The purpose of this work is to quantify the effects that errors in genotyping have on power and the sample size necessary to maintain constant asymptotic Type I and Type II error rates (SSN) for case-control genetic association studies between a disease phenotype and a di-allelic marker locus, for example a single nucleotide polymorphism (SNP) locus. We consider the effects of three published models of genotyping errors on the chi-square test for independence in the 2 × 3 table. After specifying genotype frequencies for the marker locus conditional on disease status and error model in both a genetic model-based and a genetic model-free framework, we compute the asymptotic power to detect association through specification of the test’s non-centrality parameter. This parameter determines the functional dependence of SSN on the genotyping error rates. Additionally, we study the dependence of SSN on linkage disequilibrium (LD), marker allele frequencies, and genotyping error rates for a dominant disease model. Increased genotyping error rate requires a larger SSN. Every 1% increase in sum of genotyping error rates requires that both case and control SSN be increased by 2–8%, with the extent of increase dependent upon the error model. For the dominant disease model, SSN is a nonlinear function of LD and genotyping error rate, with greater SSN for lower LD and higher genotyping error rate. The combination of lower LD and higher genotyping error rates requires a larger SSN than the sum of the SSN for the lower LD and for the higher genotyping error rate.

Adolescent idiopathic scoliosis (AIS) is an unexplained and common spinal deformity seen in otherwise healthy children. Its pathophysiology is poorly understood despite intensive investigation. Although genetic underpinnings are clear, replicated susceptibility loci that could provide insight into etiology have not been forthcoming. To address these issues, we performed genome-wide association studies (GWAS) of ∼327 000 single nucleotide polymorphisms (SNPs) in 419 AIS families. We found strongest evidence of association with chromosome 3p26.3 SNPs in the proximity of the CHL1 gene (P < 8 × 10⁻⁸ for rs1400180). We genotyped additional chromosome 3p26.3 SNPs and tested replication in two follow-up case–control cohorts, obtaining strongest results when all three cohorts were combined (rs10510181 odds ratio = 1.49, 95% confidence interval = 1.29–1.73, P = 2.58 × 10⁻⁸), but these were not confirmed in a separate GWAS. CHL1 is of interest, as it encodes an axon guidance protein related to Robo3. Mutations in the Robo3 protein cause horizontal gaze palsy with progressive scoliosis (HGPPS), a rare disease marked by severe scoliosis. Other top associations in our GWAS were with SNPs in the DSCAM gene encoding an axon guidance protein in the same structural class with Chl1 and Robo3. We additionally found AIS associations with loci in CNTNAP2, supporting a previous study linking this gene with AIS. Cntnap2 is also of functional interest, as it interacts directly with L1 and Robo class proteins and participates in axon pathfinding. Our results suggest the relevance of axon guidance pathways in AIS susceptibility, although these findings require further study, particularly given the apparent genetic heterogeneity in this disease.

Idiopathic scoliosis (IS) is a common paediatric musculoskeletal disease that displays a strong female bias. By performing a genome-wide association study (GWAS) of 3,102 individuals, we identify significant associations with 20p11.22 SNPs for females (P=6.89 × 10⁻⁹) but not males (P=0.71). This association with IS is also found in independent female cohorts from the United States of America and Japan (overallP=2.15 × 10⁻¹⁰, OR=1.30 (rs6137473)). Unexpectedly, the 20p11.22 IS risk alleles were previously associated with protection from early-onset alopecia, another sexually dimorphic condition. The 174-kb associated locus is distal toPAX1, which encodes paired box 1, a transcription factor involved in spine development. We identify a sequence in the associated locus with enhancer activity in zebrafish somitic muscle and spinal cord, an activity that is abolished by IS-associated SNPs. We thus identify a sexually dimorphic IS susceptibility locus, and propose the first functionally defined candidate mutations in an enhancer that may regulate expression in specific spinal cells.