1. Chapter 9.
Productivity
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

2. Outline Trends in Healthcare Productivity: Consequences of PPS
Productivity Definitions and Measurements
Productivity Benchmarking
Multifactor Productivity
Commonly Used Productivity Ratios
Hours per Patient Day or Visit
Adjustment for Inputs
Skill-Mix Adjustment to Worked Hours
Cost of Labor
Adjustments for Output Measures
Service/Case-Mix Adjustments
Productivity Measures Using Direct Care Hours
Productivity – Quality Relationship
Productivity Dilemmas
Multiple Dimensions of Productivity: New Methods
Data Envelopment Analysis (DEA)
Productivity Improvement
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

3. Trends in Productivity: Consequences of PPS
The recent decades’ changes in reimbursement strategies aimed to end waste and promote innovative and cost-efficient delivery systems.
productivity gains from PPS have not materialized to the extent predicted.
Hospitals now employ more people to treat fewer patients, and the increase is not accounted for by the greater severity of patient illness in the late 1980s and in1990s.
Although employers, insurers and public are spending less on inpatient care, the rising use of outpatient procedures has simply increased costs in that area which counters the savings (Altman, Goldberger, and Crane, 1990).
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

4. Trends in Productivity: Consequences of PPS
The constraints that force healthcare institutions into the role of cost centers, coupled with shifting patterns of inpatient acuity, tight healthcare labor markets, and society's expectations of high quality of care are leading healthcare organizations to a "productivity wall." When the wall is reached, it is quality of care that inevitably is sacrificed for the sake of productivity and profit (Kirk, 1990).
It must be recognized that there are limits to ratcheting up productivity.
It is not always possible to do more with less.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

5. Productivity Definitions and Measurements
Productivity is one measure of the effective use of resources within an organization, industry, or nation.
The classical productivity definition measures outputs relative to the inputs needed to produce them. That is, productivity is defined as the number of output units per unit of input
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

6. Productivity Definitions and Measurements
Sometimes, an inverse calculation is used that measures inputs per unit of output. Care must be taken to interpret this inverse calculation appropriately; the greater the number of units of input per unit of output, the lower the productivity.
For example, traditionally productivity in hospital nursing units has been measured by hours per patient day (HPPD). That requires an inversion of the typical calculations: meaning total hours are divided by total patient days.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

7. Example 9.1
Nurses in Unit A worked collectively a total of 25 hours to treat a patient who stayed 5 days, and nurses in Unit B worked a total of 16 hours to treat a patient who stayed 4 days. Calculate which of the two similar hospital nursing units is more productive.
Solution:
First, define the inputs and the outputs for the analysis. Is the proper measure of inputs the number of nurses or of hours worked? In this case the definition of the input would be total nursing hours. When the total number of nursing hours worked per nurse is used as the input measure, then the productivity measures for the two units are:
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

8. Productivity Definitions and Measurements
Productivity Benchmarking. Productivity must be considered as a relative measure; the calculated ratio should be either compared to a similar unit, or compared to the productivity ratio of the same unit in previous years. Such comparisons characterize benchmarking. Many organizations use benchmarking to help set the direction for change.
Historical Benchmarking is monitoring an operational units’ own productivity or performance over the last few years. Another way of benchmarking is to identify the best practices (best productivity ratios of similar units) across health organizations and incorporate them in one’s own.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

9. Productivity Definitions and Measurements
Multifactor Productivity. Example 9.1 demonstrated a measure of labor productivity. Because it looks at only one input, nursing hours, it is example of a partial productivity measure. Looking only at labor productivity may not yield an accurate picture.
Newer productivity measures tend to include not only
labor inputs, but the other operating costs for the product
or service as well.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

10. Example 9.2
A specialty laboratory performs lab tests for the area hospitals. During its first two years of operation the following measurements were gathered:
Measurement Year Year 2
Price per test ($)
Annual tests 10, ,700
Total labor costs($) 150, ,000
Material costs ($) 8, ,400
Overhead ($) 12, ,200
Determine and compare the multifactor productivity for historical benchmarking. .
Solution:
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

11. Commonly Used Productivity Ratios
Hours Per Patient Day (or Visit)
inpatient
outpatient
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

12. Commonly Used Productivity Ratios
Example 9.3:
Annual statistical data for two nursing units in Memorial Hospital are as follows:
Measurements Unit A Unit B
Annual Patient Days 14, ,000
Annual Hours Worked 210, ,000
Calculate and compare hours per patient day for two units of this hospital.
Solution:
hours
hours
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

13. Commonly Used Productivity Ratios
Example 9.4:
Performsbetter Associates – a two-site group practice, requires productivity monitoring. The following initial data are provided for both sites of the practice:
Measurements Suburban Downtown
Annual Visits 135, ,000
Annual Paid Hours 115, ,000
Calculate and compare the hours per patient visit for the suburban and the downtown locations of this practice.
Solution:
hours or 51 minutes.
hours or 69 minutes.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

14. Adjustments for Inputs
Skill-Mix Adjustment weigh the hours of personnel of different skill levels by their economic valuation.
One approach is to calculate weights based on the average wage or salary of each skill class. To do that, a given skill class wage/salary would be divided into the top class skill salary.
If RNs, LPNs and Aides are earning $35.00, $28.00, and $17.50 an hour, respectively;
Then, one hour of a nurse aide’s time is economically equivalent to 0.5 hours of a RN's time; and one hour of a LPN's time is equal to 0.8 hours of a RN's time. .
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

15. Adjustments for Inputs
Adjusted Hours = 1.0*(RN hours) + 0.8*(LPN hours) + 0.5*(Aide hours)
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

16. Adjustments for Inputs
Adjusted Hours = 1.0*(RN hours) + 0.8*(LPN hours) + 0.5*(Aide hours)
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

17. Adjustments for Inputs
Similarly, in outpatient settings, if one hour of a nurse practitioner's (NP) time is economically equivalent to 0.6 hours of a specialist's (SP) time, and if one hour of a general practitioner’s (GP) time is equal to 0.85 hours of a specialist’s time, adjusted hours would be calculated as: .
Adjusted Hours = 1.0 (SP hours) (GP hours) (NP hours)
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

18. Adjustments for Inputs
Example 9.5: Using data from Example 9.3, and economic equivalencies of 0.5 Aide = RN, 0.8 LPN = RN, calculate the adjusted hours per patient day for Unit A and Unit B.
Unit A at Memorial Hospital employs 100% RNs.
The current skill mix distribution of Unit B is 45% RNs, 30% LPNs, and 25% nursing aides (NAs).
Compare unadjusted and adjusted productivity scores.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

19. Adjustments for Inputs
Solution:
The first step is to calculate adjusted hours for each unit.
For Unit A, since it employs 100% RNs, there is no need for adjustment. For Unit B:
Adjusted Hours (Unit B) = 1.0 (180,000*.45) (180,000*.30) (180,000*.25).
Adjusted Hours (Unit B) = 1.0 (81,000) (54,000) (45,000).
Adjusted Hours (Unit B) = 146,700.
In this way, using the economic equivalencies of the skill-mix, the number of hours is standardized as 146,700 instead of 180,000.
Standardized Cost of Labor.
hours.
hours.
Using adjusted hours, Unit A, which appeared productive according
to the first measure (see example 9.3), no longer appears as productive.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

20. Adjustments for Inputs
Standardized Cost of Labor. Total labor cost comprises the payments to various professionals at varying skills. To account for differences in salary structure across hospitals or group practices, cost calculations can be standardized using a standard salary per hour for each of the skill levels .
Labor Cost = RN wages (RN hours) +
LPN wages (LPN hours) +
NA wages (Aide hours).
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

21. Adjustments for Inputs
Example 9.6:
Performsbetter Associates in Example 9.4 pays $110, $85, and $45 per hour, respectively, to its SPs, GPs and NPs in both locations.
Currently, the suburban location staff comprises of 50% SPs, 30% GPs, and 20% NPs.
The downtown location, on the other hand, comprises 30% SPs, 50% GPs, and 20% NPs.
Calculate and compare the labor cost of care, and labor cost per visit for both locations.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

22. Adjustments for Inputs
Solution:
First, calculate “Labor Cost of Care” for each location.
Labor Cost = SP wages (SP hours) + GP wages (GP hours) + NP wages (NP hours),
Labor CostSuburban = $110 (115,000*0.50) + $85 (115,000*0.30) + $45 (115,000*0.20).
Labor CostSuburban = $110 (57,500) + $85 (34,500) + $45 (23,000).
Labor CostSuburban = $10,292,500.
Labor CostDowntown = $110 (112,000*.30) + $85 (112,000*0.50) + $45 (112,000*0.20).
Labor CostDowntown = $110 (33,600) + $85 (56,000) + $45 (22,400).
Labor CostDowntown = $9,464,000.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

23. Adjustments for Outputs
Service-Mix Adjustments. Service-mix adjustment is useful tool for comparison of, for instance, two community hospitals that provide different services or have significantly different distributions of patients among their services. The service-mix adjusted volume is weighted by a normalized service-intensity factor. .
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

24. Adjustments for Outputs
Service-Mix Adjustments .
Example 9.7:
Two hospitals, each with unadjusted volume of 10,000 patient days per month, provide only two services, S1 and S2, requiring respectively 3 and 7 hours of nursing time per patient day.
Hospital A has a service-mix distribution of 2000 patient days for S1 and 8000 patient days for S2.
Hospital B has 8000 days for S1 and 2000 days for S2.
Calculate adjusted patient days for both hospitals.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

25. Adjustments for Outputs
Service-Mix Adjustments
Solution:
In this case, total unadjusted volume is simply the sum of the volume for each service
in each hospital, or Unadjusted Volume = X1 + X2.
Hospital-A
Hospital-B
Service S1 (3 hours/patient day)
X1=2000
X1=8000
Service S2 (7 hours/patient day)
X2=8000
X2=2000
Total Unadjusted Volume
10,000 .
Adjusted Volume = W1X1 + W2X2.
Adjusted volume for Hospital-A = 0.6*2, *8,000 = 12,400.
Adjusted volume for Hospital-B = 0.6*8, *2,000 = 7,600.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

26. Adjustments for Outputs
Case-Mix Adjustments. The methodology for case-mix adjustment is similar to that for service-mix adjustment. Although most hospitals rely on advanced acuity systems, each system is based on the weight factors for the different acuity categories.
Patients in each category require similar amounts of nursing care over a given 24 hour time period; however, across categories the care requirements differ significantly.
For acuity, the focus is on patients’ direct care requirements.
The ratio of the hours of direct care provided to the total hours worked is another measure of productivity.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

27. Adjustments for Outputs
Case-Mix Adjustments
Example 9.8:
Unit A and Unit B (from Example 9.3), a medical care unit in Memorial Hospital, classify patients into four acuity categories (Type I through Type IV), with direct care requirements per patient day being respectively, 0.5, 1.5, 4.5, and 6.0 hours.
Annual distributions of patients in these four acuity categories in Unit A were 0.15, 0.25, 0.35, and 0.25.
Annual distributions of patients in Unit B were 0.15, 0.30, 0.40, and 0.15.
Calculate the case mix for these two units, and determine which unit has been serving more severe patients.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

28. Adjustments for Outputs
Case-Mix Adjustments
Solution: . . . . . .
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

29. Adjustments for Outputs
Case-Mix Adjustments
Once the case-mix is determined, the output side of the productivity ratios can be adjusted by simply multiplying volume (patient days, discharges, visits) by case-mix index as:
Adjusted Patient Days = Patient Days * Case-mix index.
Adjusted Discharges = Discharges * Case-mix index.
Adjusted Visits = Visits * Case-mix index.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

30. Productivity Measures Using Direct Care Hours
Hours of Direct Care. “Hours of direct care” is an important component of productivity ratios. It serves as a building block for other ratios.
To illustrate its development, let us assume that patients are categorized into acuity groupings requiring H1, H2, H3, …., Hm hours of direct nursing care per patient day.
Further, assume that there are N1, N2, N3, .…, Nm annual patient days in units 1 through m.
The total amount of direct nursing care in nursing unit j would be calculated as:
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

31. Productivity Measures Using Direct Care Hours
Percentage of Hours in Direct Care. This is an additional measure can be derived from the “Hours of Direct Care” calculation, as the ratio of direct care hours to total care hours.
Percentage of Adjusted Hours in Direct Care. We also can determine the percentage of adjusted nursing hours as adjusted for skill-mix in direct patient care.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

32. Productivity Measures Using Direct Care Hours
Example 9.9:
Using information from Examples 9.3 and 9.8
calculate:
hours of direct care
percentage of hours in direct care, and
percentage of adjusted hours in direct care
for Units A and B of Memorial Hospital.
Compare these results in terms of percentage of
adjusted hours in direct care.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

33. Productivity Measures Using Direct Care Hours
Solution:
Memorial Hospital uses an acuity classification system with 4 categories of direct hours of care per patient day: 0.5, 1.5, 4.0, and 6.0 hours.
The annual distributions of patients in these four acuity categories in Unit A were 0.15, 0.25, 0.35, and 0.25.
The annual distributions of patients in Unit B were 0.15, 0.30, 0.40, and 0.15.
Annual patient days for Unit A were 14,000, and for unit B 10,000.
Annual hours worked were 115,000 and 112,000, respectively.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

34. Productivity Measures Using Direct Care Hours
Solution: . .
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

35. Productivity Measures Using Direct Care Hours
Solution: .
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

36. Figure 9.1 Productivity and Quality Tradeoff
Hospital A
Hospital B
Quantity of Inputs
(Staffing Level)
Quality of Output
I2 I1 QA QB A
QA” Q
A’’ A’ B I
IA”
Source: Shukla, R.K. Theories and Strategies of Healthcare: Technology-Strategy-Performance,
Chapter 4, Unpublished Manuscript, Printed with permission.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

37. Productivity Wall?
Quality is difficult to measure, and its definition is ambiguous
The relationships between quantity of care provided and quality are often uncertain
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

38. Many people confuse. . .
The concepts of productivity, efficiency, and effectiveness.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

39. It’s quite simple really!
Efficiency-- using the minimum number of inputs for a given number of outputs
Effectiveness-- refers to outputs; are the proper inputs being used to produce the appropriate outcomes?
Productivity-- a broader concept than efficiency; refers to effective use of a given set of resources
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

40. But efficiency has varying dimensions..
Technical Efficiency-- relationship between various inputs and related outputs; use minimum combination of resources for a given level of quantity or level of care.
Allocative (Economic) efficiency-- adds cost to the measure of technical efficiency.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

41. Graphically, Assume NPs and MDs can be substituted. The hospital
Iso-cost
Nurse
Practitioners
(NPs)
MDs 4 3 2 1 C B A
Isoquant
Assume NPs and MDs can
be substituted. The hospital
can either use 3 MDs and
2 NPs (pt. A), or 1 MD and
5 NPs (pt. B). Both result
in the same level of quality
and can produce the same
quantity of output.
Are points A and B both technically efficient?
Is point C technically efficient, why or why not?
Remember what an isoquant is? Are all points on an
isoquant technically efficient? economically efficient?
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

42. Let’s expand our discussion. . .
Data envelopment analysis is a recently developed technique that can be used to measure the multiple dimensions of productivity.
It allows multiple inputs and outputs to be used in a linear programming model that develops a score of technical efficiency.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

43. Data Envelopment Analysis (DEA)
DEA can be used to measure productivity of hospitals, physicians, group practices, or any other unit of analysis, referred to as the decision making unit (DMU)
The technical efficiency score of optimally producing DMUs equals 1 (and lies on the isoquant). All other DMUs are measured against these technically efficient DMUs, and have a score of between 0 and 1.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

44. DEA-- A Simple Example Physicians Inputs P1 P2 P3 P4 Visits 2 1 3 2
Medications
Inefficiency
Physicians P1, P2, and P3 are
technically efficient, ceteris
paribus, and would receive an
efficiency score of 1. Physician 4,
however is inefficient and must
reduce either visits and or use of
medications to become as efficient as
his/her peers. The amount of the
reduction necessary is called inefficiency.
Supplies 4 3 2 1 P2 P4 P1 P3
LOS
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

45. DEA-- An Application Ozcan and Luke (1993), A National Study of the Efficiency of Hospitals in Urban Markets
The study examines the contribution of various hospital characteristics to hospital technical efficiency
Outputs included:
Treated cases
Outpatient visits
Teaching FTEs
Inputs included:
Capital
Plant complexity
Labor
Supplies
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

46. DEA Applications, cont.
Slack values allow the manager to determine just how much the input/output mix must be changed for inefficient DMUs to reach efficiency
DEA is also useful for benchmarking or development of report cards, making it particularly useful in a managed care environment
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

47. Improving Healthcare Productivity
Develop productivity measures for all operations in their organization,
Look at the system as a whole (do not sub-optimize) in deciding on which operations/procedures to focus productivity improvements.
3. Develop methods for achieving productivity improvements, and especially benchmarking by studying peer healthcare providers that have increased productivity; and reengineer care delivery and business processes.
4. Establish reasonable and attainable standards and improvement goals.
5. Consider incentives to reward workers for contributions and to demonstrate management’s support of productivity improvements.
6. Measure and publicize improvements.
Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

48. The End Chapter 9: Quantitatve Methods in Health Care Management
Yasar A. Ozcan