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. Author manuscript; available in PMC: 2023 Jan 27.
Published in final edited form as: Stat Methods Med Res. 2022 Feb 6;31(4):579–593. doi: 10.1177/09622802211013578

Table 4.

Mean (SD) of overall mixture effect estimators in simulation scenarios with low signal (R2 = 0.1)

Method Scenario 1 Scenario 2 Scenario 3
ρ = 0.2 ρ = 0.8 ρ = 0.2 p = 0.8 Observed Σ
TRUTH 30 30 8 8 27
Preserved Type I error
 WQS - data splitting 25.9 (6.7) 29.1 (6.8) 8.6 (2.4) 7.9 (1.9) 24.7 (6.4)
 Modified WQS
  L1 - data splitting 17.6 (7.9) 27.2 (6.7) 7.0 (2.5) 7.5 (1.9) 20.8 (6.6)
  L1 - permutation test 32.0 (5.9) 32.0 (5.2) 9.0 (1.8) 8.5 (1.5) 27.2 (5.4)
  L2 - data splitting 26.3 (7.0) 29.0 (6.9) 8.3 (2.4) 7.9 (1.9) 24.2 (6.3)
  L2 - permutation test 34.5 (5.0) 32.0 (5.2) 9.8 (1.7) 8.6 (1.5) 27.7 (4.9)
Inflated Type I error
 WQS - no data splitting 34.5 (5.0) 32.3 (5.2) 10.0 (1.7) 8.6 (1.5) 28.6 (4.8)