Phase I of a Clinical Trial A clinical test on humans of a new drug is normally
ID: 3208233 • Letter: P
Question
Phase I of a Clinical Trial A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of healthy volunteers. For example, a phase I test of bexarotene involved only 14 subjects. Assume that we want to treat 14 healthy humans with this new drug and we have 16 suitable volunteers available. If the subjects are selected and treated in sequence, so that the trial is discontinued if anyone displays adverse effects, how many different sequential arrangements are possible if 14 people are selected from the 16 that are available? If 14 subjects are selected from the 16 that are available, and the 14 selected subjects are all treated at the same time, how many different treatment groups are possible? If 14 subjects are randomly selected and treated at the same time, what is the probability of selecting the 14 youngest subjects?Explanation / Answer
a) the trial will stop when a subject displays adverse effect. This means the trial can stop after one subject or after two subjects or three subjects or after four subjects and so on, and it can be successful with also a possibility of 14 subjects not showing adverse effects.
Sequence for
1 subject = 16 ways (any of 16 can be tested and the trial stopped)
2 subjects = 16 (any of 16) * 15 (any of the remaining 15)
3 subjects = 16 (any of 16) * 15 (remaining 15) * 14 (remaining 14)
...
14 subjects = 16*15*14*13*12*10*9*8*7*6*5*4*3
Adding these 14 terms you will get an answer 15028459777216
b) 14 to be selected from 16, hence 16 C 4 which is equal to 16 C 2 which equals 120. 120 groups are possible
c) Probability of selecting 14 youngest out of 16 = Count of sequence having 14 youngest/ Count of sequence of selecting 14 out of 16
that is 1/120 which equals 0.0083
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