Question

Clinical Trials are underway to get an H1N1 (swine flu) vaccination to the public as quickly as possible. In one trial at Vanderbilt University Hospital, patients are randomly assigned to one of the four treatment groups:

1) Placebo

2) Experimental 1: 7.5 mcg of hemagglutinin

3) Experimental 2: 15 mcg of hemagglutinin

4) Experimental 3: 30 mcg of hemagglutinin

There are 200 patients in the trial; 20 are randomly assigned to the Placebo group and 60 are randomly assigned to each of the experimental groups. Patients will be monited for 6 months to see if they contract H1N1. Physicians in charge of the trial have conjectured that

15 % of the placebo patients will contract H1N1 in 6 months

8 % of the Experimental 1 patients will contract H1N1 in 6 months

4 % of the Experimental 2 patients will contract H1N1 in 6 months

1 % of the Experimental 3 patients will contract H1N1 in 6 months

a) Suppose that a patient in the trial is selected at random. What is the probability that the patient contracts H1N1 within 6 months?

b) Suppose that a patient contracts H1N1 within 6 months. What is the probability that this patient was assigned to the placebo group?

c) Suppose that a patient does not contract H1N1 within 6 months. What is the probability that this patient was assigned to the Experimental 3 group?

Answer 1

a)

	Number of patient	Percent of contract H1N1	Total number of contract H1N1
Placebo	20	15%	3
Exp 1	60	8%	4.8
Exp 2	60	4%	2.4
Exp 3	60	1%	0.6

The probability that the selected patient contracts H1N1 within 6 months is,

b)

Let 'B' is the event that patient contracts H1N1 within 6 months and 'A' is the event that this patient was assigned to the placebo group

Hence the required probability is obtained using condition probability law such that,

Where denominator P(B), is the probability that a patient contracts H1N1 within 6 months which is obtained in part (a)

And numerator is the probability that a patient who contract H1N1 was assigned to the placebo group.

( 10% patient assigned to Placebo and 30% assigned to each of the three experiment)

C)

Let 'D' is the event that patient doesnot contracts H1N1 within 6 months and 'C' is the event that this patient was assigned to the Experiment 3 group

Hence the required probability is obtained using condition probability law such that,

Where denominator P(D), is the probability that a patient doesnot contracts H1N1 within 6 months such that,

And numerator is the probability that a patient who doesnot contract H1N1 was assigned to the experiment 3 group.