Introductory Biostatistics

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 Šf 0 : 53 þ 3 ð 0 : 5 Þ^3 þ 3 ð 0 : 5 Þ^3 ½ 1 
ð 0 : 5 Þ^3 Šg¼ 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

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