Search

In a clinical comparison of responses to two treatments, patients are admitted sequentially and given one of the two treatments. The allocation is determined randomly, to decrease the possibility of personal bias in the selection of subjects for the test. To balance the assignments, the probability of receiving one treatment is a function of the proportion of patients previously assigned to that treatment. A local limit theorem for the distribution of the number of patients assigned to the first treatment is developed. Let V(,i) and W(,i) denote the i('th) patient's responses. Assume that (V(,i),W(,i)), i (GREATERTHEQ) 1, are independent and identically distributed, and independent of the allocation. Under additional conditions on (V(,i),W(,i)) and the allocation rule, it is shown that, in a Sequential Probability Ratio Test, the allocation procedure doesn't affect the error probabilities, but it does affect the distribution of the sample size. This analysis is extended and a similar result is derived in the case that V(,1) and W(,1) are from a one-parameter exponential family and we are testing if V(,1) and W(,1) have the same distribution.