experience DLT, the trial is stopped. If one experiences DLT, a new
cohort of two patients is enrolled at the same dose, escalating to next-
higher dose only if no DLT is observed. The new design helps to
escalate a little easier; the resulting MTD would have a little higher
expected toxicity rate.
12.4 ½ 0 : 63 þ 3 ð 0 : 4 Þð 0 : 6 Þ^2 ð 0 : 6 Þ^3 f 0 : 53 þ 3 ð 0 : 5 Þ^3 þ 3 ð 0 : 5 Þ^3 ½ 1 ð 0 : 5 Þ^3 g¼ 0 :256.
12.5 z 1 b¼ 0 :364, corresponding to a power of 64%.
12.6 z 1 b¼ 0 :927, corresponding to a power of 82%.
12.7 z 1 b¼ 0 :690, corresponding to a power of 75%.
12.8 z 1 b¼ 0 :551, corresponding to a power of 71%.
12.9 d¼42 events and we need
N¼
ð 2 Þð 42 Þ
2 0 : 5 0 : 794
¼120 subjects
or 60 subjects in each group.
12.10 n¼
ð 1 : 96 Þ^2 ð 0 : 9 Þð 0 : 1 Þ
ð 0 : 05 Þ^2
¼139 subjects
If we do not use the 90% figure, we would need
nmax¼
ð 1 : 96 Þ^2 ð 0 : 25 Þ
ð 0 : 05 Þ^2
¼385 subjects
12.11 nmax¼
ð 1 : 96 Þ^2 ð 0 : 25 Þ
ð 0 : 1 Þ^2
¼99 subjects
12.12 nmax¼
ð 1 : 96 Þ^2 ð 0 : 25 Þ
ð 0 : 15 Þ^2
¼43 subjects
12.13 (a)With 95% confidence, we need
nmax¼
ð 1 : 96 Þ^2 ð 0 : 25 Þ
ð 0 : 01 Þ^2
¼9604 subjects
With 99% confidence, we need
nmax¼
ð 2 : 58 Þ^2 ð 0 : 25 Þ
ð 0 : 01 Þ^2
¼ 16 ;641 subjects
526 ANSWERS TO SELECTED EXERCISES