Department of Psychiatry and Behavioral Sciences, Stanford University School of Medicine, Stanford, CA 94305-5723, USA.
Mol Psychiatry. 2012 Jan;17(1):108-14. doi: 10.1038/mp.2010.117. Epub 2010 Nov 9.
Advances in high-throughput biology and computer science are driving an exponential increase in the number of hypothesis tests in genomics and other scientific disciplines. Studies using current genotyping platforms frequently include a million or more tests. In addition to the monetary cost, this increase imposes a statistical cost owing to the multiple testing corrections needed to avoid large numbers of false-positive results. To safeguard against the resulting loss of power, some have suggested sample sizes on the order of tens of thousands that can be impractical for many diseases or may lower the quality of phenotypic measurements. This study examines the relationship between the number of tests on the one hand and power, detectable effect size or required sample size on the other. We show that once the number of tests is large, power can be maintained at a constant level, with comparatively small increases in the effect size or sample size. For example at the 0.05 significance level, a 13% increase in sample size is needed to maintain 80% power for ten million tests compared with one million tests, whereas a 70% increase in sample size is needed for 10 tests compared with a single test. Relative costs are less when measured by increases in the detectable effect size. We provide an interactive Excel calculator to compute power, effect size or sample size when comparing study designs or genome platforms involving different numbers of hypothesis tests. The results are reassuring in an era of extreme multiple testing.
高通量生物学和计算机科学的进步正在推动基因组学和其他科学领域中假设检验数量的指数级增长。使用当前基因分型平台的研究通常包含一百万个或更多的测试。除了货币成本之外，由于需要进行多次测试校正以避免大量假阳性结果，这种增加还会带来统计成本。为了防止由此导致的效力损失，有人建议采用数万的样本量，但对于许多疾病来说，这可能不切实际，或者可能降低表型测量的质量。本研究考察了测试数量与效力、可检测的效应大小或所需样本量之间的关系。我们表明，一旦测试数量很大，效力就可以保持在一个恒定的水平，而效应大小或样本量的相对较小的增加即可实现。例如，在 0.05 的显着性水平下，与 100 万次测试相比，需要将样本量增加 13%，才能维持 1000 万次测试的 80%效力，而与单次测试相比，10 次测试则需要将样本量增加 70%。当以可检测的效应大小的增加来衡量时，相对成本较低。我们提供了一个交互式 Excel 计算器，用于在比较涉及不同数量假设检验的研究设计或基因组平台时计算效力、效应大小或样本量。在极端多重检验的时代，这些结果令人放心。
