For the PTPN22 data in Table 4, if one affected sib per sibpair is selected for association as in (Begovich et al., 2004), X2 = 31.42 leads to p-value of 2.1 ×10−8 (with Fisher’s exact test, the p-value is 5.6 ×10−8), and 95%CI of OR is (1.55–2.50). We know this is an underuse of the samples as the second sibs in sibpairs were discarded. Using all sibs in sibpairs without correction leads to the incorrect result of X2 =53.26, p-value of 2.9 ×10−13, and 95% CI of OR of (1.73–2.62). The overall ratio of effective sample size and the apparent sample size is: α = (86 + 377 × 2 × 2/3)/(86 + 377 × 2) ≈ 0.70. Using the Eq.(10) and Eq.(11), the modified X2 = 45.73 leads to p-value of 1.36 ×10−11, and modified 95% CI of OR (1.70–2.66). Compared to the one-sib-per-pair dataset, even though the conclusion on statistical significance is unchanged, the p-value is 1500 times smaller.
