Faculty of Industrial Engineering and Management Technion – Israel Institute of Technology

1. Can We Make Simulation More Accessible To Emergency Department Decision Makers David Sinreich and Yariv Marmor Faculty of Industrial Engineering and Management Technion – Israel Institute of Technology Emergency Multidisciplinary Research Unit SMBD - Jewish General Hospital, August 29, 2005

2. The Healthcare Industry and Numbers • The annual Canadian expenditure on healthcare in 2001 was estimated at $64.2 billion (~$2100 per person). • According to 2005 issue of healthcare in Canada (CIHI) the healthcare expenditure in 2004 grow to about $100 billion (~$3200 per person) and accounted for 10% of the GDP. • Hospitals represented 30% of the total healthcare expenditure in 2004.

3. The Healthcare Industry and Numbers • The annual U.S. expenditure on healthcare in 2003 was estimated at $1.5 trillion (~$5000 per person) and is expected to reach $2.8 trillion by the year 2011. • Healthcare accounted for 13.2% of the GDP in 2000 and may reach 17% of the GDP by 2011. • Hospitals represented 31.7% of the total healthcare expenditure in 2001. This expenditure is expected to decrease to 27% by 2012. • According to the American College of Emergency Physicians (June 2003), the cost of Emergency Department (ED) operations amounted to 5% of the total US healthcare expenditure.

4. The Healthcare Industry and Numbers • The ICBS reports that the annual healthcare spending in Israel in 2003 reached $10.1 billion (~$1700 per person), which accounts for 8.8% of the GDP. • This level of expenditure is similar to other OECD countries such as Germany 10.9%, France 9.7%, Sweden 9.2% and Australia 9.1% (number reflect expenditure in 2002) • Hospitals accounted for 26.1% of the national expenditure on healthcare in 2001.

5. The Healthcare Industry and Numbers • The ICBS reports that the annual healthcare spending in Israel in 2003 reached $10.1 billion (~$1700 per person), which accounts for 8.8% of the GDP. • This level of expenditure is similar to other OECD countries such as Germany 10.9%, France 9.7%, Sweden 9.2% and Australia 9.1% (number reflect expenditure in 2002) • Hospitals accounted for 26.1% of the national expenditure on healthcare in 2001. These numbers are a clear indication that increasing the efficiency and productivity of hospital and ED operations is critical to the success of the entire healthcare system

6. The Emergency Department • The ED serves as the hospital’s “gate keeper“ and is the most difficult department to manage. • The ED has to handle efficiently and effectively a random arrival stream of patients. • The ED has to be highly versatile and flexible. • The ED is required to have the ability to react quickly to fast unfolding events.

7. The Emergency Department • There are 2.5 million patient visits each year at the 25 EDs in Israel. This translates to about 270 patient visits on average per day. • On average there 30 - 40 beds in these EDs. • Based on these number, there are around 7 - 8 patient turnarounds a day, this translates to an average length of stay of 3 - 3.5 hours. • In reality there are 4 - 6 times more patient arrivals during pick hours (between 11 – 13 and 19 – 22) compared to other hours of the day.

8. Simulation of Healthcare and ED Systems • Hospital management is reluctant to accept change, particularly if it comes from a 'black-box' type of tool. • Management often does not realize the benefits of using simulation-based analysis tools. • Management is well aware of the time and cost that have to be invested in building detailed simulation models. • Management believes that spending money on operational issues only diverts funds from patient care. • Lack of experts with experience in modeling large, complex systems.

9. Generic Activities Fixed Processes Modeling Options The Model's Basic Building Blocks Generic Processes High abstraction level Flexible enough to model any system and scenario Difficult to use requires knowledge and experience Medium abstraction level Flexible enough to model any system which uses a similar process Simple and intuitive to use after a brief and short introduction Low abstraction level Can only model and analyze the system it was designed for Simple and easy to use after a quick explanation

10. Increasing Acceptance of Simulation in Healthcare It is essential to build up the models’ credibility: • Hospital management should be directly involved in the development of simulation projects. • The development of simulation projects should be done in-house by hospital personal.

11. As a result the tool has to be: Increasing Acceptance of Simulation in Healthcare • General, and flexible • Include default values for most of the system parameters. • Simple to use • Include a decision support system

12. Essential Basic Condition For the tool to be general and flexible The process patients go through when visiting an ED has to be determined mainly by the patient type (Internal, Orthopedic, Surgical etc.) rather than by the hospital in which it is performed.

13. The Field Study • Funded by the Israel National Institute for Health Policy (NIHP). • 5 out of the 25 – 27 general hospitals operating in Israel participated in the study. • Hospitals 1 and 3 are large (over 700 beds). Hospital 5 is medium (400 - 700 beds). Hospital 2 and 4 are small (less than 400 beds). • Hospital 5 is a regional hospital and the rest are inner-city hospitals. • Hospitals 1 and 3 are level 1 trauma centers and the rest are level 2 centers.

14. The Field Study • Teams of supervised students equipped with standardized code lists of the different process elements conducted time and motion studies in the selected hospitals. • Data was also gathered from each hospital’s information system. • Additional data was gathered trough interviews with the hospital top management, ED chief physician and ED head nurse.

15. Processes and Patient Types • Through observations, gathered data and interviews, 19 individual process charts each representing a typical patient types were identified.

16. Resource 1 Resource 1 Resource 1 Resource Activity Activity 70% 30% Decision Activity Activity Process Chart

18. 1 2 g a b a b g A A B B A C C D D E E D B D A B The Similarity Measure - Activities i j bji eij bij e12=2, b12=2, b21=2 a12=0.33

19. b a b g g a A A B B C D D E The Similarity Measure - Relationships c12 = 0+2+0+0+0+0+0+0+0 = 2 d12 = 0+0+2+2+0+1+0+1+0 = 6 r12 = 2/(6+2) =0.25

20. The Sensitivity of the Similarity Measure The similarity measure is sensitive to: • The absence of an activity or to additional activities a resource is expected to perform. • The absence of a relationship or to an additional relationship between activities. The similarity measure is not sensitive to: • The order in which activities are expected to be performed.

21. 5 5 5 5 4 4 4 3 3 3 3 3 2 2 2 1 1 1 1 I FT S O I I_A O I_S T I_W S_W O_W I S O I FT S O 1 I 88 55 24 66 70 46 89 43 32 23 32 59 52 33 64 80 5 2 43 1 O 53 62 77 32 36 86 35 59 12 37 60 14 74 89 40 40 66 1 S 79 89 42 37 39 61 58 68 31 47 58 31 74 59 49 61 1 FT 94 56 23 48 43 57 67 45 28 29 37 44 51 32 56 2 I 66 40 23 89 73 25 59 38 39 18 25 63 53 44 2 O 46 51 72 32 50 71 30 45 6 23 43 9 67 2 S 64 71 51 37 45 55 46 62 32 38 45 31 3 I 52 23 1 53 51 7 57 27 27 9 10 3 O_W 46 51 25 14 15 52 28 88 16 84 3 S_W 37 41 2 5 5 31 16 100 30 3 I_W 45 19 0 23 26 3 29 36 3 T 54 64 22 23 24 46 34 4 I_S 79 54 27 61 72 39 4 O 57 56 53 18 26 4 I_A 59 27 32 77 5 I 55 25 16 5 O 32 52 5 S 65 5 FT Clustering the Patient Processes Average Similarity Level – 0.44

22. Clustering the Patient Processes • Full enumeration and ranking was used to determine the best way to divide the processes into: Two clusters Three clusters Four clusters

23. Clustering the Processes Into Two Groups • The first group included all the internal patient types from all 5 hospitals: 1Int, 1FT, 2Int, 3Int, 3W_Int, 4Int_S, 4Int_A, 5Int, 5FT. • The best combined average similarity value for two clusters (0.579, 0.571) was 0.575.

24. Clustering the Patient Processes • Full enumeration and ranking was used to determine the best way to divide the processes into: Two clusters Three clusters Four clusters

25. Clustering the Processes Into Three Groups • The best combined average similarity value for three clusters was 0.638. • The chosen clustering option was ranked as number 17 with a combined average similarity value of (0.656, 0.746, 0.544) 0.623.

26. 1 I 1 O 1 S 1 FT 2 I 2 O 2 S 3 I 3 O_W 3 S_W 3 I_W 3 T 4 I_S 4 O 4 I_A 5 I 5 O 5 S 5 FT “When good is better than best” (Petroski 1994) 5 5 5 5 4 4 4 3 3 3 3 3 2 2 2 1 1 1 1 I FT S O I I_A O I_S T I_W S_W O_W I S O I FT S O 88 55 24 66 70 46 89 43 32 23 32 59 52 33 64 80 5 2 43 53 62 77 32 36 86 35 59 12 37 60 14 74 89 40 40 66 79 89 42 37 39 61 58 68 31 47 58 31 74 59 49 61 94 56 23 48 43 57 67 45 28 29 37 44 51 32 56 66 40 23 89 73 25 59 38 39 18 25 63 53 44 46 51 72 32 50 71 30 45 6 23 43 9 67 64 71 51 37 45 55 46 62 32 38 45 31 52 23 1 53 51 7 57 27 27 9 10 46 51 25 14 15 52 28 88 16 84 37 41 2 5 5 31 16 100 30 45 19 0 23 26 3 29 36 54 64 22 23 24 46 34 79 54 27 61 72 39 57 56 53 18 26 Average Similarity Level – 0.656 59 27 32 77 55 25 16 Average Similarity Level – 0.746 32 52 Average Similarity Level – 0.544 65 Combined Average Similarity Level – 0.623

27. Clustering the Patient Processes • Full enumeration and ranking was used to determine the best way to divide the processes into: Two clusters Three clusters Four clusters

28. Clustering the Processes Into Four Groups • The best combined average similarity value for four clusters was 0.683. • The chosen clustering option was ranked as number 76 with a combined average similarity value of (0.669, 0.746, 0.654, 0.558) 0.666. • The first group included all acute internal patient types: 1Int, 2Int, 3Int, 4Int_S, 4Int_A, 5Int. • The second group included most orthopedic patients types: 1O, 2O, 4O, 5O. • The third group included most surgical patients types: 1S, 2S, 3O_W, 3S_W, 3T, 5S. • The forth group included all ambulatory patients types: 1FT, 3Int_W, 5FT.

29. Clustering the Patient Processes • Full enumeration and ranking was used to determine the best way to divide the processes into: Two clusters Three clusters Four clusters • The clustering options chosen were compared to the best similarity result of 1000 random clustering solutions into 4 groups • For a selection probability (0.25, 0.25, 0.25, 0.25) the best combined average similarity value was 0.554. • For a selection probability (0.315, 0.21, 0.315, 0.16) the best combined average similarity value was 0.56.

30. Conclusions Based on this analysis it is safe to argue that in the hospitals that participated in this study, patient type has a higher impact in defining the operation process than does the specific hospital in which the patients are treated.

31. As a result the tool has to be: Increasing Acceptance of Simulation in Healthcare • General, and flexible • Include default values for most of the system parameters. • Simple to use • Include a decision support system

32. The Relative Precision of the Time Elements • Since a time study is basically a statistical sampling process, it is important to estimate the precision of the gathered data. Average Duration and Standard Deviation over all observed elements i for patient type p at all the hospitals The number of times element i was observed for each patient type p The maximum number of times patient type p goes through an element that is only performed once during the ED process Precision as a proportion of the gathered element

33. The Relative Precision of the Time Elements The contribution of element i to the totalprocess time of patient type p The relative weight of element i for patient type p The relative precision of elementi The relative precision for patient typep Over 20,000 process elements were observed and recorded.

34. Precision of the Different Time Elements

35. Conclusions The combined precision values indicate, that aggregating element duration regardless of patient type and the hospital in which the patients are treated, improves the precision levels of all the different elements.

36. As a result the tool has to be: It is possible and it makes sense to develop a simulation tool That is based on a generic unified process Increasing Acceptance of Simulation in Healthcare • General, and flexible • Include default values for most of the system parameters.

37. As a result the tool has to be: Increasing Acceptance of Simulation in Healthcare • General, and flexible • Include default values for most of the system parameters. • Simple to use • Include a decision support system

38. The Structure of the Simulation Tool Decision Support System Graphical User Interface based on the Generic Process Mathematical Models ARENA’s Simulation Model

40. Imaging Center

41. Specialists

42. Scheduling Medical Staff

43. The Structure of the Simulation Tool Decision Support System Graphical User Interface based on the Generic Process Mathematical Models ARENA’s Simulation Model

44. Mathematical Model Development The following mathematical models were developed based on the gathered information: • Patient arrivals to the ED • Patient Arrivals at the Imaging Center • Staff’s walking time

45. Estimating the Patient Arrival Process • The gathered data reveals that the number of patients arriving at the ED differs from hour to hour and from day to day • Statistical tests reveal that the square-root of the patients' arrival process can be described by a normal distribution. • Let Xpihd be a random variable normally distributed with a mean of that represents the square-root of the number of patients of type p who arrive at the ED of hospital i at hour h on day d.

46. The square-root of the number of patients of type p who arrive at the ED of hospital i at hour h on day d in week w The average square-root estimator of the number of patients of type p arriving at hospital i per hour Number of data weeks received from the hospitals' information systems and number of hospitals The patient arrival factor The estimated adjusted arrival data values of patients of type p who arrive at hospital i at hour h on day d in week w The number of patients of type p who arrive during hour h on day d Estimating the Patient Arrival Process The patient arrival process is similar for all the hospitals surveyed therefore it was decided to combine the gathered data from all hospitals

47. Estimating the Patient Arrival Process The number of patients of type p who arrive at hospital i at hour h on day d

48. Estimating the Patient Arrival Process In the case a new hospital whishes to use the simulation tool all that is needed are the values obtained from the hospital's computerized information systems. The rest of the process, which includes calculating the formulas, is performed automatically by the simulation tool. It is clear from these factors that hospital 1 is larger than the other two hospitals

49. Validating The Model Internal Patients on Monday Internal Patients on Saturday

50. Validating The Model Surgical Patients on Wednesday