1. Refer to the example of the "minimization" method of adaptive stratification discussed in class. The randomization of patients was stratified by performance status, age, disease-free interval and type of metastatic lesion. Suppose a total of 40 patients have been given each treatment (A and B) (80 total) and their distributions by treatment group and levels of the prognostic factors are as shown in the notes (see slide 38 of lecture 4).

a, Let "lack of balance" be measured using the range as defined in the notes. Suppose the rule for patient treatment assignment is as follows:

i) Assign the next treatment with prob(A)=prob(B)=1/2 if B(A) and B(B), the out-of-balance functions for treatment A and B, are equal;

ii) If B(A)

iii) If B(A)>B(B) assign B with probability 4/5.

Describe a procedure for generating two randomization schedules for this study, one for use when B(A)=B(B) and one to use when they are not equal. For each schedule generate 10 treatment assignments using your proposed procedure. These assignments will be used for the next group of patients enrolled.

b, Below is a table contains the characteristics of the first 80 patients randomized.

Factor Level A B

Performance status Ambulatory 30 31

Non-ambulatory 10 9

Age <50 18 17

>50 22 23

Disease-free interval <2 31 32

>2 9 8

Dominant metastatic Visceral 19 21

lesion Osseous 8 7

Soft tissue 13 12

The next patient (No. 81) enrolled had the following characteristics:

Accession Performance Disease-Free

No. Status Age Interval Lesion

81 Ambulatory <50 >2 Osseous

Calculate the out-of-balance function as described above and indicate which treatment each of these patients would receive based on your randomization schedules.