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Table 1 P-values from sample-wise and gene-wise robust tests on four datasets, before and after batch correction

From: Alternative empirical Bayes models for adjusting for batch effects in genomic studies

  

Sample-wise tests

Gene-wise tests

Dataset

ComBat

Mean

Variance

Skewness

Kurtosis

Mean

Variance

Skewness

Kurtosis

Bladder cancer

None

<0.0001

0.6495

0.0539

0.3149

<0.0001

0.3353

<0.0001

0.0012

 

Mean-only

0.9998

0.9557

0.1496

0.6236

0.2011

0.3618

<0.0001

0.0012

 

Mean/variance

1

0.8989

0.1826

0.2737

0.2538

0.9816

<0.0001

0.0012

Nitric oxide

None

0.1007

0.3565

0.1009

0.866

<0.0001

0.0005

<0.0001

0.9887

 

Mean-only

0.9997

0.577

0.9838

0.9485

0.4595

0.0042

<0.0001

0.9887

 

Mean/variance

1

0.982

0.9847

0.7013

0.7245

0.6219

<0.0001

0.9791

Oncogenic signature

None

0.0011

<0.0001

0.0001

0.0235

<0.0001

0.0001

<0.0001

0.5711

 

Mean/variance

1

0.7486

0.5553

0.9202

0.0363

0.8919

<0.0001

0.5711

Lung cancer

None

<0.0001

<0.0001

<0.0001

<0.0001

<0.0001

0.0106

<0.0001

0.4853

 

Mean/variance

1

0.9872

0.0003

0.9612

0.0016

0.9971

<0.0001

0.4853

  1. The four datasets have different degrees of batch effect. The bladder cancer dataset has differences in batch mean, but does not show any batch effect in the variance. Mean-only ComBat is sufficient to adjust this dataset as there is no need to adjust the variance. In the nitric oxide dataset, the gene-wise test reports significant differences in both the mean and the variance. The full mean/variance ComBat is necessary to remove batch effects in this data. The mean/variance ComBat cannot adjust the skewness or kurtosis. All four datasets exhibit certain levels of batch effect in the skewness and/or kurtosis, which may call for methods that adjust these higher order moments. Results comparing robust and non-robust F tests are summarized in Additional file 3