Empirical Type I error rates and power of DeLIVR over 100 runs with both correlated and uncorrelated pleiotropy. Gene: NT5DC2; Tests: “nonlinear” refers to (2.8), “robust” refers to (2.12)
. | Models . | . | DeLIVR . | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
. | No. of invalid IVs . | . | 0 . | . | 1 . | . | 2 . | . | 3 . | ||||
Horizontal pleiotropy . | Tests . | . | Nonlinear . | Robust . | . | Nonlinear . | Robust . | . | Nonlinear . | Robust . | . | nonlinear . | robust . |
Correlated and uncorrelated | Null | 0.03 | 0.07 | 0.84 | 0.07 | 0.99 | 0.03 | .96 | .05 | ||||
Linear | 0.01 | 0.03 | — | 0.08 | — | 0.09 | - | .06 | |||||
Quadratic | 0.74 | 0.52 | — | 0.60 | — | 0.47 | - | .34 | |||||
Cubic | 0.47 | 0.59 | — | 0.38 | — | 0.33 | - | .40 | |||||
Uncorrelated | Null | 0.04 | 0.08 | 0.86 | 0.06 | 0.88 | 0.07 | .98 | .07 | ||||
Linear | 0.02 | 0.06 | — | 0.01 | — | 0.06 | - | .02 | |||||
Quadratic | 0.80 | 0.57 | — | 0.62 | — | 0.51 | - | .27 | |||||
Cubic | 0.45 | 0.53 | — | 0.31 | — | 0.23 | - | .14 |
. | Models . | . | DeLIVR . | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
. | No. of invalid IVs . | . | 0 . | . | 1 . | . | 2 . | . | 3 . | ||||
Horizontal pleiotropy . | Tests . | . | Nonlinear . | Robust . | . | Nonlinear . | Robust . | . | Nonlinear . | Robust . | . | nonlinear . | robust . |
Correlated and uncorrelated | Null | 0.03 | 0.07 | 0.84 | 0.07 | 0.99 | 0.03 | .96 | .05 | ||||
Linear | 0.01 | 0.03 | — | 0.08 | — | 0.09 | - | .06 | |||||
Quadratic | 0.74 | 0.52 | — | 0.60 | — | 0.47 | - | .34 | |||||
Cubic | 0.47 | 0.59 | — | 0.38 | — | 0.33 | - | .40 | |||||
Uncorrelated | Null | 0.04 | 0.08 | 0.86 | 0.06 | 0.88 | 0.07 | .98 | .07 | ||||
Linear | 0.02 | 0.06 | — | 0.01 | — | 0.06 | - | .02 | |||||
Quadratic | 0.80 | 0.57 | — | 0.62 | — | 0.51 | - | .27 | |||||
Cubic | 0.45 | 0.53 | — | 0.31 | — | 0.23 | - | .14 |
Empirical Type I error rates and power of DeLIVR over 100 runs with both correlated and uncorrelated pleiotropy. Gene: NT5DC2; Tests: “nonlinear” refers to (2.8), “robust” refers to (2.12)
. | Models . | . | DeLIVR . | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
. | No. of invalid IVs . | . | 0 . | . | 1 . | . | 2 . | . | 3 . | ||||
Horizontal pleiotropy . | Tests . | . | Nonlinear . | Robust . | . | Nonlinear . | Robust . | . | Nonlinear . | Robust . | . | nonlinear . | robust . |
Correlated and uncorrelated | Null | 0.03 | 0.07 | 0.84 | 0.07 | 0.99 | 0.03 | .96 | .05 | ||||
Linear | 0.01 | 0.03 | — | 0.08 | — | 0.09 | - | .06 | |||||
Quadratic | 0.74 | 0.52 | — | 0.60 | — | 0.47 | - | .34 | |||||
Cubic | 0.47 | 0.59 | — | 0.38 | — | 0.33 | - | .40 | |||||
Uncorrelated | Null | 0.04 | 0.08 | 0.86 | 0.06 | 0.88 | 0.07 | .98 | .07 | ||||
Linear | 0.02 | 0.06 | — | 0.01 | — | 0.06 | - | .02 | |||||
Quadratic | 0.80 | 0.57 | — | 0.62 | — | 0.51 | - | .27 | |||||
Cubic | 0.45 | 0.53 | — | 0.31 | — | 0.23 | - | .14 |
. | Models . | . | DeLIVR . | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
. | No. of invalid IVs . | . | 0 . | . | 1 . | . | 2 . | . | 3 . | ||||
Horizontal pleiotropy . | Tests . | . | Nonlinear . | Robust . | . | Nonlinear . | Robust . | . | Nonlinear . | Robust . | . | nonlinear . | robust . |
Correlated and uncorrelated | Null | 0.03 | 0.07 | 0.84 | 0.07 | 0.99 | 0.03 | .96 | .05 | ||||
Linear | 0.01 | 0.03 | — | 0.08 | — | 0.09 | - | .06 | |||||
Quadratic | 0.74 | 0.52 | — | 0.60 | — | 0.47 | - | .34 | |||||
Cubic | 0.47 | 0.59 | — | 0.38 | — | 0.33 | - | .40 | |||||
Uncorrelated | Null | 0.04 | 0.08 | 0.86 | 0.06 | 0.88 | 0.07 | .98 | .07 | ||||
Linear | 0.02 | 0.06 | — | 0.01 | — | 0.06 | - | .02 | |||||
Quadratic | 0.80 | 0.57 | — | 0.62 | — | 0.51 | - | .27 | |||||
Cubic | 0.45 | 0.53 | — | 0.31 | — | 0.23 | - | .14 |
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