective of applied microeconomics. It addresses both theoretical and practical complexities entailed in incorporating hospital quality into the estimation of hospital cost functions. That literature is extended with an empirical analysis that examines the use of 15 Patient Safety Indicators (PSIs) as measures of hospital quality. A total operating cost function is estimated on 2,848 observations from five states drawn from the period 2001 to 2007. In general, findings indicate that the PSIs are successful in capturing variation in hospital cost due to adverse patient safety events. Measures that rely on the aggregate number of adverse events summed over PSIs are found to be superior to risk-adjusted rates for individual PSIs. The marginal cost of an adverse event is estimated to be $22,413. The results contribute to a growing business case for inpatient safety in hospital services.


Hospital cost functionQualityAdverse events

1 Introduction

The landmark Report of the Institute of Medicine (IOM), “To Err is Human,” warned the U.S. public of the significant risk of medical errors associated with hospital inpatient care [28]. The Report attracted widespread interest, and has provoked considerable recent effort toward increasing patient safety and improving the overall quality of hospital care. In the current era of rapidly escalating hospital costs, quality improvement efforts also raise economic concerns. There is some evidence of cost savings associated with reduction of medical errors [16, 45]; however, improving the quality of patient care in hospitals has complex cost implications, and much remains to be learned about the cost of achieving high quality performance [25]. Concern over the breadth of medical errors and quality improvement elevates the importance of understanding the relationship between hospital quality and cost.

The economics discipline contains a theoretically-based and empirically-tested framework for analyzing the production and cost efficiency of an individual enterprise such as a hospital. The hospital multi-product cost function, the specific modeling tool within that framework, models the relationship between total hospital production cost and quantity of various outputs produced, accounting for input prices, and in its empirical application controlling for other observable factors that have been demonstrated to account for significant variation in hospital costs. Standard economic theory assumes that the firm minimizes cost in choosing inputs to the production process to produce outputs at a given level of quality. While measurement of hospital level cost is straightforward, hospital quality is multidimensional and difficult to quantify. Hence variation in quality levels complicates the theoretical and empirical modeling of hospital cost.

Over the past 30 years, considerable progress has been made in refining the hospital multi-product cost function. The form of the cost function and the cost determinants have been well developed [30], and we now know much about the importance of different factors in influencing hospital costs. However, conceptual and measurement challenges in pinpointing the cost/quality relationship has contributed to failure of the hospital cost function to account adequately for the effects of quality on hospital costs. Yet it has long been established that if quality of service is not controlled in a cost function, biases result [7].

This paper estimates a hospital cost function that draws on new measures of hospital quality that have been developed in the decade since the publication of the IOM Report. It contributes to the science of hospital cost function estimation by examining how the new measures of quality variation perform in that empirical framework, and produces new insights regarding the reduction in cost that are achievable by reducing medical errors. The paper is organized as follows. Section 2 presents a theoretical framework for addressing the relationship between hospital quality and costs and summarizes the treatment of quality in the hospital cost function literature. The third section describes the empirical model. Section 4 presents the results. The fifth section provides discussion and conclusions.

2 Background

2.1 Conceptual framework

According to statistician and celebrated industry consultant W.E. Deming, continuous quality improvement efforts, when properly applied, ultimately will lead to financial savings [12]. However in the case of hospitals, quality is a multi-dimensional attribute and the path from quality improvement to cost savings is not straightforward. In theory, hospital cost and quality could move in the same general direction, in which case the impact of quality improvements is cost-increasing. For example, high nurse staffing ratios and/or the extra resources required by hospitals that have a teaching as well as a therapeutic mission are cost increasing features that have been found to be associated with higher observed hospital quality [29, 39]. Innovative and expensive new high technology services are also cost-increasing [13, 33].

At the same time, low quality can be associated with lapses in care that lead to adverse events such as infections due to medical care or post-operative respiratory, vascular, or metabolic complications. Such events have been shown to increase hospital costs [16, 45]. Here the relationship between low quality and cost is indirect, involving additional resource utilization due to extra care that needs to be provided to repair damages or problems caused by the lapse in patient care leading to the adverse event. This could take the form of further days of hospitalization complicated by conditions such as fever, pneumonia, or blood infections, greater intensity of services (e.g. days spent in intensive care units), more ancillary services and/or extra medications. Conversely, efforts aimed at reduction of preventable adverse events and complications will avert the need for additional services, and lead to cost savings.

The overall relationship between quality and cost consists of the combined effect of several different factors operating jointly. For instance, higher nurse staffing levels and/or sophisticated information systems have a direct and positive impact on costs, but also reduce the probability of expensive adverse events, thereby simultaneously having an indirect effect that is cost-reducing. A hospital with a low registered nurse to patient ratio and/or a low level of investment in information technology may experience errors in transmission of patient care information, infrequent evaluation of patients for pressure ulcers or deep vein thrombosis, or failure to adhere to known methods of preventing central line infections. Quality improvement effort through increases in registered nurse staffing or expansion of information technology will result in reduction of such adverse events. The total impact on cost will vary across the range of quality improvement effort. At low levels of cost-increasing investment in quality improvement, the marginal cost will be relatively low, but because rates of medical error due to poor quality care will be tend to be higher, the overall impact of quality improvement will be cost reduction. Conversely, at relatively high levels of quality improvement effort, lower rates of medical error may already be achieved, so that the cost-increasing impact of quality improvement outweighs the cost saving due to reduction of adverse events, and the overall effect of further investment in quality improvement is positive.

2.2 Literature review

Quality of care has numerous dimensions, and no single measure will be capable of capturing its full spectrum in a cost function or elsewhere. There is a broad range of approaches that hospital cost function research studies have taken to control for quality. In reviewing the role of quality in the hospital cost function, we note that the literature is extensive and an exhaustive review is beyond the scope of this paper. Rather, this review highlights several key papers with the objective of outlining the progression of the science of hospital function cost estimation with respect to incorporation of quality measures.

As noted, in addition to its theoretical complexities, the quality of hospital care has presented repeated problems of measurement and data availability. Consequently, many hospital cost function studies have not included explicit quality measures, confounding the impact on quality of cost containment policies [20]. With the growing number of stochastic frontier cost function analyses, in which the residual cost is interpreted as insufficient effort at cost control or “inefficiency,” disregard for quality has posed more immediate and vexing problems [23]. For example, if hospital quality is cost-increasing overall, failure to account for this in the cost function will result in confounding of inefficiency measures, in which it is difficult to differentiate between higher residual costs resulting from unobserved superior quality and higher costs resulting from managerial inefficiency or slack.

In the absence of observed measures, some researchers have incorporated unobserved quality into cost functions by application of economic theory in a simultaneous equation model [20], and by exploiting the structure of the error term in a panel data model [8]. Hospital cost function studies that have included observed quality controls have relied heavily on structural measures of hospital quality. The most common measure is teaching activity, generally measured by either the ratio of interns and residents to beds, or binary variables representing teaching hospitals [5, 19, 21, 24, 37]. In the narrow sense, teaching per se represents the specific hospital output of medical education [2, 6], so that teaching is at best a proxy variable for hospital quality. However, teaching hospitals have been shown to have higher adjusted survival rates than non-teaching hospitals [27, 39], and there is widespread agreement that quality of care tends to be higher in teaching hospitals [39]. Other structural measures used have included the presence of high technology services [13, 32], board certification of staff [18], hospital accreditation, and registered nurses as a percent of full-time nursing staff [32].

Other studies have incorporated process and/or outcomes measures as quality controls. In particular, readmission and mortality rates have been widely used in hospital cost function studies [9, 17, 38]. As specific measures of phenomena, these are precisely quantified, but as controls for overall quality in the cost function they have a low ratio of signal to noise [35, 41, 42], and may lead to incorrect assessments of provider performance [40]. A study of VA hospitals that focused on the cost-quality relationship incorporated mortality and readmission rates and directly addressed the issue of measurement error in observed quality [10]. Results suggested that mortality and readmission rates were not good proxy measures, as they were inadequately adjusted for risk, and appeared rather to serve as controls for severity/complexity. The same study included the process measure of outpatient follow-up after inpatient discharge, and suggested that the hospital that performs poorly at tracking and general coordination of its patients faces higher overall treatment costs. A subsequent frontier study of VA hospitals used inpatient satisfaction measures as well as hospital mortality and readmission rates that were more carefully adjusted for case-mix [44]. Despite the improved controls for severity on the latter measures, readmission was statistically insignificant in explaining cost, and mortality was practically insignificant.

In the aftermath of the IOM Report, the Agency for Healthcare Research and Quality (AHRQ) developed an evidence-based methodology for identifying potentially preventable adverse patient safety events. The Patient Safety Indicator (PSI) algorithms link information contained in standardized hospital discharge data to generate hospital level PSI event rates. PSIs apply to medical conditions and surgical procedures that have been shown to have complication/adverse event rates that vary substantially across institutions and for which evidence suggests that high rates are associated with deficiencies in the quality of care [1]. The 20 PSIs are increasingly being used by health professionals as screening tools and by researchers as measures of hospital quality [15, 36, 43]. Two studies of which we are aware have incorporated PSIs into stochastic frontier cost functions [11, 38]. The study by Rosko and Mutter, which included six risk-adjusted PSIs as quality controls, did not report on whether an association was found between the PSI rates and costs. The analysis by Carey, Burgess and Young did report significant positive associations between three PSIs and cost, although did not comment on the specific cost implications of using the PSIs as quality measures.

No single measure will be capable of fully capturing the intricate relationship between hospital costs and quality. In this paper, we go beyond previous studies in exploring the potential for using PSIs as controls for quality in the cost function in the presence of other measures of quality that simultaneously account for variation in cost. In the next section, we describe an empirical strategy which addresses that objective.

3 Empirical model

3.1 Theoretical issues

We adopt the theoretical design of the short-run multi-product cost function. This formulation excludes the cost of capital under the assumption that hospitals cannot adjust the capital stock over a short time horizon in response to changing demand or changing input prices. Hospitals do, however, utilize optimal quantities of the easily adjustable variable inputs, including nurse hours, staffed beds, ancillary services from radiology, laboratory and pharmacy, and supplies.

In pure theoretic form, the economic cost function is a model of total short-run costs as a function of outputs and input prices. However, hospitals are heterogeneous in other factors that drive costs, and the hospital cost function literature has adopted a ‘hybrid’ approach to explaining costs, that includes measures of case-mix of admitted patients, competitive pressure emanating from other hospitals, ownership status, and in some instances, controls for quality.

3.2 Data and variables

The model was estimated using annual data from five states (Arizona, California, New Jersey, Texas and Wisconsin) for the years 2001–2007. Our main sources of data were the Medicare Cost Reports (MCR) and state administrative data, supplemented by the American Hospital Association Annual Survey Database (AHA). The state data (discharge abstracts) were obtained from the AHRQ Healthcare Cost and Utilization Project (HCUP) State Inpatient Databases, the Texas Department of State Health Services Center for Health Statistics, and the California Office of Statewide Health Planning and Development.

The dependent variable was hospital total costs, obtained from the MCR, and expressed in 2007 dollars. It excluded costs associated with capital-related investments, and non-reimbursable cost centers unrelated to patient care. We included the number of hospital beds as a proxy measure of the level of fixed costs in the short run cost function. The key output variables were number of discharges and number of outpatient visits. Inpatient output intensity differences not captured by number of discharges were incorporated by inclusion of average length of stay. While the number of discharges models a single hospital stay consisting of the admission process, ancillary services and surgical services, the average length of stay measure captures routine nursing and hotel services [21]. We controlled for the prices of inputs to production by including the index of local area wage rates used by Medicare for reimbursing hospitals under the Prospective Payment System. Data on prices of other inputs were unavailable; however, labor accounts for the majority of hospital expenses, and local wages are likely correlated with the prices of other inputs.

To capture the resource intensity of patient workload, we included the Medicare inpatient case-mix index, which correlates highly with a hospital’s overall case-mix index [38], and which is standard in hospital cost function analyses [8, 19, 30]. Outpatient case mix measures are less available; however, we included the percentage of outpatient visits that involved surgeries [11]. We included a Herfindahl-Hirschman Index (HHI) measure of hospital competition, using the county as market area. The HHI is calculated as the sum of the squared market shares of individual firms competing in the same market. If price competition characterizes the market, theoretically the HHI measure is positively associated with costs, as more hospitals competing with each other places downward pressure on costs. Alternatively, a negative HHI effect suggests quality competition, as a greater number of hospitals are associated with higher hospital costs, driven more by cost-increasing services and technology.

We also entered a set of indicator variables to control for ownership type (for-profit, nonprofit, and public), for whether the hospital was a member of a multi-hospital system, as well as state specific indicator variables as fixed effects. Variables measuring quality that we hypothesized to be cost-increasing included a binary measure for major teaching mission, the portion of full-time equivalent nurse staff that were registered nurses, and an index of high technology services. The high tech variable is a discrete indicator that takes a value of one though five, depending on how many of five high technology services the hospital offered in a given year.1

As measures of cost-increasing adverse events, we drew upon 15 of the 16 PSIs for which the AHRQ software produces a full set of hospital level event rates. We omitted the PSI for failure to rescue, which indicates death during hospitalization, rendering the cost implications ambiguous. Table 1 lists the 15 PSIs and descriptions of the inclusion/exclusion criteria defining which patients are at risk for each of the 15 PSIs (included in the denominator in calculating event rates). Table 2 presents further detail on each PSI. Columns 2–4 list mean values of the number of patients included in the denominator, the number of actual events, and the unadjusted PSI event rates (actual events/denominator). Column 5 lists the mean values of the risk-adjusted event rates. These account for variation in the hospitals’ case-mixes, which are benchmarked against the average case-mix of a baseline reference file that reflects a large proportion of the U.S. hospitalized population.2 The AHRQ software algorithm adjusts for risk according to age, gender, modified DRG and co-morbidities. Finally, column 6 lists the mean values of number of events the hospital would have had if it had the same risk level as the reference population, the same number of patients in the denominator, and the hospital’s actual performance in the given year. We constructed the number of risk-adjusted events by multiplying the population included in the denominator (column 2) by the risk-adjusted event rate (column 5) for each hospital year.
Table 1

Patient Safety Indicator (PSI) descriptions


Inclusion/exclusion criteria

01 Complications from anesthesia

Cases of anesthetic overdose, reaction, or endotrachial tube misplacement excluding drug use and self-inflicted injury

03 Decubitus ulcer

Cases of decubitus ulcer with a length of stay of more than 5 days, excluding patients with paralysis, patients in Major Diagnostic Categories (MDCs) 9 or 14, and patients admitted from a long term care facility

06 Iatrogenic pneumothorax

Cases of iatrogenic pneumothorax. Excludes trauma, thoracic surgery, lung or pleural biopsy, or cardiac surgery patients, and MDC 14

07 Infection due to medical care

Cases of secondary ICD-9-CM codes 9993 or 00662, excluding immuno-compromised cancer patients and patients with stays of less than 2 days

08 In hospital hip fracture

Case of in-hospital hip fracture, excluding patients in MDC 8, suggesting fracture present on admission

09 Post-operative hematoma

Cases with ICD-9-CM codes for post-operative hemorrhage or hematoma in any secondary diagnosis field AND code for post-operative control of hemorrhage or hematoma in any secondary procedure code field

10 Post-operative physiologic and metabolic derangements

Cases of specified physiologic or metabolic derangement in elective surgery discharges, excluding obstetric admissions, patients with a principal diagnosis of diabetes, and patients with diagnoses suggesting increased susceptibility to derangement

11 Post-operative respiratory failure

Cases of acute respiratory failure among elective surgical discharges, excluding MDCs 4 & 5 and obstetric admissions

12 Post-operative pulmonary embolism or deep vein thrombosis

Cases of deep vein thrombosis or pulmonary embolism in surgical patients, excluding obstetric patients

13 Postoperative sepsis

Cases of sepsis among elective surgery patients with length of stay more than 3 days, excluding principal diagnosis of infection and obstetric patients

14 Postoperative wound dehiscence

Cases with ICD-9-CM codes for reclosure of postoperative disruption of abdominal wall (54.61) in any secondary procedure field

15 Accidental puncture or laceration

Cases with ICD-9-CM code denoting technical difficulty (e.g., accidental cut, puncture, perforation or laceration during a procedure) in any secondary diagnosis field

17 Birth trauma—injury to neonate

Cases of birth trauma, injury to neonate live born births excluding some pre-term births and infants with osteogenic imperfecta

18 Obstetric trauma—vaginal delivery with instrument

Cases of obstetric trauma (3rd or 4th degree lacerations) in instrument-assisted vaginal deliveries

19 Obstetric trauma—vaginal delivery without instrument

Cases of obstetric trauma (3rd or 4th degree lacerations) in vaginal deliveries without instrument assistance

Table 2

Hospital level mean valuesa of Patient Safety Indicator (PSI) measures

Patient safety indicator

Population included in denominator

Number of actual events

PSI rate

Risk adjusted rate

Number of risk adjusted events

01 Complications from anesthesia






03 Decubitus ulcer






06 Iatrogenic pneumothorax






07 Infection due to medical care






08 Post-operative hip fracture






09 Post-operative hematoma






10 Post-operative physiologic and metabolic derangements






11 Post-operative respiratory failure






12 Post-operative pulmonary embolism or deep vein thrombosis






13 Postoperative sepsis






14 Postoperative wound dehiscence






15 Accidental puncture or laceration






17 Birth trauma—injury to neonate






18 Obstetric trauma—vaginal delivery with instrument






19 Obstetric trauma—vaginal delivery without instrument






aCalculated means of hospital level values

As quality controls in the cost function, we incorporated the PSIs in two different ways. First, we entered risk-adjusted event rates, following the previous literature. Second, given the large number of PSIs, the lack of a composite event rate, and the small frequency of occurrence of some PSIs, we took an alternative approach by summing the number of events across the 15 PSIs for each observation. In the second approach, we computed both the number of risk-adjusted events and the actual number of events. The former more closely captures the true variation in quality while the latter more closely captures the actual cost impact of an event. Table 3 displays descriptive statistics for variables included in the regression analyses. As seen in the Table, there is very little difference between the total number of risk-adjusted events and the total raw number of events in our sample. This indicates that on average, the risk level of our sample is close to that of the reference population. The data contain 2,848 observations observed over the period 2001–2007.
Table 3

Descriptive statistics



Standard deviation

Total cost (millions of 2007 dollars)






Outpatient visits



Average length of stay (days)



Inpatient case-mix



Outpatient case-mix






Herfindahl index of competition (HHI)



% For-profit hospital


% Not for profit hospital


% Government hospital


% Hospital system membership


Teaching indicator variable


High technology service index



RN % of nurse workforce


Number of risk-adjusted adverse events



Raw number of adverse events



N = 2,848

3.3 Estimation

The cost function is not derived from a specific production technology, hence no particular functional form is called for, and the literature contains an extensive number of empirical models employing a variety of functional forms. The most common is the translog, in which the dependent and independent variables are logarithmically transformed, and the second power and interactions among the output variables are included as regressors [19, 46, 47]. The drawback to this form is collinearity due to the large number of parameters to be estimated, such that some precision of the translog estimates is sacrificed for functional flexibility. The focus of this paper is marginal effects, and trading off accuracy of coefficients for additional flexibility did not seem warranted. Moreover, the input price data available for this exercise is limited, further weakening the precision capability of the translog which relies on joint estimation with share equations (following Shephard’s Lemma) [30]. Alternatively, we followed the literature in applying the log linear specification, which is equivalent to the translog cost function where the coefficients of the second-order terms are restricted to zero [44].

Our data is longitudinal with a 7 year unbalanced panel. Exploratory analysis revealed low levels of within variation in many of the variables including the PSI variables, precluding use of a fixed effects model. Fixed effects estimation would also require exclusion of the teaching indicator variable, which was time invariant. Random effects models do not have these limitations; however, random effects estimation assumes no correlation between observed variables and unobservable individual hospital effects, an assumption that has generally been viewed as unwarranted in hospital cost functions [8]. An alternative approach for addressing intra-cluster correlation in longitudinal data is that of generalized estimating equations (GEE) [31]. We applied GEE models using SAS v9.1 PROC GENMOD, to account for hospital level clustering and to obtain robust standard errors for regression coefficients.

Our estimating equation takes the form:
$$ {C_{{it}}} = {P_{{it}}}*ex{p^{{f + e}}} \to ln\,{C_{{it}}} - ln\,{P_{{it}}} = f + {e_{{it}}} $$
$$ f = \alpha + {\sum_j}{\beta_{{jit}}}ln{Y_{{jit}}} + {\sum_r}{\zeta_{{rit}}}*{X_{{rit}}}. $$

Cit represents the total operating costs of hospital i in year t, Pit represents input prices, ln is the function of natural logarithms, and exp is the exponential function. We subtract the log of input price from the log of costs in order to maintain the assumption of linear homogeneity in input prices. The Yjs represent the multiple outputs and the fixed input, and the Xks represent the remaining regressors including the quality variables. Finally, α, the βs, and the ζs are parameters to be estimated.

4 Results

Table 4 reports the results of the regression models. Model 1 is a benchmark analysis that does not include PSI measures. The key economic variables exhibit the expected signs and high levels of significance. The HHI was insignificant, suggesting that neither price nor non-price competition dominated market conduct among the hospitals in our sample. For-profit hospitals had the lowest cost relative to government hospitals (the reference group), followed by nonprofit hospitals. System member hospitals were not significantly different in cost from independent hospitals. All three quality measures hypothesized to be cost-increasing exhibited the expected positive associations at p ≤ 0.0001.
Table 4

Regression coefficients and standard errors


Model 1a

Model 2

Model 3

Model 4


8.5798** (0.149)

8.5756** (0.1467)

8.7576** (0.1782)

8.7651** (0.1783)

Log of Discharges

0.6527** (0.0193)

0.6548** (0.0190)

0.6374** (0.0211)

0.6367** (0.0209)

Log of Outpatient visits

0.1852** (0.0140)

0.1781** (0.0139)

0.1827** (0.0141)

0.1835** (0.0140)

Log of Average length of stay

0.4189** (0.0392)

0.4236** (0.0395)

0.4148** (0.0394)

0.4124** (0.0396)

Log of number of beds

0.0802** (0.0177)

0.0838** (0.0176)

0.0764** (0.0175)

0.0774** (0.0175)

Inpatient case-mix index

0.4277** (0.0426)

0.3975** (0.0420)

0.4207** (0.0417)

0.4154** (0.0417)

Outpatient case-mix index

0.6274** (0.1676)

0.6099** (0.1593)

0.6141** (0.1640)

0.6211** (0.1641)

Herfindahl index (HHI)

−0.0026 (0.0203)

−0.0001 (0.0202)

−0.0004 (0.0202)

−0.0005 (0.0201)

For-profit hospital indicator

−0.2105** (0.0321)

−0.2000** (0.0321)

−0.2086** (0.0319)

−0.2111** (0.0319)

Nonprofit hospital indicator

−0.1102** (0.0286)

−0.1032** (0.0287)

−0.1091** (0.0284)

−0.1123** (0.0283)

System member indicator

0.0226 (0.0145)

0.0191 (0.0145)

0.0220 (0.0144)

0.0223 (0.0143)

Teaching hospital indicator

0.1467** (0.0264)

0.1324** (0.0258)

0.1186** (0.0262)

0.1191** (0.0259)

High technology service index

0.0291** (0.0059)

0.0288 ** (0.0058)

0.0263** (0.0058)

0.0255** (0.0057)

RN % nurse workforce

0.5425** (0.0870)

0.5302** (0.0806)

0.5396** (0.0855)

0.5402** (0.0852)

Risk-adjusted rate of postoperative hemorrhage or hematoma

6.1527** (2.2005)

Risk-adjusted rate of pulmonary embolism or deep-vein thrombosis

2.3554* (1.0229)

Risk-adjusted rate of accidental puncture or laceration

7.6198** (2.2276)

Risk-adjusted rate of obstetric trauma: vaginal delivery with instrument

0.1458** (0.0476)

Risk-adjusted number of adverse events

0.1490* (0.0695)

Raw number of adverse events

0.1450* (0.0637)

aModels included state fixed effects

*p < 0.05, **p < 0.01

Of the models that incorporated PSIs, a preliminary regression (not shown) entered all 15 PSI risk-adjusted events rates. Of the 15, only five were positively associated with cost and statistically significant at a level of 5% or better: PSI 09 (post-operative hematoma), PSI12 (post-operative pulmonary embolism or deep vein thrombosis), PSI15 (accidental puncture or laceration), PSI 18 (obstetric trauma in vaginal delivery with instrument), and PSI 19 (obstetric trauma in vaginal delivery without instrument).3 A second preliminary regression included the five risk-adjusted rates that were significant in the initial preliminary regression. Model 2 in Table 4 selectively includes the four PSIs that were significant in both preliminary regressions. Each of the four PSIs is positively related to cost and significant at the 5% level of significance (PSI12) or the 1% level (PSI09, PSI15, and PSI18). Models 3 and 4 enter the PSIs using the number of risk-adjusted events and the raw number of events summed across the 15 PSIs, respectively. The coefficients are the same to two decimal places and are significant at p = 0.0320 in the former case and at p = 0.0229 in the latter case.4

We next addressed the potential for endogeneity bias that might be occurring if the PSI variables are determined within the system, or correlated with the unobservables contained in the error term. To address this issue, we applied the Hausman test [22, 34] for endogeneity. This involved a first-stage regression in which the PSI variables were regressed on the remaining variables in the model. In a second stage, we regressed log costs on the predicted variable and the residual from the first stage. The test is equivalent to a standard test of significance on the latter explanatory variable in the second stage. We were unable to detect a significant relationship for any of the representations of the PSIs in our models. From these results, we accepted the null hypothesis of no endogeneity arising from the PSIs.

In order to estimate the performance of the PSIs in the cost function, we explore two avenues. First, we ask what can be learned from the magnitudes of the coefficients on the PSI variables. Do the coefficients on the PSIs indicate increases in cost that are consistent with results of patient level analyses of the excess cost of these adverse events? To answer this question, we calculate the marginal costs of adverse events, as useful approximations of excess costs as indicated by the cost function estimates. For the function expressed in Eq. 1, the marginal cost of an adverse event has the form:
$$ M{C_{{PSI}}} = \frac{{\partial {C_{{it}}}}}{{\partial PSI}} = \frac{{\partial \ln {C_{{it}}}}}{{\partial PSI}}*{C_{{it}}} = \zeta *{\hat{C}_{{it}}} $$
where ζ is the estimated coefficient on the PSI variable in question. Table 5 shows the mean values of the marginal cost of an adverse event according to the different specifications of the PSIs in Models 2–4, averaged across observations. As seen, the coefficients on the risk-adjusted event rates yield marginal costs of an additional event ranging from $22,489 for PSI18 (obstetric trauma—vaginal delivery with instrument) to $1.175 million for PSI15 (accidental puncture or laceration). In contrast, the marginal cost of a risk-adjusted event indicated by any of the PSIs (as calculated from summed values of events) is $23,022. The marginal cost of unadjusted event indicated by any of the PSIs is $22,413. As a comparator to these estimates, we refer to the literature on excess charges associated with PSIs [45]. Column 4 lists the estimates for each of the four event rates of interest, and of the weighted average of the 15 summed patient safety events of interest, using the estimated excess cost measures of Zhan and Miller [45] applied to the number of raw events in our data, and expressed in 2007 dollars. The risk-adjusted event rates clearly generate implausibly high estimates of marginal cost. In contrast, the raw number of events summed across PSIs generates an average marginal cost of an adverse event of $19,927, a figure that is in the general range of our measure of marginal costs.
Table 5

Mean values of marginal and excess cost estimates


PSI measure

Marginal cost: PSI ($)

Excess cost: PSIa ($)

Marginal cost: discharge ($)

Model 1 (benchmark)



Model 2 (risk-adjusted event rates)













OB trauma w/instrument




Model 3

Raw # of events summed across 15 PSIs




Model 4

Risk-adjusted # of events summed across 15 PSIs



aBased on patient level estimated excess charges attributable to medical injuries measured by PSIs [45]

Second, we explore how coefficients on other key variables differ across models, and examine the impact of omitting the PSIs. We consider these differences by following previous research and observing measures of the marginal cost of a discharge with and without the PSI measures [10]. If the main inpatient output variable is capturing variation due to excess cost of adverse events, we would expect to find lower values of marginal cost in models that included PSI measures. For the functional form in (1), the marginal cost of a discharge is equal to:
$$ M{C_{{DIS}}} = \frac{{\partial {C_{{it}}}}}{{\partial DI{S_{{it}}}}} = \frac{{\partial \ln {C_{{it}}}}}{{\partial \ln DI{S_{{it}}}}}*\frac{{{C_{{it}}}}}{{DI{S_{{it}}}}} = \beta *\frac{{{{\hat{C}}_{{it}}}}}{{DI{S_{{it}}}}} $$
where β is the coefficient on the natural log of discharges.5 Table 5 displays the mean values of the marginal cost of a discharge averaged over observations, for each of Models 1–4. In Model 2, the marginal cost is slightly higher than in benchmark Model 1. In Models 3 and 4, the marginal cost is approximately 2.4% lower than in the benchmark model, consistent with expectations if the PSI variable is capturing the cost due to adverse events.

Finally, we note that the magnitude of the coefficients on teaching, high technology, and nurse staffing all fall to some degree in the models in which the PSIs are introduced. This result is contrary to our theoretical expectations in which higher levels of cost-increasing quality variables would reduce the probability of adverse event occurrence. We attribute this result to positive correlation in our data between the cost-increasing quality variables and the PSIs. A more dynamic modeling structure might reveal higher marginal effects associated with cost increasing quality measures in models that include PSIs than in models that do not, reflecting reduction in adverse events over time due to quality improvement efforts related to increases in nurse staffing and/or high technology services.

5 Discussion

This paper has focused on the relationship between hospital quality and cost by exploring the use of PSIs as quality measures in the context of the microeconomic construct of the hospital cost function. In all three cost function models that we estimated, PSIs were positively associated with cost. Apart from the direction and statistical significance of their association, however, the measures that relied on risk-adjusted rates of individual PSIs did not produce authentic values of excess cost due to specific adverse events. We attribute this to the small number of events for most PSIs. Moreover, we observed an association for just 4 of the 15 PSIs that we examined, so that only a fraction of the information contained in the full set of PSIs was usefully incorporated into our model. However, in models in which we summed events across the 15 PSIs, results suggested excess costs that were not generally divergent form those of a previous patient level study. Comparison with results of a benchmark model also pointed to the summed PSI event measures as superior to the individual risk-adjusted event rates in capturing cost variation due to adverse events.

We consider that all of our PSI models are an improvement over models that rely on outcomes measures of quality based on mortality and readmission rates. The relationship between preventable adverse events and quality is considerably more immediate than that of mortality or readmission, for which the variability is highly influenced by patient characteristics known to influence risk, and which have a higher random component. An improved hospital cost function model will enhance the capability of stochastic frontier cost function analyses in identifying efficiency variation among hospitals, and will also provide a better means of studying many other important issues related to hospital cost growth such as effects of competition, organizational change, productive efficiency, and service specialization.

There are limitations to our analysis. This is an observational study, and we acknowledge that no method can completely identify causality from observational data. Absent a randomized controlled experiment, examination of the effect of variables of interest on outcome variables is subject to parameter estimate bias to the extent of correlation between measured variables of interest and omitted variables that are significantly associated with the outcomes variables. It is possible, for example, that unmeasured severity that contributes to cost may also render some patients more vulnerable to PSIs than others.

While availability of the PSIs opens new opportunities for measuring hospital quality, identification of adverse events from administrative data has inherent imperfections, and the literature recognizes a moderate albeit unavoidable trade-off between the expediency in constructing the PSIs and their reliability in screening [26]. We acknowledge that our measures are at best proxy measures of quality, limiting their capacity to generate predictions based on statistical analyses. Moreover, many of the PSIs have frequencies that are so small that entering their risk adjusted rates into a hospital cost function turns up insignificant results. Nonetheless, the PSIs are well-established as the best approach to identifying adverse events from readily available data, and the results of our study are valuable in demonstrating the use of PSIs as a quality measure in the hospital cost function, and are also informative in demonstrating the potential for returns to investment in hospital quality improvement.

Finally, this paper contributes, from a unique perspective, to the growing business case for patient safety. Hospital quality improvement is a vexing and immediate concern in current health policy, complicated by high recent high cost growth in hospital services. In an environment of economic constraints, the potential trade-offs between cost savings and quality improvements become increasingly important, as value in health care delivery is a goal that must be pursued. While the objective of patient safety is to prevent harm to patients, it is vitally important that resources are utilized as efficiently as possible if the maximum safety benefits are to be realized.


Following Bazzoli et al. [3], the five high technology services are transplant, open heart surgery, certified trauma center, positron emission tomography, and extracorporeal shock-wave lithrotriper.


Data contained in the AHRQ State Inpatient Databases is applied to the observed rates in the risk-adjustment process.


Application of the Belsley Kuh Welsch statistics [4] indicated that multicollinearity among the PSIs was not causing instability among their coefficients.


Results of a fifth model (not shown) that entered unadjusted event rates produced results similar to those of Model 2.


We used smearing estimators [14] for retransformation from the log scale to the raw scale in Eqs. 2 and 3, by multiplying predicted values by the mean of exponentiated residuals.


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© Springer Science+Business Media, LLC (outside the USA) 2010