Hospital Quality, Efficiency, and Input Slack Differentials (Text Version)

Slide Presentation from the AHRQ 2008 Annual Conference

On September 9, 2008, Vivian Valdmanis, Ph.D., Michael Rosko, Ph.D., and Ryan Mutter, Ph.D., made this presentation at the 2008 Annual Conference. Select to access the PowerPoint® presentation (1.4 MB).

Slide 1

Hospital Quality, Efficiency, and Input Slack Differentials

• Vivian Valdmanis, Ph.D.
  University of the Sciences in Philadelphia
  Philadelphia, PA
• Michael Rosko, Ph.D.
  Widener University
  School of Business Administration
  Chester, PA
• Ryan Mutter, Ph.D.
  Agency for Healthcare Research and Quality
  Rockville, MD
• AHRQ Annual Meeting
  September 10, 2008

Slide 2

Research Impetus

• Health care reform continues to dominate at least part of the political debate on how best to eliminate the economic hardships astronomical health care costs impose on more and more Americans.
• Most research and practical-based studies focus on the cost-quality-access nexus, often arguing that there are tradeoffs among these three objectives.
• However, it can be argued that quality and efficiency may be directly related, especially when considering the relatively higher social costs associated with in-hospital patient safety events.

Slide 3

Objective

• To use advances in data envelopment analysis (DEA) to assess the tradeoffs between quality and efficiency, including input slack values, in U.S. hospitals

Slide 4

Strengths of DEA

• DEA easily accommodates multiple inputs and multiple outputs.
• DEA doesn't impose a particular functional form relating inputs to outputs.
• DEA directly compares an observation against one or more actual peers.
• DEA allows inputs and outputs to be measured in very different units.

Slide 5

Weaknesses of DEA

• DEA is an extreme point technique, so "noise" (even symmetrical noise with zero mean) can cause significant problems.
• DEA is good at estimating "relative" efficiency but does not measure "absolute" efficiency.
• DEA is a nonparametric technique so statistical hypothesis tests are difficult to carry out.
• DEA requires that a separate linear program be solved for observation, which can be computationally intensive.

Slide 6

DEA illustrated

The graph has a vertical axis of x2 and a horizontal axis of x1. The graph for L(u) is plotted.

Slide 7

DEA illustrated

The graph has a vertical axis of u2 and a horizontal axis of u1. The graph for P(u) is plotted.

Slide 8

DEA illustrated

The graph has a vertical axis of x2 and a horizontal axis of x1. The graph for u(j) is plotted with an intersection for x(j).

Slide 9

Graph

The graph has a vertical axis of x and a horizontal axis of u. The graph for CRS is plotted, indicating points A, B, and C.

Slide 10

Graph

The graph has a vertical axis of x and a horizontal axis of u. The graph for CRS and NIRS is plotted, indicating points A, A*, B, and C.

Slide 11

Graph

The graph has a vertical axis of x and a horizontal axis of u. The graph for CRS, L(u,xIN,S), and L(u,xIC,S) is plotted, indicating points A, B, C.

Slide 12

Weak Disposability of Inputs

The graph has a vertical axis of x2 and a horizontal axis of x1.The graph for the degree of congestion in input x2 is plotted.

Slide 13

Corner Solution

The graph has a vertical axis of x2 and a horizontal axis of x1. The graph for the Corner Solution is plotted in relation to L(u).

Slide 14

Allocative Inefficiency

The graph has a vertical axis of x2 and a horizontal axis of x1. The graph for the isoquant and isocost line is plotted.

Slide 15

Output Efficiency

The graph has a vertical axis of u2 and a horizontal axis of u1. The graph for OE = 0A*/0A > 1 is plotted.

Slide 16

Output Congestion

The graph has a vertical axis of u2 and a horizontal axis of u1. The graph for output congestion is plotted.

Slide 17

Input Based Malmquist

The graph has a vertical axis of u and a horizontal axis of x. Graph + and Graph t are plotted.

Slide 18

Output Based Malmquist

The graph has a vertical axis of u and a horizontal axis of x. Graph + and Graph t are plotted.

Slide 19

Graph

The graph has a vertical axis of u and a horizontal axis of x. ZAP and LVIV are plotted.

Slide 20

Subvectors (Inputs)

The graph has a vertical axis of x2 and a horizontal axis of x1.

Slide 21

Subvectors (Output)

The graph has a vertical axis of u2 and a horizontal axis of u1.

Slide 22

The Concept of a Frontier

The graph has a vertical axis of output and a horizontal axis of input. Infeasible, just feasible: efficient, and feasible...but inefficient are plotted.

Slide 23

Choice of Technology

The graph has a vertical axis of output and a horizontal axis of input. CRS and VRS are plotted.

Slide 24

Choice of Orientation

The graph has a vertical axis of output and a horizontal axis of input. CRS, output orientation, and input orientation are plotted.

Slide 25

Input Orientation

The graph has a vertical axis of input 2 (e.g. labor) and a horizontal axis of input 1 (e.g. capital).E (as a convex combination of B and C) is plotted.

Slide 26

Help on the Web

• Ali Emrouznejad's DEAZone:
  • www.DEAzone.com
• Tim Anderson's DEA Homepage:
  • http://www.emp.pdx.edu/dea/homedea.html

Slide 27

Software

• Any software with LP capability:
  • SAS
  • GAMS
  • LINDO
• Commercial Software:
  • Banxia's Frontier Analyst
  • EMQ's OnFront
  • Thanassoulis' PIMSoft/DEASoft
• Free Software:
  • Coelli's DEAP
  • Scheel's EMS
  • Wilson's FEAR
  • Coming: Morgunov and Zelenyuk's "Just DEA It!"

Slide 28

Data Sources

• American Hospital Association (AHA) Annual Survey of Hospitals
• Medicare Hospital Cost Reports (for number of patient days in non-acute care units)
• AHRQ (for measures of patient safety and hospital competition)
• Solucient, Inc. (for data on county level HMO enrollment and number of residents without healthcare insurance)

Slide 29

Analytical File

• Hospitals included in this study are those defined by the AHA as short term, community hospitals that report complete data.
• Since quality variables from the application of the Patient Safety Indicator (PSI) module of the AHRQ Quality Indicator (QI) software to the Healthcare Cost and Utilization Project (HCUP) State Inpatient Databases (SID) were important in this analysis, this study was restricted to 34 states supplying HCUP data. 
• This yielded an analytical file of 1,377 urban hospitals in 2004.

Slide 30

Undesirable Events

• The following risk-adjusted PSIs that Savitz, Jones, and Bernard (2005) indicate are sensitive to nurse staffing:
  • Failure to rescue
  • Infection due to medical care
  • Postoperative respiratory failure
  • Postoperative sepsis

Slide 31

Model

• We employ DEA techniques to ascertain the necessary increases in inputs needed to reduce poor hospital outcomes.
• To this end we use a two-step process.
• First, we measure technical efficiency of our sample hospitals based on the works by Debreu and Farrell and updated in terms of economic efficiency by Färe, Grosskopf, and Lovell.
• We opted for DEA due to the flexibility of this approach, which is particularly suited to study hospital productive performance.

Slide 32

Model (continued)

• One of the benefits of DEA is that we can measure some outputs as weakly disposable. In our case, we use the nurse-sensitive measures of quality.
• We surmise that as hospitals increase the production of patient care, if they do not maintain quality of care, these poor outcomes may also increase, hence the weak disposability.

Slide 33

Model (continued)

• Using the Färe, Grosskopf, and Lovell approach, we measured "congestion," which reflects how much total productivity is reduced by the presence of these bad hospital outcomes, or in other words, an increase in social costs.

Slide 34

Formal Definitions

• Below we present the formal definitions of our technologies:

Slide 35

Adjusting Outputs

• Once we derived the congestion score, we "discounted" the outputs by that score. This was accomplished by dividing the outputs by the congestion measure, since an increase in outputs may lead to an increased probability of producing the attendant undesirable bads.

Slide 36

Relationship between Desirable (y2) and Undesirable Outputs (y1)

The graph has a vertical axis of desirable output and a horizontal axis of undesirable output.

Slide 37

Slack Differential

• Once we have the adjusted outputs, we re-run the DEA linear programs, but this time we are interested in the additive slack values ala Cooper, Seiford, and Zhu (2000).
• Unlike the multiplicative congestion measure, which inhibits the production of all goods, slack does not impede total production, but may either represent a quality input or excessive inputs that lead to inefficiency.

Slide 38

What these differences mean

• If the difference between slacks is positive, it would suggest that the hospital is employing excess input that leads to inefficiency.
• If the difference is negative, it implies that inputs need to be increased to improve quality of care. In fact, the difference indicates the amount of inputs that need to be increased.

Slide 39

The slide shows a sample document presenting a table containing "Means" and "SD" results for various "Variables."

Slide 40

Descriptive Statistics of Efficiency Scores

• If the efficiency score equals 1, the hospital is deemed efficient. Any score greater than 1 indicators inferior performance.
• If congestion is greater 1, then output congestion exists and bad outcomes impede optimal production of hospital care outputs.
• Note: A portion of a table presenting "Mean," "SD," "Minimum," and "Maximum" results for various "Scores" is shown.

Slide 41

Mean Efficiency Score Values

The slide shows a table presenting "CRS Efficiency," "VRS Efficiency," "Scale Efficiency," and "Congestion" results for various "Characteristics."

Slide 42

Quality-Based Results

The slide shows a table presenting "High Quality," "Medium Quality," and "Low Quality" results for various measures.

Slide 43

Summary and Conclusions

• From our results, we find certain hospital characteristics are associated with inefficiency and congestion, which we use to model quality of care:
  • For-profit hospitals exhibited the least amount of inefficiency vis-à-vis their public counterparts
  • A majority of hospitals in our sample were operating at diseconomies of scale
  • Teaching hospitals and members of systems also performed better relative to their counterparts
  • Input slack demonstrated that public hospitals tended to have too many full-time-equivalent physicians (FTE) other personnel and acute care beds.

Slide 44

Summary and Conclusions (continued)

• There is an association between high quality hospitals and higher total expenditures and the use of high-tech services.
• Higher quality hospitals had relatively less labor per bed than hospitals with medium quality.
• An interesting finding from our analysis is that there appears to be a need for more Licensed Practical Nurses (LPNs) in hospitals producing poor outcomes.
• The policy implication includes more evidence that costs and quality do not necessarily need to be traded off, but rather both these objectives can be met with the resources at hand.

Slide 45

Contributions

• In this paper, we add to the existing literature on hospital care and congestion by examining nurse sensitive measures of quality, adding to the Clement et al. paper that used excess mortality.
• We look at hospital outcomes that could be confounded by congestion, similar to the Ferrier et al. study that assessed economic outcomes.
• We add to the overall congestion literature by using both the Färe et al. and Cooper et al. approach for deriving first congestion, then slack.