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Table 6 Outlier maps arranged in the decreasing order of the \(Z(\beta )\) scores

From: Entropic measures of complexity in a new medical coding system

Map

Map description

H(B)

UR

m

v

\({Z(\beta )}\)

3473

Closure of other fistula of thorax

10.95

7.92

243

1977

4.26

3950

Angioplasty of other non-coronary vessel(s)

10.22

10.22

1196

1196

3.88

3929

Other (peripheral) vascular shunt or bypass

10.22

10.22

1191

1191

3.88

304

Radical laryngectomy

9.61

5.81

56

784

3.57

9223

Radioisotopic teleradiotherapy

9.58

9.58

768

768

3.55

3926

Other intra-abdominal vascular shunt or bypass

9.49

9.49

720

720

3.50

3821

Biopsy of blood vessel

9.45

9.45

699

699

3.48

3979

Other endovascular procedures on other vessels

9.43

9.43

689

689

3.47

8120

Arthrodesis of unspecified joint

9.18

9.18

582

582

3.34

5684

Closure of other fistula of ureter

9.13

6.13

70

560

3.31

8129

Arthrodesis of other specified joints

9.11

9.11

552

552

3.30

409

Other operations on lymphatic structures

8.99

8.99

510

510

3.24

8687

Fat graft of skin and subcutaneous tissue

8.98

6.04

66

506

3.24

5783

Repair of fistula involving bladder and intestine

8.98

6.13

70

505

3.23

3342

Closure of bronchial fistula

8.78

7.03

131

440

3.13

5784

Repair of other fistula of bladder

8.78

6.19

73

440

3.13

8382

Graft of muscle or fascia

8.78

8.78

440

440

3.13

3794

Implantation or replacement of automatic cardioverter/defibrillator, total system [aicd]

8.75

5.25

38

432

3.12

3958

Repair of blood vessel with unspecified type of patch graft

8.72

8.72

421

421

3.10

8605

Incision with removal of foreign body or device from skin and subcutaneous tissue

8.70

8.70

415

415

3.09

3956

Repair of blood vessel with tissue patch graft

8.65

8.65

402

402

3.06

046

Transposition of cranial and peripheral nerves

8.56

8.56

378

378

3.02

8663

Full-thickness skin graft to other sites

8.56

5.81

56

378

3.02

3991

Freeing of vessel

8.49

8.49

360

360

2.98

3957

Repair of blood vessel with synthetic patch graft

8.48

8.48

358

358

2.98

3951

Clipping of aneurysm

8.48

8.48

357

357

2.97

0474

Other anastomosis of cranial or peripheral nerve

8.45

8.45

350

350

2.96

843

Revision of amputation stump

8.45

8.45

349

349

2.96

3959

Other repair of vessel

8.43

8.43

346

346

2.95

8080

Other local excision or destruction of lesion of joint, unspecified site

8.43

8.43

345

345

2.95

8683

Size reduction plastic operation

8.41

8.41

340

340

2.94

8609

Other incision of skin and subcutaneous tissue

8.39

8.39

335

335

2.93

0404

Other incision of cranial and peripheral nerves

8.35

8.35

327

327

2.91

3897

Central venous catheter placement with guidance

8.32

5.58

48

320

2.89

3925

Aorta-iliac-femoral bypass

8.32

8.32

320

320

2.89

8196

Other repair of joint

8.29

8.29

313

313

2.88

8381

Tendon graft

8.29

8.29

312

312

2.87

8383

Tendon pulley reconstruction other than hand

8.29

8.29

312

312

2.87

  1. As before, m is the number of candidate codes in a map whereas v is the number of valid representations in a map. The UR measure (obtained by \(\log _2(m)\)) can directly be compared to H(B) (obtained by \(\log _2(v)\)). When \(UR < H(B)\), UR has underestimated the expected coding complexity. When \(UR > H(B)\), UR has overestimated the expected coding complexity. Otherwise, the measures are equal. The map id and description correspond to ICD-9-CM code and description, respectively