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Table 3 Power comparison between OWC and the other six tests. Data are simulated from \(N(\varvec{A}\times \triangle , \varvec{R})\). \(\varvec{A}\) has three or four nonzero elements with different signs which represent whether the causal variants are risk or protective. \(\triangle\) denotes the different settings of effect sizes. R is the corresponding LD matrix of gene EPB41. Power (%) is estimated under \(2.5\times 10^{-6}\) significance level

From: A gene based combination test using GWAS summary data

No. causal variants

nonzero \(\triangle\)

nonzero \(\varvec{A}\)

AT

S2T

ST

GATES

aSPU

sumSTAAR

OWC

3

U(1,5)

(1,1,1)

85.0

35.0

86.0

55.2

85.5

54

96.5

3

U(2,6)

(1,1,− 1)

71.0

70.5

17.0

58.0

67.0

50.5

85.5

3

U(2,6)

(1,− 1,− 1)

70.0

68.5

17.0

65.5

63.5

52.3

87.5

3

N(3,4)

(1,1,1)

82.5

60.0

83.0

74.0

87.0

71.8

94.0

3

N(3,4)

(1,1,− 1)

68.0

69.0

32.5

72.0

69.0

68.6

82.0

3

N(3,4)

(1,− 1,− 1)

65.5

60.5

32.0

76.0

73.0

67.8

86.5

3

(4,2,1)

(1,1,1)

64.0

3.5

68.5

13.5

78.5

7.9

95.0

3

(4,2,1)

(1,1,− 1)

18.0

3.0

18.5

12.5

31.5

16.1

79.0

3

(4,2,1)

(1,− 1,− 1)

3.0

4.0

0.5

12.0

8.5

9.0

76.0

3

(8,4,2)

(1,1,1)

99.0

98.0

99.5

98.5

98.5

96.5

99.5

3

(8,4,2)

(1,1,− 1)

97.0

96.5

98.5

94.5

98.5

93.9

99.0

3

(8,4,2)

(1,− 1,− 1)

96.0

96.0

0.5

94.0

97.0

87.5

98.0

3

(4,4,2)

(1,1,− 1)

69.0

45.0

45.0

28.5

65.6

43.5

93.5

3

(2,5,4)

(1,− 1,− 1)

92.5

74.5

76.0

65.5

62.0

79.3

99.5

4

(4,4,2,1)

(1,1,1,1)

97.0

47.5

98.5

24.5

98.5

53.2

99.5

4

(4,4,2,1)

(1,1,1,− 1)

95.5

47.0

95.5

24.5

97.5

50.9

99.0

4

(4,4,2,1)

(1,1,− 1,− 1)

71.0

45.0

0.5

24.0

70.5

52.2

93.0

5

(4,4,4,2,1)

(1,1,1,1,1)

100.0

84.5

99.5

35.5

99.5

87.2

100.0

5

(4,4,4,2,1)

(1,1,1,1,− 1)

99.5

84.0

99.0

35.0

98.5

82.1

99.5

5

(4,4,4,2,1)

(1,1,1,− 1,− 1)

98.0

84.0

99.0

34.0

98.5

81.7

99.5

  1. The comparison methods sum test(ST), squared sum test (S2T) and adaptive test (AT) mentioned in the paper are equivalent to the methods burden test (\(L_B\)), the sum of squared score test (\(S_Q\)) and the combination of \(L_B\) and \(S_Q\), respectively. Let \(S_S\) denote the score test and \(L_W\) denote the weighted sum statistic. The proposed combination method OWC is a combination of \(L_B\), \(L_W\), \(S_S\), and \(S_Q\). sumSTAAR is a fexible framework for gene-based association studies using GWAS summary statistics