Question

9.40 Experimental design. The clinical trial was a com- pletely randomized experiment that assigned 240 patients at random among four treatments as follows: ANTIBIOTIC PILL PLACEBO PILL 53 64 Steroid spray Placebo spray 60 63 (a) Outline the design of the experiment. (b) How will you label the 240 subjects? (c) Explain briefly how you would do the random assignment of patients to treatments. Assign the first five patients who will receive the first treatment.

Can skip A. Mainly need help with B & C.

Thank you!

Answer 1

(b) We basically have two group of treatments: The 'spray' group and the 'pill' group. Let

Each of these groups have two levels: A non-placebo (steroid spray for spray group and antibiotic pill for pill group) and a placebo. Lets call them 1st and 2nd group respectively.

Then, we can label the responses as: y_{ijk}, which denotes the response of the kth individual who recieved the treatment from ith spray group and jth pill group.

For eg. The y_{123} denotes the response of the 3rd patient among those who were given steroid spray (1st spray group) and a placebo pill (2nd pill group).

(c)

The following method could work:

-Label the patients 1,...,240

-Draw a random sample without replacement of size 53 and assign them the first treatment. Out of the remaining 240-53 = 187, draw a random sample of size 64 and assign the second treatment and so on..

We draw 53 sized SRSWOR from 1 to 240, using the following R code:

sample(1:240,53,replace=FALSE)

The first 5 entries of the vector we got are: 86 72 162 2 31

Thus the patients labelled 2, 31,72,86 and 162 are the first five patients to get the first treatment. Their responses will be labelled y_{111},y_{112},...,y_{115} respectively.