Genome scan meta-analysis of schizophrenia and bipolar disorder, part I: Methods and power analysis

Abstract

This is the first of three articles on a meta-analysis of genome scans of schizophrenia (SCZ) and bipolar disorder (BPD) that uses the rank-based genome scan meta-analysis (GSMA) method. Here we used simulation to determine the power of GSMA to detect linkage and to identify thresholds of significance. We simulated replicates resembling the SCZ data set (20 scans; 1,208 pedigrees) and two BPD data sets using very narrow (9 scans; 347 pedigrees) and narrow (14 scans; 512 pedigrees) diagnoses. Samples were approximated by sets of affected sibling pairs with incomplete parental data. Genotypes were simulated and nonparametric linkage (NPL) scores computed for 20 180-cM chromosomes, each containing six 30-cM bins, with three markers/bin (or two, for some scans). Genomes contained 0, 1, 5, or 10 linked loci, and we assumed relative risk to siblings (lambda(sibs)) values of 1.15, 1.2, 1.3, or 1.4. For each replicate, bins were ranked within-study by maximum NPL scores, and the ranks were averaged (R(avg)) across scans. Analyses were repeated with weighted ranks ((sqrt)N[genotyped cases] for each scan). Two P values were determined for each R(avg): P(AvgRnk) (the pointwise probability) and P(ord) (the probability, given the bin's place in the order of average ranks). GSMA detected linkage with power comparable to or greater than the underlying NPL scores. Weighting for sample size increased power. When no genomewide significant P values were observed, the presence of linkage could be inferred from the number of bins with nominally significant P(AvgRnk), P(ord), or (most powerfully) both. The results suggest that GSMA can detect linkage across multiple genome scans.

Figure 1

Determining P_ord: observed and expected ordered R_avg values. The black line shows the 120 observed R_avg values, sorted with the first-place bin on the right. The light gray line and vertical error bars show the mean ± 2 SD of the jth-place bin from 5,000 random permutations. In the absence of linkage, R_avg values lower than the expected distribution are observed infrequently throughout the genome. With linkage, they are clustered among the highest values of R_avg, as shown here. As shown in table 1, P_ord is the probability of observing a given value of R_avg (black line) by chance, given its place in the order of observed R_avg values, which is determined from the distribution of ordered R_avg values (light gray line and error bars).

Figure 2

Marker maps for simulation studies. Genotypes were simulated for 180-cM chromosomes, on each of which six 30-cM bins (segments) were structured as shown. Marker locations are M1, M2, M3. For the SCZ data sets, some studies had 10-cM marker spacing (A) and others had 15-cM spacing (B); all BP data sets were simulated with 10 cM spacing. Linked (disease) and unlinked (nondisease) chromosomes were created (C). Disease loci (indicated by “D”) were located midway between two markers, either in the first (edge) or third (middle) bin. Genomes consisted of 20 chromosomes (120 bins); see table 5 for structures of genomes.

Figure 3

Mean average rank by bin for unlinked replicates. Shown are the means ± SD of the average ranks of each bin (over all chromosomes) in the 1,000 unlinked replicates of the SCZ data set. “Edge” bins (1 and 6) have lower summed ranks than “mid” bins (2–5). This contributed to an inflated type I error rate when P_ord values were computed by permuting the order of ranks in each study by bin, and was corrected by permuting by chromosome so that summed ranks of edge and middle bins were compared with their own distributions.

Figure 4

Mean number of bins per replicate achieving genomewide significance. Shown is the mean number of bins (in 100 replicates per model) with P⩽.0004167 (the threshold for genomewide significance = .05/120), for weighted analyses. Diamonds represent SCZ data sets, squares represent BP-N data sets, and circles represent BP-VN data sets. Blackened symbols represent data for λ_sibs=1.3, unblackened symbols represent data for λ_sibs=1.15.

Figure 5

Power to detect linked bins (unweighted analyses). Shown are the proportions of bins containing linked loci that achieved P_AvgRnk⩽.05 (blackened symbols) or ⩽.01 (unblackened symbols), for each model (see table 5), for simulated replicates of SCZ (A), BP-VN (B) and BP-N (C) data sets. Squares represent md1 replicates, diamonds represent ed1 replicates, circles represent ed1md4 replicates, and triangles represent ed2md8 replicates. See tables 2, 3, and 4 for characteristics of each data set. N=100 per model.

Figure 6

Number of loci with nominally significant P_AvgRnk, P_ord, or both. Data from table 7 are shown for the BP-VN (9 studies) and SCZ (20 studies) data sets weighted analysis, with P_ord computed by permuting by chromosome, for λ_sibs=1.15. Blackened bars represent mean number of bins with both values <.05, diagonally striped bars represent bins with only P_AvgRnk<.05, and white bars represent bins with only P_ord<.05. Sets of bars are labeled by data set (BP or SCZ) and the number of linked loci in the data set (1 = md1, 5 = ed1md4, and 10 = ed2md8). Shown are the number of bins with these values for disease + adjacent bins (left-most six sets of bars), bins on chromosomes containing no disease locus (next six sets), and bins in completely unlinked data sets (the average of BP-VN-unlinked and SCZ-unlinked, which were virtually identical). See text for details.