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. Author manuscript; available in PMC: 2022 May 1.
Published in final edited form as: Med Care. 2021 May 1;59(5):418–424. doi: 10.1097/MLR.0000000000001510

Table 2.

Comparison of BIC and TCIC backward selection models

No. variables Bayesian Information Criterion (BIC) models Time-Cost Information Criterion (TCIC) models p-value, BIC/TCIC c-statistics
Next variable to be removed Reduction in time cost (sec) Model time cost (sec) BIC Harrell’s C-Statistic Next variable to be removed Reduction in time cost (sec) Model time cost (sec) TCIC Harrell’s C-Statistic
19 -Stroke 7 368 52167 0.7213 (0.7128– 0.7298) -10-Word immediate recall 78 368 52167 0.7213 (0.7128–0.7298) 1.00
18 -Pain 5 360 52153 0.7209 (0.7124–0.7294) -Depression 49 289 52117 0.7205 (0.7120–0.729) 0.37
17 -Hearing aid 3 355 52144 0.7209 (0.7124–0.7294) -Eyesight 27 241 52078 0.7203 (0.7118–0.7288) 0.27
16 -Eyesight 27 352 52136 0.7209 (0.7124–0.7294) -Pain 5 214 52057 0.7203 (0.7117–0.7288) 0.23
15 -Depression 49 325 52128 0.7208 (0.7123–0.7294) -Hearing aid 3 209 52054 0.7202 (0.7117–0.7287) 0.20
14 -10-Word immediate recall 78 276 52122 0.7206 (0.7121–0.7291) -Stroke 7 205 52051 0.7202 (0.7117–0.7287) 0.40
13 -Education 5 198 52119 0.7198 (0.7113–0.7283) -IADL dependency 25 198 52048 0.7198 (0.7117–0.7287) 1.00
12 -IADL dependency 25 193 52118 0.7197 (0.7112–0.7283) -Education 5 173 52047 0.7184 (0.7099–0.727) 0.01
11 -Cancer 13 168 52120 0.7182 (0.7097–0.7268) -Cancer 13 168 52050 0.7182 (0.7097–0.7268) 1.00
10 -Ability to drive 12 155 52129 0.7166 (0.708–0.7252) -Ability to drive 12 155 52065 0.7166 (0.708–0.7252) 1.00
9 -ADL dependency 21 144 52145 0.7148 (0.7062–0.7233) -10-Word delayed recall 79 144 52081 0.7148 (0.7062–0.7233) 1.00
8 -Heart failure 3 122 52182 0.7116 (0.7030–0.7202) -ADL dependency 21 65 52107 0.7101 (0.7014–0.7187) 0.23
7 -Diabetes 9 119 52226 0.7088 (0.7002–0.7174) -Heart failure 3 44 52149 0.7065 (0.6979–0.7152) 0.11
6 -10-Word delayed recall 79 110 52281 0.7047 (0.6960–0.7133) -Diabetes 9 41 52200 0.7037 (0.6951–0.7124) 0.54
5 -Smoking 8 32 52367 0.6992 (0.6905–0.7079) -Smoking 8 32 52262 0.6992 (0.6905–0.7079) 1.00
4 -Volunteer 3 24 52468 0.6914 (0.6826–0.7003) -Volunteer 3 24 52374 0.6914 (0.6826–0.7003) 1.00
3 -Difficulty climbing stairs 14 20 52622 0.6827 (0.6738–0.6916) -Difficulty climbing stairs 14 20 52534 0.6827 (0.6738–0.6916) 1.00
2 -Gender 4 7 52937 0.6575 (0.6481–0.6668) -Gender 4 7 52855 0.6575 (0.6481–0.6668) 1.00
1 -Age 3 3 53005 0.6489 (0.6395–0.6583) -Age 3 3 52929 0.6489 (0.6395–0.6583) 1.00

Abbreviations: sec - seconds; N/A - not applicable; IADL – instrumental activities of daily living; ADL – activities of daily living; BIC – Bayesian information criterion; TCIC – time-cost information criterion.

Rounding may lead to small inconsistencies in time cost totals within models.

Table shows that both traditional and time-cost selection started with a 19 variable model with a total time cost of 368 seconds. To get to the 18 variable model, traditional selection removed the Stroke variable which cost 7 seconds, resulting in an 18 variable model with a total time cost of 360 seconds. Alternatively, time-cost selection removed the 10-word immediate recall variable which cost 78 seconds, resulting in an 18 variable model with a total time cost of 289 seconds. The list below 18 shows the variables retained in the 18 variable model.

Both traditional and time-cost selection identified the 12 variable model as the optimum (bolded). However, the traditional method excludes education, while the TCIC method excludes IADL dependency.

If the goal is to identify the best model under 60 seconds, the traditional backward selection would identify a 5 variable model as optimal while the time-cost backward selection method would identify a 7 variable model as optimal (shaded).