@booklet {davidazriel-ooaibrtiadrn2011,
	title = {On Optimal Allocation in Binary Response Trials; Is Adaptive Design Really Necessary?},
	howpublished = {Discussion Papers},
	year = {2011},
	month = {3},
	abstract = {We consider the classical problem of selecting the best of two treatments in clinical trials\&nbsp;with binary response. The target is to find the design that maximizes the power of the relevant\&nbsp;test. Many papers use a normal approximation to the power function and claim that Neyman\&nbsp;allocation that assigns subjects to treatment groups according to the ratio of the responses{\textquoteright}\&nbsp;standard deviations, should be used. As the standard deviations are unknown, an adaptive\&nbsp;design is often recommended. The asymptotic justification of this approach is arguable, since\&nbsp;it uses the normal approximation in tails where the error in the approximation is larger than\&nbsp;the estimated quantity. We consider two different approaches for optimality of designs that are\&nbsp;related to Pitman and Bahadur definitions of relative efficiency of tests. We prove that the\&nbsp;optimal allocation according to the Pitman criterion is the balanced allocation and that the\&nbsp;optimal allocation according to the Bahadur approach depends on the unknown parameters.\&nbsp;Exact calculations reveal that the optimal allocation according to Bahadur is often close to\&nbsp;the balanced design, and the powers of both are comparable to the Neyman allocation for\&nbsp;small sample sizes and are generally better for large experiments. Our findings have important\&nbsp;implications to the design of experiments, as the balanced design is proved to be optimal or\&nbsp;close to optimal and the need for the complications involved in following an adaptive design for\&nbsp;the purpose of increasing the power of tests is therefore questionable.},
	url = {/files/dp568.pdf},
	author = {David Azriel, Micha Mandel, and Micha Mandel and Yosef Rinott}
}
