Table 1 Mean squared error (MSE) of the causal effect estimates from the competing methods on the NMR metabolite and blood cell trait data.

From: Selecting likely causal risk factors from high-throughput experiments using multivariable Mendelian randomization

 

Setting A

Setting B

\({R}^{2}\):

0.1

0.3

0.5

0.1

0.3

0.5

Scenario 1:

IVW

0.6727

0.1675

0.0784

0.5949

0.1619

0.0629

Lars

0.1292

0.0447

0.0298

0.1559

0.0648

0.0372

Lasso

0.0604

0.0289

0.0162

0.1046

0.0503

0.0307

Elastic Net

0.0673

0.0300

0.0162

0.1161

0.0480

0.0287

MR-BMA

0.0340

0.0175

0.0105

0.0534

0.0368

0.0306

Best model

0.0717

0.0320

0.0156

0.0921

0.0514

0.0376

Scenario 2:

IVW

22.9516

6.0594

2.6257

23.2495

5.7715

2.4802

Lars

0.0354

0.0367

0.0094

0.0321

0.0212

0.0143

Lasso

0.0064

0.0047

0.0039

0.0105

0.0086

0.0074

Elastic Net

0.0064

0.0044

0.0034

0.0098

0.0078

0.0067

MR-BMA

0.0051

0.0039

0.0032

0.0088

0.0076

0.0063

Best model

0.0114

0.0081

0.0061

0.0150

0.0121

0.0096

Scenario 3:

IVW

1.6200

0.4272

0.1742

2.3140

0.6208

0.2566

Lars

0.3461

0.1151

0.0482

0.5892

0.1669

0.0844

Lasso

0.0161

0.0067

0.0040

0.0378

0.0225

0.0166

Elastic Net

0.0168

0.0074

0.0044

0.0451

0.0224

0.0169

BMA

0.0066

0.0034

0.0019

0.0235

0.0165

0.0149

Best model

0.0128

0.0051

0.0027

0.0444

0.0242

0.0177

  1. We mark in bold font the lowest MSE in each experimental setting. Scenario 1: NMR metabolites, d = 12 risk factors, Scenario 2: NMR metabolites, d = 92 risk factors, and Scenario 3: blood cell traits, d = 33 risk factors. Setting A includes four true causal risk factors which increase the risk and Setting B includes eight true causal risk factors of which half are protective and the other half increases the risk
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