Computer simulation of patient flow through an operating suite

David E. Clark, MD FACSDepartment of Surgery,

Maine Medical Center, Portland ME

Stata Conference 2014

The problem

• Operating Rooms (ORs) may generate up to 40% of hospital revenue – efficiency is financially important

• Delays and rescheduling are frustrating and demoralizing for patients and staff

• In extreme cases, patient safety may suffer if vital resources are unavailable due to suboptimal management

Preop

Model of an operating suite

P2

P3

P4

P1

OR1

OR2

RR

Simulation Software

• Special-purpose simulation programs (e.g., Arena, Flexsim, Simulink) take care of “housekeeping” and displays, but may be expensive, restrict flexibility, and be more difficult to learn and debug

• General-purpose programming languages (including Stata) easily available, familiar, and flexible, but require the user to construct “housekeeping” and displays

Tools available in Stata

• Basic structure a matrix with rows (observations) and columns (up to 32,767 variables)

• Loops (“forvalues”, “foreach”)• Replication (“expand”, “expandcl”)• Reshaping (“wide”, “long”)• Summarization (“egen”) • Subroutines (“program”, “.do” files)• Time-to-event modeling (“streg”, etc.)• Reporting (“list”, “save”, “append”, “replace”)

Available hospital data

• Patients: Day, procedure, surgeon, scheduled OR/times (in/out etc.), actual OR/times, destination from OR (RR vs ICU), RR times, etc.

• Rooms: Availability for different types of procedures, at different times of day

• Policies: Staffing, scheduling, priority rules, “bumping”

Data Structure

• Must allow for transfer of information between patients and rooms

• Must allow for change in status over time

• Must allow for replication with different random variables

• Must allow for visualization of status, reporting of summary statistics, and modification of structural assumptions

Input distributions

• Time to event, bounded on (0,∞)

• Fit a parametric distribution (many possibilities)

• Model covariates using regression

• Derive transition probabilities (hazards)

0.0

02.0

04.0

06.0

08.0

1P

roba

bilit

y de

nsity

0 60 120 180 240 300 360 420 480 540 600Duration of operative procedure (minutes)

Methods: Derive distributions

• Patient data in normal (“long”) format

• Estimate two-parameter log-logistic distributions for procedure duration, recovery room duration, turnaround time

• Parametric time-to-event regression (“streg”) using predicted procedure duration, procedure type, surgeon, following self, first case, add-on case

Methods: Initialize patients/rooms

• For a given day, convert patient data to “wide” format – that is, all variables are in the same row

• Add room data on same row

For example, at 0600…

Rep Rsch

_P1

Tin

_P1

Tout

_P1

Stat

_P1

Rsch

_P2

Tin

_P2

Tout

_P2

Stat

_P2

Stat

_R1

Trem

_R1

1 1 0730 0930 Pre 1 1000 1300 N/A

Methods: Use replicants to create output distributions

• After initialization, “expand” 30 to 3000

• Run program and periodically

“egen mvar = mean(var)”

“egen sdvar = sd(var)”

etc.

to accumulate statistics of interest

• Display one realization of simulation

Methods: Step through entire day at 5-minute intervals

• Loop using “forvalues”

• Determine patient status at new time t, and whether status should change either deterministically (scheduled or actual) or probabilistically (simulated with random variables).

• Update room status depending on which patient is now in room and/or scheduled to be in room

Methods: Sequence of procedures at each time step

• Identify patients arriving in preop status• Move next priority patient to OR when

patient ready and room available• Move OR patient to RR if procedure

finished (random number exceeds hazard function at time t); restrict room for “turnaround time”

• Move RR patient out of RR if required time complete

Rep Rsch

_P1

Tin

_P1

Tout

_P1

Stat

_P1

Rsch

_P2

Tin

_P2

Tout

_P2

Stat

_P2

Stat

_R1

Trem

_R1

1 1 0730 0930 R1 1 1000 1300 P1 105

Example: Patient/room dataAt 0745, 0845, 0945

Rep Rsch

_P1

Tin

_P1

Tout

_P1

Stat

_P1

Rsch

_P2

Tin

_P2

Tout

_P2

Stat

_P2

Stat

_R1

Trem

_R1

1 1 0730 0930 R1 1 1000 1300 Pre P1 45

Rep Rsch

_P1

Tin

_P1

Tout

_P1

Stat

_P1

Rsch

_P2

Tin

_P2

Tout

_P2

Stat

_P2

Stat

_R1

Trem

_R1

1 1 0730 0930 RR 1 1000 1300 Pre Turn

Methods: Periodic adjustments

• Determine time remaining for current case in each room, total time remaining to complete all cases, free time remaining

• Reprioritize patients scheduled in each room, including new emergency cases

• Identify next case scheduled in room with greatest anticipated overtime, and reassign that case to room with greatest anticipated free time

Results: Output for a typical day

R1 R2 R3 R4 R5 R6 R7 R8

0700

0715

0730 P1 P11

0745 P1 P3 P5 P11 P18

0800 P1 P3 P5 P8 P11 P18 P23

0815 P1 P3 P5 P8 TURN P15 TURN P23

0830 P1 P3 P5 P8 TURN P15 TURN P23

0845 P1 P3 TURN P8 P12 P15 P19 P23

0900 P1 P3 TURN P8 P12 TURN P19 TURN

0915 P1 TURN TURN TURN TURN TURN TURN TURN

0930 TURN TURN TURN TURN TURN TURN

0945 TURN P4 P6 P9 P13 P16 P20 P24

Results

• Runtime about 10 minutes to simulate a 24-hour day with 300 replications – not affected much by number of replications

• Most time-consuming for computer (and most difficult to code) is reassignment of cases from overbooked rooms

• Limited by incomplete data on patient destination after Recovery Room

Validation: Cumulative statistics

Dashed: Mean scheduledSolid: Mean actualShaded: Simulated 90% CI

51

01

52

02

5

09:00 12:00 15:00 18:00 21:00

Friday OR Census

Solid: Mean actualShaded: Simulated 90% CI

51

01

52

02

5

09:00 12:00 15:00 18:00 21:00

Friday RR Census

Expand and modify

• Started small, now allow for 50-100 patients in 24 rooms

• Summarize multiple days with same structure (day of week, block schedule)

• Add information about RR destinations

• Verify assumptions about OR staffing RR staffing, scheduling policies, etc.

• Predict effects of changing staffing/policies

Conclusions

• Stata has some useful features for simulation and enables a working model

• Stata would be even better if commands could reference variable names, e.g., replace st_R7=3 if st_P3=7

• Plan to post improved version of this program on ideas.repec.org

• StataCorp and/or developers should take note of “SAS Simulation Studio”