From data to robust surgery schedules¶

Learning the uncertainty of surgery duration from open data (VitalDB, 6,385 operations) and measuring what it changes in operating-room schedules. Code in src/; this notebook shows the results.

In [1]:
import sys; sys.path.insert(0, '../src')
import json, pandas as pd
from IPython.display import Image
pd.set_option('display.precision', 3); pd.set_option('display.width', 160)
from data import load, split, FEATURES

1. Data¶

In [2]:
df = load(); tr, ca, te = split(df)
print(len(df), 'cases;', len(tr), 'train,', len(ca), 'calibration,', len(te), 'test (grouped by patient)')
df['duration'].describe()

6385 cases; 3836 train, 1268 calibration, 1281 test (grouped by patient)
Out[2]:
count    6385.000
mean      188.755
std       109.532
min        27.333
25%       103.217
50%       165.283
75%       250.900
max       835.767
Name: duration, dtype: float64
In [3]:
Image('../figures/00_durations.png')
Out[3]:
No description has been provided for this image

Durations are right-skewed (mean above median) and vary a lot even within one procedure: that variability is what a schedule must absorb.

2. Point predictions¶

In [4]:
pd.read_csv('../results/point_metrics.csv')
Out[4]:
model MAE_min RMSE_min within_30min R2
0 B0 global median 84.387 111.547 0.192 -0.054
1 B1 procedure history 48.280 71.911 0.488 0.562
2 GBM median 43.898 65.165 0.511 0.640

3. Prediction intervals (nominal 80%)¶

In [5]:
pd.read_csv('../results/interval_metrics.csv')
Out[5]:
method coverage mean_width_min interval_score worst_department_coverage
0 I1 procedure history 0.781 146.186 236.772 0.467
1 I2 quantile GBM 0.689 123.588 235.272 0.567
2 I3 conformal 0.820 151.359 226.167 0.767
3 I4 CQR 0.816 149.610 230.498 0.600
4 I5 CQR by department 0.815 150.136 230.600 0.600
In [6]:
Image('../figures/01_intervals_examples.png')
Out[6]:
No description has been provided for this image
In [7]:
Image('../figures/02_coverage.png')
Out[7]:
No description has been provided for this image

Over 10 random splits, and paired on the same splits:

In [8]:
pd.read_csv('../results/repeated_splits.csv')
Out[8]:
method coverage_mean coverage_sd width_mean score_mean score_sd worst_dept_cov_mean
0 I1 procedure history 0.765 0.015 146.344 241.721 8.562 0.638
1 I2 quantile GBM 0.677 0.016 122.817 238.715 7.518 0.609
2 I3 conformal 0.805 0.010 150.272 236.847 8.432 0.766
3 I4 CQR 0.801 0.013 148.495 231.463 6.626 0.738
4 I5 CQR by department 0.803 0.013 149.628 231.858 6.424 0.761
In [9]:
pd.read_csv('../results/repeated_splits_paired.csv')
Out[9]:
method versus mean_difference sd splits_where_better
0 I4 CQR I1 procedure history -10.26 4.98 10
1 I4 CQR I2 quantile GBM -7.25 1.66 10
2 I4 CQR I3 conformal -5.38 4.87 9
3 I5 CQR by department I4 CQR 0.39 0.48 0
In [10]:
Image('../figures/02b_repeated_splits.png')
Out[10]:
No description has been provided for this image

4. Scheduling under uncertainty¶

200 simulated days, 4 rooms of 480 minutes, 24 elective cases on the waiting list; exact set-packing model solved with HiGHS, then played with the real durations.

In [11]:
s = pd.read_csv('../results/schedule_summary.csv'); s
Out[11]:
policy param overtime_min rooms_in_overtime overtime_30 idle_min utilisation cases excess_vs_median overtime_se
0 ML median 0.00 54.465 0.554 0.426 26.116 0.946 12.560 9.268 2.835
1 fixed buffer 0.05 39.884 0.450 0.335 36.298 0.924 12.005 9.132 2.347
2 fixed buffer 0.10 31.166 0.357 0.260 46.979 0.902 11.595 9.868 2.052
3 fixed buffer 0.15 20.454 0.268 0.186 64.401 0.866 11.210 7.104 1.814
4 fixed buffer 0.20 17.755 0.228 0.154 73.770 0.846 10.865 9.615 1.612
5 fixed buffer 0.30 13.264 0.160 0.124 100.420 0.791 10.175 10.185 1.422
6 historical 0.00 112.816 0.796 0.696 8.866 0.982 12.460 11.808 4.267
7 quantile 0.60 44.950 0.531 0.393 29.975 0.938 10.710 9.717 2.435
8 quantile 0.70 30.960 0.405 0.280 39.244 0.918 10.075 8.624 1.946
9 quantile 0.80 19.249 0.295 0.177 54.150 0.887 9.280 7.018 1.697
10 quantile 0.90 7.932 0.154 0.090 84.736 0.824 7.765 6.537 0.987
11 robust (learned set) 0.50 29.175 0.356 0.258 50.839 0.894 12.920 7.208 2.016
12 robust (learned set) 1.00 16.737 0.199 0.139 81.623 0.830 12.105 6.705 1.587
13 robust (learned set) 1.50 10.259 0.130 0.096 109.378 0.772 11.455 6.174 1.150
14 robust (learned set) 2.00 8.311 0.102 0.070 130.843 0.727 10.715 7.884 1.168
15 robust (learned set) 3.00 4.616 0.074 0.045 143.546 0.701 9.415 9.235 0.840
In [12]:
Image('../figures/03_schedule_frontier.png')
Out[12]:
No description has been provided for this image

5. A first step towards FHIR¶

The first cases exported as HL7 FHIR R4 Patient, Encounter and Procedure resources:

In [13]:
b = json.load(open('../data/fhir_bundle_sample.json')); print(len(b['entry']), 'resources')
print(json.dumps(b['entry'][2]['resource'], indent=1)[:700])

60 resources
{
 "resourceType": "Procedure",
 "id": "procedure-1",
 "status": "completed",
 "subject": {
  "reference": "Patient/patient-5955"
 },
 "encounter": {
  "reference": "Encounter/encounter-1"
 },
 "code": {
  "text": "Low anterior resection"
 },
 "category": {
  "text": "Colorectal"
 },
 "performedPeriod": {
  "start": "2000-01-01T08:00:00+00:00",
  "end": "2000-01-01T11:12:22+00:00"
 },
 "reasonCode": [
  {
   "text": "Rectal cancer"
  }
 ],
 "extension": [
  {
   "url": "urn:surgery-duration-uncertainty:approach",
   "valueString": "Open"
  },
  {
   "url": "urn:surgery-duration-uncertainty:emergency",
   "valueBoolean": false
  }
 ]
}