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. Author manuscript; available in PMC: 2019 May 16.
Published in final edited form as: J R Stat Soc Ser C Appl Stat. 2018 Mar 15;68(2):461–474. doi: 10.1111/rssc.12271

Table 3.

Simulation Truth and Results. πDTR = true probability of death within 100 days for each combination of disease type (r), dose level (d), disease bulk (Z), with π̄ (Z) = the fixed safety threshold. Unsafe doses are given in grey. ŪTR = true expected utility for each (r, d, Z). Optimal doses are underlined.

Bulk (→) LBD (Z = 0) HBD (Z = 1)
Types (↓) Dose (→) d = 1 d = 2 d = 3 π̄D d = 1 d = 2 d = 3 π̄D
Scenario 1 CLL (r = 1)
πDTR
 0.02 0.02 0.02 0.15 0.10 0.10 0.10 0.30
ŪTR 46.32 46.32 46.32 44.04 44.04 44.04
Pr(Stop) 0.00 0.00 0.00 0.00 0.00 0.00
Pr(Select) 0.33 0.37 0.30 0.33 0.34 0.33
ALL (r = 2)
πDTR
 0.10 0.10 0.10 0.20 0.25 0.25 0.25 0.40
ŪTR 50.52 50.52 50.52 37.97 37.97 37.97
Pr(Stop) 0.00 0.01 0.00 0.03 0.03 0.02
Pr(Select) 0.33 0.35 0.32 0.32 0.36 0.33
NHL (r = 3)
πDTR
 0.05 0.05 0.05 0.20 0.15 0.15 0.15 0.40
ŪTR 49.18 49.18 49.18 38.35 38.35 38.35
Pr(Stop) 0.00 0.00 0.00 0.00 0.00 0.00
Pr(Select) 0.33 0.34 0.33 0.35 0.31 0.34
Scenario 2 CLL (r = 1)
πDTR
 0.02 0.45 0.60 0.15 0.04 0.70 0.84 0.30
ŪTR 42.34 22.86 16.00 39.73 9.49 4.63
Pr(Stop) 0.00 0.89 0.97 0.00 0.98 1.00
Pr(Select) 1.00 0.00 0.00 1.00 0.00 0.00
ALL (r = 2)
πDTR
 0.40 0.60 0.05 0.20 0.64 0.84 0.10 0.40
ŪTR 23.81 15.82 40.41 10.99 4.62 36.02
Pr(Stop) 0.67 0.92 0.00 0.81 0.98 0.00
Pr(Select) 0.00 0.00 1.00 0.00 0.00 1.00
NHL (r = 3)
πDTR
 0.65 0.05 0.35 0.20 0.88 0.10 0.58 0.40
ŪTR 14.03 40.47 26.31 3.46 36.08 13.26
Pr(Stop) 0.95 0.00 0.55 1.00 0.00 0.68
Pr(Select) 0.00 1.00 0.00 0.00 1.00 0.00
Scenario 3 CLL (r = 1)
πDTR
 0.42 0.38 0.37 0.15 0.66 0.62 0.60 0.30
ŪTR 40.33 44.40 44.55 20.71 24.52 24.81
Pr(Stop) 0.88 0.85 0.82 0.96 0.95 0.94
Pr(Select) 0.07 0.11 0.13 0.03 0.05 0.05
ALL (r = 2)
πDTR
 0.52 0.58 0.65 0.20 0.77 0.83 0.88 0.40
ŪTR 33.99 29.43 24.52 14.34 11.01 7.57
Pr(Stop) 0.93 0.96 0.98 0.99 0.99 1.00
Pr(Select) 0.06 0.03 0.01 0.01 0.01 0.00
NHL (r = 3)
πDTR
 0.40 0.42 0.45 0.20 0.64 0.67 0.70 0.40
ŪTR 42.49 40.21 38.79 22.61 20.32 18.95
Pr(Stop) 0.73 0.77 0.84 0.85 0.87 0.94
Pr(Select) 0.19 0.16 0.07 0.12 0.11 0.04
Scenario 4 CLL (r = 1)
πDTR
 0.01 0.10 0.25 0.15 0.01 0.11 0.27 0.30
ŪTR 48.99 58.91 45.84 38.03 24.74 14.45
Pr(Stop) 0.00 0.00 0.26 0.00 0.00 0.13
Pr(Select) 0.04 0.95 0.01 1.00 0.00 0.00
ALL (r = 2)
πDTR
 0.01 0.09 0.27 0.20 0.01 0.10 0.29 0.40
ŪTR 48.82 58.66 43.95 37.54 26.47 14.55
Pr(Stop) 0.00 0.00 0.14 0.00 0.00 0.05
Pr(Select) 0.02 0.98 0.00 1.00 0.00 0.00
NHL (r = 3)
πDTR
 0.01 0.08 0.30 0.20 0.01 0.09 0.33 0.40
ŪTR 48.87 58.22 40.45 40.28 26.92 11.70
Pr(Stop) 0.00 0.00 0.29 0.00 0.00 0.12
Pr(Select) 0.01 0.99 0.00 1.00 0.00 0.00
Scenario 5 CLL (r = 1)
πDTR
 0.01 0.09 0.30 0.15 0.01 0.12 0.38 0.30
ŪTR 44.30 33.82 22.05 41.40 27.18 14.33
Pr(Stop) 0.00 0.00 0.48 0.00 0.00 0.44
Pr(Select) 1.00 0.00 0.00 1.00 0.00 0.00
ALL (r = 2)
πDTR
 0.12 0.03 0.18 0.20 0.16 0.04 0.23 0.40
ŪTR 30.68 40.15 27.96 23.62 35.88 20.52
Pr(Stop) 0.00 0.00 0.02 0.00 0.00 0.01
Pr(Select) 0.00 1.00 0.00 0.00 0.99 0.00
NHL (r = 3)
πDTR
 0.10 0.15 0.01 0.20 0.13 0.20 0.01 0.40
ŪTR 32.73 28.73 44.09 26.24 21.60 41.22
Pr(Stop) 0.00 0.01 0.00 0.00 0.00 0.00
Pr(Select) 0.00 0.00 1.00 0.00 0.00 1.00
Scenario 6 CLL (r = 1)
πDTR
 0.35 0.03 0.13 0.15 0.75 0.10 0.37 0.30
ŪTR 41.74 59.80 57.69 14.53 55.48 40.90
Pr(Stop) 0.76 0.00 0.09 0.99 0.00 0.34
Pr(Select) 0.00 0.56 0.44 0.00 0.99 0.01
ALL (r = 2)
πDTR
 0.08 0.45 0.02 0.20 0.24 0.86 0.06 0.40
ŪTR 57.75 34.95 57.83 47.19 7.81 55.07
Pr(Stop) 0.00 0.82 0.00 0.02 0.99 0.00
Pr(Select) 0.80 0.00 0.20 0.04 0.00 0.96
NHL (r = 3)
πDTR
 0.05 0.10 0.30 0.20 0.16 0.29 0.70 0.40
ŪTR 59.50 57.18 46.28 52.57 44.10 18.84
Pr(Stop) 0.00 0.01 0.51 0.00 0.03 0.91
Pr(Select) 0.53 0.47 0.01 0.89 0.11 0.00