Figure - PMC

Skip to main content

View full-text article in PMC

. Author manuscript; available in PMC: 2014 May 1.

Published in final edited form as: Genet Epidemiol. 2013 Mar 21;37(4):10.1002/gepi.21722. doi: 10.1002/gepi.21722

The two graphs illustrate the power of length (L_p = ∥f⁺∥_p − ∥f⁻∥_p)and joint tests (J_p = ∥f⁺ − f⁻∥_p) with different norms (p=1, 2, 4 and ∞). In each case the test statistic is computed and significance is assessed via permutation of case-control status. We consider a scenario where a gene contains eight causal risk variants, all with a relative risk of 2.0. Two of the risk variants have MAF=1%, the other six have MAF=0.1%. We simulated a sample of 1000 cases and 1000 controls for this setting. We then considered 9 additional settings where we added 8, 16, 24, 32, 40, 48, 56, 64 and 72 additional non-causal variants (relative risk=1), always maintaining 3:1 ratio of low MAF (0.1%) to high MAF (1%) variants in the set.

A) For L_p, as we move from no non-causal variants to 72 non-causal variants, the order of most powerful tests completely reverses, suggesting that higher norms are more optimal in situations with large numbers of non-causal variants.

B) For L_p, as we move from no non-causal variants to 72 non-causal variants, the order of most powerful tests nearly reverses, suggesting that, once again, higher norms are more optimal in situations with large numbers of non-causal variants.

The two graphs illustrate the power of length (L_p = ∥f⁺∥_p − ∥f⁻∥_p)and joint tests (J_p = ∥f⁺ − f⁻∥_p) with different norms (p=1, 2, 4 and ∞). In each case the test statistic is computed and significance is assessed via permutation of case-control status. We consider a scenario where a gene contains eight causal risk variants, all with a relative risk of 2.0. Two of the risk variants have MAF=1%, the other six have MAF=0.1%. We simulated a sample of 1000 cases and 1000 controls for this setting. We then considered 9 additional settings where we added 8, 16, 24, 32, 40, 48, 56, 64 and 72 additional non-causal variants (relative risk=1), always maintaining 3:1 ratio of low MAF (0.1%) to high MAF (1%) variants in the set.

A) For L_p, as we move from no non-causal variants to 72 non-causal variants, the order of most powerful tests completely reverses, suggesting that higher norms are more optimal in situations with large numbers of non-causal variants.

B) For L_p, as we move from no non-causal variants to 72 non-causal variants, the order of most powerful tests nearly reverses, suggesting that, once again, higher norms are more optimal in situations with large numbers of non-causal variants.