Department of Mathematics, Indiana University Northwest, Gary, IN.
Beckman Research Institute, City of Hope Institution, Duarte, CA; Department of Computational and Quantitative Medicine, City of Hope Institution, Duarte, CA; Division of Health Analytics; Evidence-based Medicine and Comparative Effectiveness Research, 1500 East Duarte Road, Duarte, CA.
J Clin Epidemiol. 2022 May;145:101-111. doi: 10.1016/j.jclinepi.2022.01.016. Epub 2022 Jan 25.
To analyze distribution of "dramatic", large treatment effects.
STUDY DESIGN & SETTING: Pareto distribution modeling of previously reported cohorts of 3,486 randomized trials (RCTs) that enrolled 1,532,459 patients and 730 non-randomized studies (NRS) enrolling 1,650,658 patients.
We calculated the Pareto α parameter, which determines the tail of the distribution for various starting points of distribution [odds ratio (OR)]. In default analysis using all data at OR ≥1, Pareto distribution fit well to the treatment effects of RCTs favoring the new treatments (P = 0.21, Kolmogorov-Smirnov test) with best α = 2.32. For NRS, Pareto fit for OR ≥2 with best α = 1.91. For RCTs, theoretical 99th percentile OR was 32.7. The actual 99th percentile OR was 25; which converted into relative risk (RR) = 7.1. The maximum observed effect size was OR = 121 (RR = 11.45). For NRS, theoretical 99th percentile was OR = 315. The actual 99th percentile OR was 294 (RR = 13). The maximum observed effect size was OR = 1473 (RR = 66).
The effects sizes observed in RCTs and NRS considerably overlap. Large effects are rare and there is no clear threshold for dramatic effects that would obviate future RCTs.
分析“显著”、大治疗效果的分布情况。
对之前报道的 3486 项随机试验（RCT）队列和 730 项非随机研究（NRS）进行帕累托分布建模，这些研究共纳入了 1532459 名患者和 1650658 名患者。
我们计算了帕累托α参数，该参数确定了分布的尾部，用于各种分布起始点的比值比（OR）。在使用所有 OR≥1 的数据进行默认分析时，帕累托分布很好地拟合了支持新治疗方法的 RCT 治疗效果（P=0.21，柯尔莫哥洛夫-斯米尔诺夫检验），最佳α=2.32。对于 NRS，帕累托拟合 OR≥2，最佳α=1.91。对于 RCT，理论 99 百分位 OR 为 32.7。实际 99 百分位 OR 为 25；转换为相对风险（RR）为 7.1。最大观察到的效应大小为 OR=121（RR=11.45）。对于 NRS，理论 99 百分位为 OR=315。实际 99 百分位 OR 为 294（RR=13）。最大观察到的效应大小为 OR=1473（RR=66）。
RCT 和 NRS 中观察到的效应大小有很大的重叠。大效应是罕见的，没有明显的阈值可以排除未来的 RCT。
