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Table 2 Estimated type-1 error rates with simulation data based on simulated RNA-seq data from negative binomial distribution. Estimated type-1 error rates by BALLI, DESeq2, edgeR, LLI, and voom and their 95% confidence levels were estimated for N= 12,16,20,and 24. aThe type-1 error rates are marked by bold font if their 95% confidence levels include or lower than the nominal significant level α

From: BALLI: Bartlett-adjusted likelihood-based linear model approach for identifying differentially expressed genes with RNA-seq data

 

BALLI

DESeq2

edgeR

LLI

voom

BALLI

DESeq2

edgeR

LLI

voom

α

N = 12

N = 16

0.1

0.09550 a (0.09394, 0.09706)

0.08417 (0.08278, 0.08556)

0.12172 (0.11984, 0.12360)

0.13198 (0.13030, 0.13367)

0.09912 (0.09767, 0.10057)

0.09211 (0.09097, 0.09325)

0.08428 (0.08307, 0.08549)

0.12028 (0.11911, 0.12145)

0.11853 (0.11729, 0.11977)

0.09977 (0.09868, 0.10086)

0.05

0.04863 (0.04757, 0.04969)

0.04334 (0.04243, 0.04425)

0.05604 (0.05492, 0.05716)

0.07063 (0.06926, 0.07200)

0.05013 (0.04899, 0.05126)

0.04508 (0.04429, 0.04587)

0.04333 (0.04261, 0.04404)

0.05616 (0.05528, 0.05703)

0.06345 (0.06239, 0.06452)

0.05013 (0.04937, 0.05089)

0.01

0.00989 (0.00939, 0.01039)

0.00997 (0.00954, 0.01040)

0.01267 (0.01209, 0.01326)

0.01858 (0.01798, 0.01919)

0.00997 (0.00957, 0.01037)

0.00893 (0.00847, 0.00939)

0.01008 (0.00961, 0.01056)

0.01276 (0.01225, 0.01328)

0.01469 (0.01419, 0.01519)

0.00996 (0.00969, 0.01024)

0.005

0.00524 (0.00492, 0.00557)

0.00549 (0.00517, 0.00581)

0.00689 (0.00650, 0.00729)

0.01043 (0.00992, 0.01094)

0.00488 (0.00456, 0.00519)

0.00445 (0.00414, 0.00475)

0.00543 (0.00515, 0.00572)

0.00682 (0.00653, 0.00711)

0.00803 (0.00759, 0.00846)

0.00506 (0.00483, 0.00528)

α

N = 20

N = 24

0.1

0.09198 (0.09051, 0.09346)

0.08419 (0.08282, 0.08557)

0.11844 (0.11718, 0.11971)

0.11073 (0.10925, 0.11221)

0.10023 (0.09908, 0.10139)

0.09276 (0.09156, 0.09395)

0.08521 (0.08386, 0.08657)

0.11846 (0.11686, 0.12005)

0.10867 (0.10747, 0.10987)

0.09963 (0.09833, 0.10092)

0.05

0.04463 (0.04376, 0.04549)

0.04296 (0.04205, 0.04387)

0.05748 (0.05625, 0.05871)

0.05780 (0.05662, 0.05898)

0.05048 (0.04936, 0.05159)

0.04468 (0.04394, 0.04541)

0.04268 (0.04188, 0.04348)

0.06050 (0.05953, 0.06147)

0.05518 (0.05427, 0.05608)

0.04907 (0.04815, 0.05000)

0.01

0.00861 (0.00812, 0.00911)

0.00986 (0.00936, 0.01036)

0.01271 (0.01204, 0.01338)

0.01328 (0.01267, 0.01388)

0.01016 (0.00954, 0.01077)

0.00844 (0.00810, 0.00878)

0.00940 (0.00899, 0.00982)

0.01242 (0.01203, 0.01281)

0.01212 (0.01167, 0.01257)

0.00957 (0.00907, 0.01007)

0.005

0.00457 (0.00425, 0.00489)

0.00536 (0.00501, 0.00572)

0.00688 (0.00647, 0.00730)

0.00707 (0.00661, 0.00753)

0.00521 (0.00484, 0.00559)

0.00405 (0.00386, 0.00425)

0.00497 (0.00469, 0.00525)

0.00662 (0.00639, 0.00685)

0.00625 (0.00595, 0.00655)

0.00474 (0.00440, 0.00507)