Assessing statistical significance in PLINK segmental sharing test

Abstract

Genome-wide association studies (GWAS) have been used for identifying the genetic causes of many complex traits like Alzheimer's disease, schizophrenia, as well as various cancers. Given that nearly a million genotypes are generated for each individual in a typical case-control GWAS, it is natural to ask how the GWAS data could be fully utilized. Traditionally, GWAS are known to be suffered from the weak detection of rare risk variants. Re-sequencing of candidate loci or entire genome can certainly uncover such alleles, but this would require additional genotyping resources. Imputation of genotypes at loci untyped in the study but typed in the HapMap project does provide some extra information, but not necessary for the discovery of rare variants. Purcell et al. (2007) introduced a segmental sharing analysis between pairs of unrelated individuals using GWAS data. Their idea is based on family-based linkage analysis in which one would like to know if any chromosomal region is shared more among affected members than among affected and unaffected members within pedigrees, and the segmental test can be regarded as its extension when these familial relationships become distant and varied. If one can trace back to the infinite past, every case or control in a GWAS should actually belong to one of the many descendants of a remote common ancestry. In other words, all individuals within a GWAS should be considered related members within one large pedigree rather than totally unrelated. The PLINK approach of segmental sharing analysis is to compute a (linkage) test statistic S for each independent locus (i.e., in approximate linkage equilibrium with other tested loci) across the genome, asking whether there is a higher rate of case/case sharing than expected at each position, and to look for extended regions with statistic S significantly deviated from the expectation. However, whether the statistic S observed is significant remains a crucial question. One standard approach is to generate an empirical distribution of the statistic S under the null hypothesis via permutation. An alternative approach is to derive a SNP-wise p-value threshold characteristic to the sample of interest to balance the possibility of getting excessive false positive or false negative results. Here, we derived and proposed a threshold for the PLINK segmental sharing analysis by extending the theoretical framework of Lander and Kruglyak (1995) for family-based linkage analysis.