Computer simulation of patient flow through an operating suite

1
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

2
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

3
Model of an operating suite
P1
Preop
OR1
RR
P2
P3
OR2
P4
4
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

5
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)

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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

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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

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Input distributions

• Time to event, bounded on (0,8)
• Fit a parametric distribution (many
  possibilities)
• Model covariates using regression
• Derive transition probabilities (hazards)

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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

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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
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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

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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

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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

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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 P1 105
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
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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

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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
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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

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Validation Cumulative statistics
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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

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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_R73 if st_P37
• Plan to post improved version of this program on
  ideas.repec.org
• StataCorp and/or developers should take note of
  SAS Simulation Studio