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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