Computer simulation of patient
flow through an operating suite
David E. Clark, MD FACS
Department 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
Model of an operating suite
P1
OR1
P2
Preop
RR
P3
OR2
P4
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
.008
.006
.004
0
.002
Probability density
• Time to event,
bounded on (0,∞)
• Fit a parametric
distribution (many
possibilities)
• Model covariates
using regression
• Derive transition
probabilities (hazards)
.01
Input distributions
0
60
120 180 240 300 360 420 480
Duration of operative procedure (minutes)
540
600
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
1
1
0730
0930
Pre
1
1000
1300
Stat
_P2
Stat
_R1
N/A
Trem
_R1
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
Example: Patient/room data
At 0745, 0845, 0945
Rep
Rsch
_P1
Tin
_P1
Tout
_P1
Stat
_P1
Rsch
_P2
Tin
_P2
Tout
_P2
1
1
0730
0930
R1
1
1000
1300
Rep
Rsch
_P1
Tin
_P1
Tout
_P1
Stat
_P1
Rsch
_P2
Tin
_P2
Tout
_P2
1
1
0730
0930
R1
1
1000
Rep
Rsch
_P1
Tin
_P1
Tout
_P1
Stat
_P1
Rsch
_P2
1
1
0730
0930
RR
1
Stat
_P2
Stat
_R1
Trem
_R1
P1
105
Stat
_P2
Stat
_R1
Trem
_R1
1300
Pre
P1
Tin
_P2
Tout
_P2
Stat
_P2
Stat
_R1
1000
1300
Pre
Turn
45
Trem
_R1
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
0800
P1
P3
P5
0815
P1
P3
0830
P1
0845
P11
P18
P8
P11
P18
P23
P5
P8
TURN
P15
TURN
P23
P3
P5
P8
TURN
P15
TURN
P23
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
P9
P13
P20
P24
P6
P16
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
25
Friday OR Census
15
20
Dashed: Mean scheduled
Solid: Mean actual
Shaded: Simulated 90% CI
10
25
Friday RR Census
15
5
20
Solid: Mean actual
Shaded: Simulated 90% CI
15:00
18:00
21:00
10
12:00
5
09:00
09:00
12:00
15:00
18:00
21:00
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”