2022 Volume 145, p101-111
To analyze distribution of "dramatic", large treatment effects.
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 ratiomin (ORmin)]. In default analysis using all data at ORmin ≥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 ORmin ≥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.
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