Polygenic scores have recently been used to summarise genetic effects among an ensemble of markers that do not individually achieve significance in a large-scale association study. Markers are selected using an initial training sample and used to construct a score in an independent replication sample by forming the weighted sum of associated alleles within each subject. Association between a trait and this composite score implies that a genetic signal is present among the selected markers, and the score can then be used for prediction of individual trait values. This approach has been used to obtain evidence of a genetic effect when no single markers are significant, to establish a common genetic basis for related disorders, and to construct risk prediction models. In some cases, however, the desired association or prediction has not been achieved. Here, the power and predictive accuracy of a polygenic score are derived from a quantitative genetics model as a function of the sizes of the two samples, explained genetic variance, selection thresholds for including a marker in the score, and methods for weighting effect sizes in the score. Expressions are derived for quantitative and discrete traits, the latter allowing for case/control sampling. A novel approach to estimating the variance explained by a marker panel is also proposed. It is shown that published studies with significant association of polygenic scores have been well powered, whereas those with negative results can be explained by low sample size. It is also shown that useful levels of prediction may only be approached when predictors are estimated from very large samples, up to an order of magnitude greater than currently available. Therefore, polygenic scores currently have more utility for association testing than predicting complex traits, but prediction will become more feasible as sample sizes continue to grow. Recently there has been much interest in combining multiple genetic markers into a single score for predicting disease risk. Even if many of the individual markers have no detected effect, the combined score could be a strong predictor of disease. This has allowed researchers to demonstrate that some diseases have a strong genetic basis, even if few actual genes have been identified, and it has also revealed a common genetic basis for distinct diseases. These analyses have so far been performed opportunistically, with mixed results. Here I derive formulae based on the heritability of disease and size of the study, allowing researchers to plan their analyses from a more informed position. I show that discouraging results in some previous studies were due to the low number of subjects studied, but a modest increase in study size would allow more successful analysis. However, I also show that, for genetics to become useful for predicting individual risk of disease, hundreds of thousands of subjects may be needed to estimate the gene effects. This is larger than most existing studies, but will become more common in the near future, so that gene scores will become more useful for predicting disease than has appeared to date.

A genome-wide association study using the Molecular Genetics of Schizophrenia case-control data set, followed by a meta-analysis that included over 8,000 cases and 19,000 controls, revealed that while common genetic variation that underlies risk to schizophrenia can be identified, there probably are few or no single common loci with large effects. The common variants identified here lie on chromosome 6p22.1 in a region that includes a histone gene cluster and several genes implicated in immunity. In the third of three papers looking at the genetics of schizophrenia, a genome-wide association study using the Molecular Genetics of Schizophrenia case-control data set followed by a meta-analysis further implicates the major histocompatibility complex. The study also reveals that although common schizophrenia susceptibility alleles can be detected, there are probably few or no single common loci with large effects. Schizophrenia, a devastating psychiatric disorder, has a prevalence of 0.5–1%, with high heritability (80–85%) and complex transmission1. Recent studies implicate rare, large, high-penetrance copy number variants in some cases2, but the genes or biological mechanisms that underlie susceptibility are not known. Here we show that schizophrenia is significantly associated with single nucleotide polymorphisms (SNPs) in the extended major histocompatibility complex region on chromosome 6. We carried out a genome-wide association study of common SNPs in the Molecular Genetics of Schizophrenia (MGS) case-control sample, and then a meta-analysis of data from the MGS, International Schizophrenia Consortium and SGENE data sets. No MGS finding achieved genome-wide statistical significance. In the meta-analysis of European-ancestry subjects (8,008 cases, 19,077 controls), significant association with schizophrenia was observed in a region of linkage disequilibrium on chromosome 6p22.1 (P = 9.54 × 10-9). This region includes a histone gene cluster and several immunity-related genes—possibly implicating aetiological mechanisms involving chromatin modification, transcriptional regulation, autoimmunity and/or infection. These results demonstrate that common schizophrenia susceptibility alleles can be detected. The characterization of these signals will suggest important directions for research on susceptibility mechanisms.

The question of what significance threshold is appropriate for genomewide association studies is somewhat unresolved. Previous theoretical suggestions have yet to be validated in practice, whereas permutation testing does not resolve a discrepancy between the genomewide multiplicity of the experiment and the subset of markers actually tested. We used genotypes from the Wellcome Trust Case‐Control Consortium to estimate a genomewide significance threshold for the UK Caucasian population. We subsampled the genotypes at increasing densities, using permutation to estimate the nominal P‐value for 5% family‐wise error. By extrapolating to infinite density, we estimated the genomewide significance threshold to be about 7.2 × 10⁻⁸. To reduce the computation time, we considered Patterson's eigenvalue estimator of the effective number of tests, but found it to be an order of magnitude too low for multiplicity correction. However, by fitting a Beta distribution to the minimum P‐value from permutation replicates, we showed that the effective number is a useful heuristic and suggest that its estimation in this context is an open problem. We conclude that permutation is still needed to obtain genomewide significance thresholds, but with subsampling, extrapolation and estimation of an effective number of tests, the threshold can be standardized for all studies of the same population. Genet. Epidemiol. 2008.

Missing data occur in genetic association studies for several reasons including missing family members and uncertain haplotype phase. Maximum likelihood is a commonly used approach to accommodate missing data, but it can be difficult to apply to family-based association studies, because of possible loss of robustness to confounding by population stratification. Here a novel likelihood for nuclear families is proposed, in which distinct sets of association parameters are used to model the parental genotypes and the offspring genotypes. This approach is robust to population structure when the data are complete, and has only minor loss of robustness when there are missing data. It also allows a novel conditioning step that gives valid analysis for multiple offspring in the presence of linkage. Unrelated subjects are included by regarding them as the children of two missing parents. Simulations and theory indicate similar operating characteristics to TRANSMIT, but with no bias with missing data in the presence of linkage. In comparison with FBAT and PCPH, the proposed model is slightly less robust to population structure but has greater power to detect strong effects. In comparison to APL and MITDT, the model is more robust to stratification and can accommodate sibships of any size. The methods are implemented for binary and continuous traits in software, UNPHASED, available from the author.