Question

1. A researcher wishes to test the interactive effects of three immunotherapies in combination with three diets and four exercise regimes on cancer patients.
   1. How many possible treatment combinations can patients be subjected to?
   2. If the researcher wishes to have 50 replicates per treatment combination, how many patients must be recruited into the study?
2. Two hundred cancer patients in a drug trial were classified by gender and stage:

3. 	Stage I	Stage II	Stage III
   Female	25	15	20
   Male	50	45	45

   a.   If F is the event that a patient is female and I is the event that a patient is in stage I, are F and I independent? Show why or why not.

   b.   If M is the event that a patient is male and II is the event that a patient is in stage II, are M and II independent? Show why or why not.

Answer 1

1.

a) Total number of possible treatment combinations = ( 3 x 3 x 4) = 36

b) 50 replicates per combination , so total nukber of patients needed = ( 50 x 36) = 1800

2.

We complete the table as :

  

	Stage I	Stage II	Stage III	Total
Female	25	15	20	60
Male	50	45	45	140
total	75	60	65	200

Two events A and B is said to be independent , if

  

a) note that P(F) = 60/200

P( I) = 75/200

and P( F I ) = 25/200

But   

So, F and I are not independent.

b) Similarly :

P(M) = 140/200 ; P( II ) = 60/200

and P (M II ) = 45/200

But

SO, M and II are not independent.