In all participants, the average AUC cotinine = 2341 ng/ml*hr, standard derivation = 977, skew = 1.17, and kurtosis = 2.52. Normality of AUC cotinine could not be improved with commonly used transformation functions (data not shown). However, non-normality of AUC cotinine would be expected to have only a small impact on a linkage analysis utilizing the Kong and Cox exponential model [Kong and Cox, 1997
], because the score statistic used in the exponential model is minimally affected by non-normality of data [Feingold, 2002
Three suggestive linkage peaks with LOD ≥ 1.86 were identified in Merlin for AUC cotinine [Abecasis et al., 2002
; Lander and Kruglyak, 1995
]. The strongest linkage signal appeared at 135 cM of chromosome 9 with LOD=2.81 (P=0.0002) (), between markers D9S1682 and D9S290. The support interval with LOD ≥ 2 extends 17 cM from 126 to 143 cM, between markers D9S289 and D9S164. The two other suggestive linkage peaks for AUC cotinine occur on chromosome 11 (). The first one is located at 31.4 cM with LOD=1.94 and P=0.0014 between markers D11S4190 and D11S915. The second one is located at 73.5 cM with LOD=1.96 and P=0.0013 at marker D11S1314.
Linkage peaks on Chromosomes 9 and 11. Multipoint LOD traces for AUC cotinine and residualized AUC cotinine of a) chromosome 9 and b) chromosome 11.
We performed a simulation in Merlin to estimate the empirical P-value of the three suggestive linkage peaks [Abecasis et al., 2002
; Sawcer et al., 1997
]. Under the null hypothesis with no linkage, the number of simulations with at least one linkage peak with LOD ≥ 1.94, ≥ 1.96 or ≥ 2.81 were 467, 455, or 75, respectively, in 1000 whole-genome linkage analysis simulations. Overall statistical significance of our linkage findings for AUC cotinine (all three linkage peaks) is the probability of at least three linkage peaks with LOD ≥ 1.94, 1.96 and 2.81, appearing by chance in one whole genome linkage analysis. We estimated the empirical probability of suggestive linkage between AUC cotinine and regions of chromosomes 9 and 11 as P=0.029 since only 29 such cases were observed in 1000 simulations.
False discovery rate (FDR) was defined as the expected proportion of incorrectly rejected null hypotheses [Benjamini and Hochberg, 1995
]. In the present case, FDR indicates the proportion of expected false linkage peaks among our three linkage peaks that are supported using both conventional criteria for suggestive linkage and through simulation analysis. We observed a total of 620 linkage peaks with LOD ≥ 1.94 in our 1000 simulations. The number is larger than 467 (mentioned above) because more than one peak could be observed in a single simulation. Thus, we expect one or less false linkage peak among our three identified linkage peaks. The FDR of the three linkage peaks was 0.620/3 ≈ 0.206 if the observed linkage peaks are considered independently.
Analysis of regression residuals with the Kong and Cox exponential model in Merlin identified linkage of AUC cotinine after adjustment for the covariates. Using the same model and statistic enabled the comparison of the linkage results with or without adjustment for covariates. Furthermore, this approach does not appear to be affected by possible type I error inflation due to a non-Gaussian distribution [Feingold, 2002
; Kong and Cox, 1997
; Sham et al., 2002
]. The linkage signal of the residuals was compared to the three unadjusted linkage peaks of AUC cotinine to evaluate the impact of covariates and to identify stable linkage signatures. The analysis of residuals of AUC cotinine supported the extended region of linkage on chromosome 9, with a peak located at 132.8 cM with LOD=2.01 (P=0.0012) (), at marker D9S1682. The LOD score of the regression residuals on chromosome 9 is generally lower than that of the unadjusted AUC cotinine for the same region. There was a minor shift in location of the linkage peak for adjusted AUC cotinine, which was only 2 cM away from the linkage peak of unadjusted AUC cotinine. The 2 LOD supporting interval of AUC cotinine completely overlaps the 1 LOD interval identified in the linkage analysis of the residuals.
Both suggestive linkage regions on chromosome 11 exhibited increased LOD scores with the residuals of AUC cotinine (). The location and magnitude of the first peak of the residual linkage analysis, was located at 33.9 cM with LOD=2.07 and P=0.0011 at marker D11S915, just distal to that found in the analysis of unadjusted AUC cotinine. In the second extended linkage region, both linkage analyses exhibited two peaks, i.e., at 74 cM between markers D11S1314 and D11S4207 and 85 cM, at D11S901. The LOD score of the proximal peak in this region changed minimally from the unadjusted to adjusted AUC cotinine. However, the distal peak in this region increased by nearly one LOD unit between the unadjusted and adjusted AUC cotinine linkage analyses, with a peak LOD of 2.81 (p=0.0002) at 84.8 cM, with a LOD ≥ 2.0 support interval from 81 cM to 89 cM, between markers D11S937 and D11S4147. Our initial AUC cotinine linkage findings are fully supported by the linkage analysis of residualized AUC cotinine because the LOD scores of all three linkage peaks are larger than the criterion for suggestive linkage (LOD ≥ 1.86) [Lander and Kruglyak, 1995
We further note the presence of linkage peaks for AUC cotinine (unadjusted and adjusted) with LOD scores ≥ 1 distributed on eleven chromosomes ( and Figure S1
), and note that the largest extended regions of linkage appeared on chromosomes 9 and 11.
Chromosome Regions with LOD ≥ 1.