School of Economics, Singapore Management University, 90 Stamford Road, 178903 Singapore, Singapore.
Stat Med. 2010 Nov 20;29(26):2743-56. doi: 10.1002/sim.4045.
Step-up procedures have been shown to be powerful testing methods in clinical trials for comparisons of several treatments with a control. In this paper, a determination of the optimal sample size for a step-up procedure that allows a pre-specified power level to be attained is discussed. Various definitions of power, such as all-pairs power, any-pair power, per-pair power and average power, in one- and two-sided tests are considered. An extensive numerical study confirms that square root allocation of sample size among treatments provides a better approximation of the optimal sample size relative to equal allocation. Based on square root allocation, tables are constructed, and users can conveniently obtain the approximate required sample size for the selected configurations of parameters and power. For clinical studies with difficulties in recruiting patients or when additional subjects lead to a significant increase in cost, a more precise computation of the required sample size is recommended. In such circumstances, our proposed procedure may be adopted to obtain the optimal sample size. It is also found that, contrary to conventional belief, the optimal allocation may considerably reduce the total sample size requirement in certain cases. The determination of the required sample sizes using both allocation rules are illustrated with two examples in clinical studies.
升阶程序已被证明是临床试验中比较几种治疗方法与对照的有力测试方法。本文讨论了一种确定升阶程序最优样本量的方法，该方法允许达到预定的功效水平。在单侧和双侧检验中，考虑了各种功效定义，如全对功效、任意对功效、每对功效和平均功效。广泛的数值研究证实，与均等分配相比，在治疗中对样本量进行平方根分配可以更好地逼近最优样本量。基于平方根分配，构建了表格，用户可以方便地获得所选参数和功效配置的近似所需样本量。对于招募患者困难的临床研究，或者当增加受试者会导致成本显著增加时，建议更精确地计算所需的样本量。在这种情况下，可以采用我们提出的程序来获得最优样本量。还发现，与传统观点相反，在某些情况下，最优分配可以大大减少总样本量要求。通过两个临床研究示例说明了使用两种分配规则确定所需样本量的情况。
