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Using Stochastic Frontier Analysis to Measure Hospital Inefficiency (Text Version)

Slide presentation from the AHRQ 2009 conference.

On September 14, 2009, Ryan Mutter, Ph.D. and Michael Rosko Ph.D. made this presentation at the 2009 Annual Conference. Select to access the PowerPoint® presentation (754 KB).

Slide 1

AHRQ: Agency for Healthcare Research and Quality
Advancing Excellence in Health Care

Using Stochastic Frontier Analysis to Measure Hospital Inefficiency

Ryan Mutter, Ph.D.
Agency for Healthcare Research and Quality
Rockville, MD

Michael Rosko, Ph.D.
School of Business Administration
Widener University
Chester, PA

September 14, 2009


Slide 2

Inefficiency Estimation

  • Recent interest in estimating inefficiency arises out of concerns about excessive expenditures in health care.
  • Inefficiency measurement also adds perspective to quality measurement and highlights trade-offs in quality improvement.
    • Quality improvement can increase costs by reducing overuse and expensive medical errors.
    • But quality improvement can also result in higher levels of resource use and higher costs.
  • There are many potential applications for accurate provider-level estimates of inefficiency (e.g., organizational improvement, public reporting).


Slide 3

Approaches to Inefficiency Estimation


Slide 4

Stochastic Frontier Analysis (SFA)

  • Econometric technique
    • Generates provider-level (i.e., hospital-level) estimates of inefficiency
    • Inefficiency estimates are measured as departures from a statistically derived, theoretical best-practice frontier that takes input prices, outputs, product mix, quality, case mix, and market forces into account


Slide 5

SFA (continued)


Slide 6

SFA (continued)

  • Measures cost inefficiency (i.e., the percentage by which observed costs exceed minimum costs predicted for a given level of outputs, input prices, etc.)
  • Particularly useful for determining the relative performance of hospitals
    • Hospital A is among the top 40 percent most efficient hospitals in its peer group.
  • Folland and Hofler (2001) demonstrate its usefulness for comparing the efficiency of groups of hospitals


Slide 7

SFA (continued)

  • Specified generally as TCi = f(Yi, Wi) + ei where TC represents total costs; Y is a vector of outputs; W is a vector of input prices; and e is the error term, which can be decomposed as follows ei = vi + ui where v is statistical noise ~ N(0, σ2) and u


Slide 8

SFA (continued)

  • Byproduct of the analysis is information about hospital-level variables on cost and environmental pressure variables on inefficiency


Slide 9

Data Sources

  • American Hospital Association (AHA) Annual Survey of Hospitals
  • Medicare Cost Reports
  • AHRQ Healthcare Cost and Utilization Project (HCUP)


Slide 10


  • Input prices
    • Price of labor
    • Price of capital
  • Outputs
    • Admissions
    • Outpatient visits
    • Post-admission inpatient days
  • Teaching status
    • Binary variables for member of Council of Teaching Hospitals (COTH) and non-COTH hospital with at least one full-time equivalent (FTE) medical resident
  • Time trend


Slide 11

Variables (continued)

  • A key challenge in applying SFA to health care settings is controlling for heterogeneity.


Slide 12

Variables (continued)

  • Product mix
    • Acute care beds / total beds
    • Births / total admissions
    • ED visits / total outpatient visits
    • Outpatient surgical operations / total outpatient visits
  • Outcome measures of quality
  • Patient mix
    • Medicare Case Mix Index
    • Comorbidity variables


Slide 13

Variables (continued)

  • HCUP
    • A family of health care databases and related software tools and products developed through a Federal-State-Industry partnership and sponsored by AHRQ.
    • Includes State Inpatient Databases (SID), which contain the universe of inpatient discharge abstracts from participating states.
  • Data from 24 states available to the public through the HCUP Central Distributor
  • Patient mix


Slide 14

Variables (continued)

  • The AHRQ Quality Indicators (QIs) are measures of health care quality that make use of readily available hospital inpatient administrative data, such as HCUP.
  • Free software tools available online.
  • Includes
    • Inpatient Quality Indicators (IQIs), which reflect quality of care inside hospitals including inpatient mortality for medical conditions and surgical procedures.
    • Patient Safety Indicators (PSIs), which reflect quality of care inside hospitals, but focus on potentially avoidable complications and iatrogenic events.


Slide 15

Variables (continued)

  • Quality measured by the application of the QI software to HCUP data.
  • Analysis includes the following, risk-adjusted, in-hospital rates:
    • Mortality for the following conditions
      • Acute myocardial infarction (AMI), congestive heart failure (CHF), stroke, gastrointestinal hemorrhage, pneumonia
    • Failure to rescue
    • Latrogenic pneumothorax
    • Infection due to medical care
    • Accidental puncture / laceration


Slide 16

Variables (continued)

  • The Comorbidity Software assigns variables that identify comorbidities in hospital discharge records using the diagnosis coding of ICD-9-CM.
  • Available for free online.


Slide 17

Variables (continued)

  • Patient burden of illness controlled by the inclusion of hospital-level rates per discharge of the following comorbidities identified by the Comorbidity Software:
    • Congestive heart failure
    • Pulmonary circulation disorders
    • Paralysis
    • Diabetes, uncomplicated
    • Renal failure
    • AIDS
    • Solid tumor without metastasis
    • Obesity
    • Blood loss anemia
    • Drug abuse
    • Cardiac arrhythmias
    • Peripheral vascular disorders
    • Other neurological disorders
    • Diabetes, complicated
    • Liver disease
    • Lymphoma
    • Rheumatoid arthritis
    • Weight loss
    • Deficiency anemias
    • Psychoses
    • Valvular disease
    • Hypertension
    • Chronic pulmonary disease
    • Hypothyroidism
    • Peptic ulcer
    • Metastatic ulcer
    • Coagulopathy
    • Fluid and electrolyte disorders
    • Alcohol abuse
    • Depression


Slide 18

Variables (continued)

  • Inefficiency effects variables
    • Ownership
    • Medicare share of discharges
    • Medicaid share of discharges
    • Medicare HMO penetration rate
    • Hospital competition
    • Time trend
  • See Rosko (2001)


Slide 19

SFA in the NHQR

  • SFA is used to provide trends in hospital efficiency.
    • This is a measure from the provider perspective.
  • The measure first appeared in the 2007 NHQR, the first year there was an efficiency chapter.
  • SFA became an endorsed measure in 2009.


Slide 20

Last Year's Analysis

  • Based on 1,368 urban, general, community hospitals from 26 states providing SID data
    • Represent 53% of all urban, general community hospitals
  • 2001 – 2005
  • Follow estimation approach recommended by Rosko and Mutter (2008)


Slide 21

Last Year's Analysis (continued)

  • Cost efficiency estimates converted to index numbers with a base of 100 for the year 2001
    • Places less emphasis on the specific magnitude of estimated cost efficiency


Slide 22

Last Year's Analysis (continued)


Slide 23

Last Year's Analysis (continued)

  • Ratios
    • Managers have relied on ratios that convey straightforward information.
    • Comparing SFA estimates with these ratios yields valuable insights into organizational performance.


Slide 24

Last Year's Analysis (continued)

  • Measure
    • Cost per case-mix-adjusted admission:
      • Top quartile of hospital cost efficiency.......... Estimate: $4,340 / Std. Dev.: $1,087
      • Bottom quartile of hospital cost efficiency.......... Estimate: $6,241 / Std. Dev.: $2,350
    • Full-time equivalent employees per case-mix-adjusted admission:
      • Top quartile of hospital cost efficiency.......... Estimate: .040 / Std. Dev : 0.01
      • Bottom quartile of hospital cost efficiency.......... Estimate: .055 / Std. Dev : 0.02
    • Average length of stay (days):
      • Top quartile of hospital cost efficiency.......... Estimate: 4.88 / Std. Dev : 1.33
      • Bottom quartile of hospital cost efficiency.......... Estimate: 5.22 / Std. Dev : 1.80
    • Operating margin:
      • Top quartile of hospital cost efficiency.......... Estimate: .033 / Std. Dev : 0.13
      • Bottom quartile of hospital cost efficiency.......... Estimate: -.066 / Std. Dev : 0.17


Slide 25

Last Year's Analysis (continued)

  • Some findings from the parameter estimates:
    • COTH hospitals are about 12 percent more expensive than non-teaching hospitals; minor teaching hospitals are nearly 4 percent more expensive.
    • Coefficients on infection due to medical care and accidental puncture / laceration were positive and significant.
      • Occurrences of these patient safety events are costly to hospitals.
      • Zhan and Miller (2003) estimate they are associated with excess costs of $38,656 and $8,271, respectively.


Slide 26

Last Year's Analysis (continued)

  • Further findings from the parameter estimates:
    • For-profit ownership, greater hospital competition, greater Medicare HMO penetration, and a higher share of Medicare discharges associated with increased cost-efficiency
    • Government ownership associated with reduced cost-efficiency


Slide 27

Looking ahead

  • SFA estimates will appear in the 2009 NHQR.


Slide 28


  • Copies of Rosko and Mutter (2008) and Mutter et al. (2008) are available in the back of the room.
  • Further information on HCUP data, the Quality Indicator Software, and the Comorbidity Software are available at the HCUP and QI booths.
Current as of December 2009
Internet Citation: Using Stochastic Frontier Analysis to Measure Hospital Inefficiency (Text Version). December 2009. Agency for Healthcare Research and Quality, Rockville, MD.


The information on this page is archived and provided for reference purposes only.


AHRQ Advancing Excellence in Health Care