背景:经验法则,即通过每个案例获得4个以上的控件,在统计能力上几乎没有收获,基于1型误差α=0.05。然而,评估数千或数百万关联的关联研究使用较小的α,并且可能可以获得丰富的控制。我们调查功率增益,和p值的减少,当每个病例增加超过4个控制时,小α。
方法:我们计算功率,预期p值的中位数,和最小可检测比值比(OR),作为控件/案例数量的函数,随着α的减少。
结果:随着α的减小,在每个病例的控制比例下,功率的增加大于α=0.05。对于10-6和10-9之间的α(典型的数千或数百万协会),从每箱4个控制增加到每箱10-50个控制增加功率。例如,1个对照/病例的功率=0.2(α=5×10-8)的研究具有4个对照/病例的功率=0.65,但是10个控件/案例的功率=0.78,而50个控件/案例的功率=0.84。Forsituationswhereobtainingmorethan4controlspercaseprovidessmallincreasesinpowerthrough0.9(atsmallα),预期的p值可以下降到低于α的数量级。从1个对照/病例增加到4个对照/病例,将最小可检测OR降低20.9%,从4到50个对照/病例减少了9.7%,无论α如何,结果都适用,因此也适用于“常规”α=0.05流行病学。
结论:在小α,与4个控件/案例相比,招募10个或更多的控制/案例可以增加力量,将预期p值降低1-2个数量级,并有意义地降低最小可检测OR。随着病例数量的增加,增加控制/病例比率的这些好处也会增加,虽然获益量取决于暴露频率和真实OR。只要控制与案例相当,我们的研究结果表明,在大规模关联研究中,可比较对照的共享程度更高.
The rule of thumb that there is little gain in statistical power by obtaining more than 4 controls per
case, is based on type-1 error α = 0.05. However, association studies that evaluate thousands or millions of associations use smaller α and may have access to plentiful controls. We investigate power gains, and reductions in p-values, when increasing well beyond 4 controls per
case, for small α.
We calculate the power, the median expected p-value, and the minimum detectable odds-ratio (OR), as a function of the number of controls/case, as α decreases.
As α decreases, at each ratio of controls per
case, the increase in power is larger than for α = 0.05. For α between 10-6 and 10-9 (typical for thousands or millions of associations), increasing from 4 controls per case to 10-50 controls per
case increases power. For example, a study with power = 0.2 (α = 5 × 10-8) with 1 control/case has power = 0.65 with 4 controls/
case, but with 10 controls/
case has power = 0.78, and with 50 controls/
case has power = 0.84. For situations where obtaining more than 4 controls per case provides small increases in power beyond 0.9 (at small α), the expected p-value can decrease by orders-of-magnitude below α. Increasing from 1 to 4 controls/case reduces the minimum detectable OR toward the null by 20.9%, and from 4 to 50 controls/case reduces by an additional 9.7%, a result which applies regardless of α and hence also applies to \"regular\" α = 0.05 epidemiology.
At small α, versus 4 controls/case, recruiting 10 or more controls/cases can increase power, reduce the expected p-value by 1-2 orders of magnitude, and meaningfully reduce the minimum detectable OR. These benefits of increasing the controls/case ratio increase as the number of cases increases, although the amount of benefit depends on exposure frequencies and true OR. Provided that controls are comparable to cases, our findings suggest greater sharing of comparable controls in large-scale association studies.