Controlling bias and inflation in epigenome- and transcriptome-wide association studies using the empirical null distribution

Table 4 Bias and inflation of test statistics for EWAS and TWAS across four cohorts on age and smoking status

		EWAS		TWAS
		Age	Smoking	Age	Smoking
		infl. bias \(\left (\sqrt {\lambda _{{\chi ^{2}_{1}}}}\right)\)	infl. bias \(\left (\sqrt {\lambda _{{\chi ^{2}_{1}}}}\right)\)	infl. bias \(\left (\sqrt {\lambda _{{\chi ^{2}_{1}}}}\right)\)	infl. bias \(\left (\sqrt {\lambda _{{\chi ^{2}_{1}}}}\right)\)
Uncorrected	CODAM	1.17 0.100 (1.19)	1.02 0.040 (1.03)	1.13 -0.030 (1.20)	1.05 0.100 (1.06)
	LL	1.45 -0.500 (1.94)	1.07 0.009 (1.08)	1.17 0.040 (1.39)	1.15 0.080 (1.22)
	LLS	1.30 0.100 (1.36)	1.05 -0.200 (1.08)	1.18 0.050 (1.26)	1.15 -0.010 (1.17)
	RS	1.34 0.700 (1.57)	0.99 -0.100 (1.01)	1.11 -0.005 (1.12)	1.10 -0.010 (1.12)
Corrected	CODAM	1.01 -0.000 (1.01)	1.00 0.000 (1.01)	1.02 -0.010 (1.06)	1.00 0.000 (1.00)
	LL	1.00 -0.000 (1.27)	1.00 0.000 (1.01)	1.02 0.010 (1.19)	1.02 0.010 (1.06)
	LLS	1.02 0.007 (1.05)	1.00 -0.003 (1.01)	1.03 0.001 (1.07)	1.02 -0.010 (1.02)
	RS	1.00 0.000 (1.02)	0.99 0.000 (1.01)	1.02 -0.006 (1.01)	1.01 0.001 (1.02)
	1.19 -0.030 (1.47)	1.05 0.020 (1.10)	1.04 0.030 (1.28)	1.06 -0.002 (1.14)
meta-analysis

The table shows the bias and inflation as obtained using Bayesian method to estimate the empirical null and (within parentheses) using the genomic inflation factor \(\left (\sqrt {\lambda _{{\chi ^{2}_{1}}}}\right)\) both before correction and after correction for inflation (and bias in case of empirical control). The estimated inflation for the meta-analysis results are after control for inflation and bias in the individual cohorts and (within parentheses) inflation after applying genomic control. Sample sizes of the cohorts for EWAS/TWAS were n =164/181 (CODAM), n =744/605 (LL), n =683/589 (LLS), and n =612/535 (RS)

ISSN: 1474-760X