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. Author manuscript; available in PMC: 2012 Feb 26.
Published in final edited form as: J Am Stat Assoc. 2011 Sep 1;106(495):818–831. doi: 10.1198/jasa.2011.ap09476

Table 1.

Simulation study comparing the standard CRM, EM-CRM with a single skeleton, and EM-CRM with three skeletons coupled with model selection (EM-CRMSEL), and model averaging (EM-CRMAVG)

Design Recommendation percentage at dose level
 Average
# toxicity		 Average
# patients		 Average
duration
1 2 3 4 5 6 None
Scenario 1 0.08 0.10 0.12 0.30 0.50 0.60
CRM 1 0.1 2.9 24.4 49.2 20.5 2.9 0.1 10.3 36.0 37.0
# patients 4.1 4.2 6.8 10.2 7.0 3.7
EM-CRM 1 0.1 4.5 23.9 43.7 23.2 4.6 0.1 10.1 36.0 20.7
# patients 4.9 4.7 6.8 8.8 6.9 3.9
CRM 2 0.0 0.2 12.7 68.2 18.1 0.8 0.0 9.6 36.0 37.0
# patients 4.1 3.6 6.5 14.2 6.2 1.3
EM-CRM 2 0.0 0.3 12.7 66.3 19.9 0.7 0.1 9.4 36.0 20.8
# patients 4.6 3.7 7.4 12.7 6.1 1.5
CRM 3 0.0 0.6 13.4 67.0 18.4 0.6 0.1 9.4 36.0 37.0
# patients 4.2 3.7 6.7 14.0 6.4 0.9
EM-CRM 3 0.1 0.8 13.1 65.5 19.8 0.7 0.1 9.1 36.0 20.8
# patients 4.9 4.1 7.4 12.6 6.0 1.0
EM-CRMSEL 0.0 0.6 13.2 65.4 18.8 1.8 0.1 9.6 36.0 20.7
# patients 4.8 3.8 6.9 12.0 6.5 1.9
EM-CRMAVG 0.1 0.8 13.2 64.0 20.7 1.0 0.3 9.5 35.9 20.7
# patients 4.8 3.9 7.2 11.6 6.6 1.8
Scenario 2 0.06 0.08 0.10 0.15 0.30 0.45
CRM 1 0.0 0.3 3.1 18.3 39.9 38.4 0.0 9.3 36.0 37.0
# patients 3.8 3.5 3.7 5.5 8.1 11.4
EM-CRM 1 0.0 0.4 3.3 17.0 36.9 42.3 0.0 9.0 36.0 21.8
# patients 4.3 3.6 3.9 5.6 7.6 11.0
CRM 2 0.0 0.0 0.9 17.8 57.0 24.3 0.0 8.3 36.0 37.0
# patients 3.7 3.3 4.0 7.1 10.9 7.0
EM-CRM 2 0.0 0.1 1.4 17.0 57.2 24.4 0.0 7.9 36.0 21.7
# patients 4.1 3.4 4.6 7.5 10.3 6.1
CRM 3 0.0 0.1 1.6 18.8 59.6 19.9 0.0 8.1 36.0 37.0
# patients 3.8 3.4 4.1 7.4 11.6 5.7
EM-CRM 3 0.0 0.2 2.0 17.6 59.2 21.0 0.0 7.7 36.0 21.7
# patients 4.2 3.5 4.8 7.8 10.6 5.2
EM-CRMSEL 0.0 0.1 1.5 17.1 54.4 26.8 0.0 8.3 36.0 21.7
# patients 4.2 3.4 4.2 6.8 9.8 7.5
EM-CRMAVG 0.0 0.1 1.3 15.8 55.8 26.8 0.1 8.2 36.0 21.7
# patients 4.2 3.4 4.5 6.7 9.9 7.3
Scenario 3 0.05 0.14 0.18 0.22 0.26 0.30
CRM 1 0.0 1.6 6.0 11.9 18.1 62.5 0.0 7.9 36.0 37.0
# patients 3.8 4.4 4.9 5.0 5.6 12.2
EM-CRM 1 0.0 1.7 5.2 12.6 18.3 62.1 0.0 7.8 36.0 20.9
# patients 4.2 4.5 5.0 5.5 5.5 11.3
CRM 2 0.0 0.9 8.4 24.7 30.6 35.4 0.0 7.5 36.0 37.0
# patients 3.8 4.0 6.4 8.1 7.1 6.6
EM-CRM 2 0.0 1.0 9.5 25.6 31.8 32.1 0.0 7.3 36.0 20.9
# patients 4.1 4.1 7.0 8.3 6.9 5.5
CRM 3 0.0 1.3 8.7 26.1 34.5 29.4 0.0 7.4 36.0 37.0
# patients 3.8 4.2 6.3 8.5 7.8 5.5
EM-CRM 3 0.0 1.4 10.1 28.0 35.0 25.6 0.0 7.2 36.0 20.8
# patients 4.3 4.4 7.2 8.7 7.1 4.3
EM-CRMSEL 0.0 1.0 7.4 18.7 25.1 47.7 0.0 7.5 36.0 20.9
# patients 4.2 4.3 5.9 6.9 6.4 8.3
EM-CRMAVG 0.0 0.9 8.1 21.9 29.3 39.8 0.1 7.4 36.0 20.9
# patients 4.2 4.3 6.5 7.1 6.8 7.0
Scenario 4 0.20 0.30 0.40 0.50 0.60 0.70
CRM 1 25.4 50.8 17.7 4.0 0.4 0.0 1.7 10.8 35.5 36.6
# patients 13.4 12.5 6.0 2.6 0.8 0.2
EM-CRM 1 25.6 50.3 16.4 4.3 0.7 0.0 2.7 10.5 35.3 18.1
# patients 15.0 10.9 5.3 2.8 1.0 0.3
CRM 2 20.9 44.9 28.2 4.3 0.1 0.0 1.7 10.9 35.5 36.6
# patients 12.1 11.8 8.8 2.5 0.4 0.0
EM-CRM 2 21.1 43.8 27.8 4.1 0.2 0.0 3.0 10.6 35.2 18.1
# patients 13.6 10.7 8.0 2.3 0.5 0.1
CRM 3 22.1 48.2 24.2 3.7 0.2 0.0 1.6 10.7 35.5 36.6
# patients 12.8 12.3 7.8 2.2 0.3 0.0
EM-CRM 3 21.6 47.9 24.1 3.5 0.1 0.0 2.9 10.4 35.2 18.2
# patients 14.2 11.3 7.1 2.3 0.4 0.0
EM-CRMSEL 21.9 46.4 24.3 4.2 0.4 0.0 2.8 10.7 35.2 18.2
# patients 14.0 10.7 7.1 2.6 0.7 0.1
EM-CRMAVG 20.4 46.1 23.9 4.0 0.2 0.0 5.4 10.4 34.5 17.9
# patients 13.6 10.9 7.0 2.4 0.6 0.1
Scenario 5 0.08 0.12 0.20 0.30 0.40 0.50
CRM 1 0.1 5.3 22.5 35.5 25.6 11.0 0.1 10.0 36.0 37.0
# patients 4.2 4.9 6.9 8.1 6.7 5.0
EM-CRM 1 0.1 6.0 21.1 34.4 25.6 12.7 0.1 9.7 36.0 20.5
# patients 4.9 5.2 6.6 7.6 6.6 5.0
CRM 2 0.0 1.3 20.9 49.1 24.3 4.3 0.0 9.3 36.0 37.0
# patients 4.2 4.2 8.4 11.3 6.0 2.0
EM-CRM 2 0.0 1.7 21.8 47.6 24.5 4.3 0.1 9.0 36.0 20.4
# patients 4.7 4.4 9.0 10.3 5.7 1.9
CRM 3 0.1 1.9 22.0 49.3 23.9 2.9 0.0 9.1 36.0 37.0
# patients 4.2 4.4 8.5 11.2 6.2 1.4
EM-CRM 3 0.1 2.6 22.5 48.1 23.6 3.1 0.1 8.8 36.0 20.4
# patients 5.0 4.9 8.9 10.4 5.5 1.4
EM-CRMSEL 0.1 2.0 20.0 46.0 25.3 6.5 0.1 9.3 36.0 20.4
# patients 4.9 4.6 7.8 9.5 6.3 2.8
EM-CRMAVG 0.1 2.0 20.1 45.2 27.4 5.0 0.3 9.1 35.9 20.3
# patients 4.9 4.7 8.2 9.3 6.3 2.4
Scenario 6 0.05 0.10 0.30 0.50 0.60 0.70
CRM 1 0.1 23.7 54.9 19.6 1.7 0.0 0.0 10.9 36.0 37.0
# patients 3.8 8.4 12.5 7.8 2.7 0.8
EM-CRM 1 0.4 27.1 47.9 22.0 2.3 0.1 0.0 10.9 36.0 20.5
# patients 4.4 8.9 10.5 7.6 3.5 1.1
CRM 2 0.0 9.0 70.1 20.2 0.7 0.0 0.0 10.9 36.0 37.0
# patients 3.7 5.7 16.4 8.4 1.5 0.2
EM-CRM 2 0.1 8.4 69.6 21.1 0.8 0.0 0.0 10.8 36.0 20.4
# patients 4.2 6.4 15.0 8.2 1.9 0.3
CRM 3 0.0 9.8 69.8 19.7 0.7 0.0 0.0 10.8 36.0 37.0
# patients 3.7 6.1 16.4 8.2 1.5 0.1
EM-CRM 3 0.0 9.3 68.0 21.9 0.8 0.0 0.0 10.6 36.0 20.4
# patients 4.2 6.8 15.1 8.1 1.6 0.2
EM-CRMSEL 0.0 9.8 68.3 20.9 0.9 0.1 0.0 10.9 36.0 20.5
# patients 4.2 6.9 14.2 8.1 2.3 0.5
EM-CRMAVG 0.0 11.0 66.0 22.0 0.9 0.0 0.1 10.8 36.0 20.5
# patients 4.2 6.9 14.1 7.9 2.5 0.4
Scenario 7 0.02 0.03 0.04 0.05 0.30 0.50
CRM 1 0.0 0.0 1.4 15.9 46.2 36.5 0.0 9.8 36.0 37.0
# patients 3.2 3.0 3.1 4.7 8.1 13.8
EM-CRM 1 0.0 0.0 2.0 14.1 43.2 40.7 0.0 9.6 36.0 23.9
# patients 3.4 3.1 3.2 4.8 8.1 13.2
CRM 2 0.0 0.0 0.0 7.0 66.3 26.7 0.0 9.1 36.0 37.0
# patients 3.2 3.0 3.1 4.5 12.1 10.0
EM-CRM 2 0.0 0.0 0.0 6.1 65.3 28.5 0.0 8.8 36.0 23.9
# patients 3.3 3.0 3.3 5.0 11.9 9.4
CRM 3 0.0 0.0 0.0 5.9 70.0 24.1 0.0 8.9 36.0 37.0
# patients 3.2 3.0 3.1 4.5 13.3 8.9
EM-CRM 3 0.0 0.0 0.0 4.6 69.5 25.9 0.0 8.6 36.0 23.9
# patients 3.3 3.0 3.3 5.0 13.0 8.3
EM-CRMSEL 0.0 0.0 0.0 5.3 68.9 25.8 0.0 8.9 36.0 23.9
# patients 3.4 3.0 3.1 4.9 12.2 9.4
EM-CRMAVG 0.0 0.0 0.1 5.8 65.9 28.2 0.0 9.0 36.0 23.9
# patients 3.4 3.0 3.3 4.7 11.5 10.1
Scenario 8 0.50 0.60 0.70 0.80 0.85 0.90
CRM 1 18.5 0.1 0.0 0.0 0.0 0.0 81.4 9.5 18.7 21.8
# patients 17.5 1.0 0.2 0.0 0.0 0.0
EM-CRM 1 16.3 0.1 0.0 0.0 0.0 0.0 83.6 8.8 17.3 9.4
# patients 15.7 1.2 0.3 0.1 0.0 0.0
CRM 2 16.7 0.2 0.0 0.0 0.0 0.0 83.1 9.4 18.4 21.5
# patients 17.0 1.2 0.2 0.0 0.0 0.0
EM-CRM 2 14.0 0.2 0.0 0.0 0.0 0.0 85.8 8.6 16.7 9.1
# patients 15.0 1.4 0.3 0.0 0.0 0.0
CRM 3 18.7 0.1 0.0 0.0 0.0 0.0 81.2 9.4 18.6 21.7
# patients 17.4 1.1 0.2 0.0 0.0 0.0
EM-CRM 3 14.8 0.1 0.0 0.0 0.0 0.0 85.1 8.7 17.0 9.2
# patients 15.5 1.2 0.3 0.0 0.0 0.0
EM-CRMSEL 14.8 0.2 0.0 0.0 0.0 0.0 85.1 8.6 16.8 9.2
# patients 15.1 1.3 0.3 0.1 0.0 0.0
EM-CRMAVG 10.6 0.1 0.0 0.0 0.0 0.0 89.3 7.4 14.4 8.3
# patients 12.9 1.2 0.3 0.0 0.0 0.0