Testing for association based on excess allele sharing in a sample of related cases and controls

Relationship between genomic distance-based regression and kernel machine regression for multi-marker association testing

To detect genetic association with common and complex diseases, two powerful yet quite different multimarker association tests have been proposed, genomic distance-based regression (GDBR) (Wessel and Schork [2006] Am J Hum Genet 79:821–833) and kernel machine regression (KMR) (Kwee et al. [2008] Am J Hum Genet 82:386–397; Wu et al. [2010] Am J Hum Genet 86:929–942). GDBR is based on relating a multimarker similarity metric for a group of subjects to variation in their trait values, while KMR is based on nonparametric estimates of the effects of the multiple markers on the trait through a kernel function or kernel matrix. Since the two approaches are both powerful and general, but appear quite different, it is important to know their specific relationships. In this report, we show that, under the condition that there is no other covariate, there is a striking correspondence between the two approaches for a quantitative or a binary trait: if the same positive semi-definite matrix is used as the centered similarity matrix in GDBR and as the kernel matrix in KMR, the F-test statistic in GDBR and the score test statistic in KMR are equal (up to some ignorable constants). The result is based on the connections of both methods to linear or logistic (random-effects) regression models.

Familial transmission of schizophrenia in Palau: A 20-year genetic epidemiological study in three generations

Our genetic epidemiological studies of schizophrenia and other psychotic disorders (SCZ) in the isolated population of Palau have been ongoing for 20 years. Results from the first decade showed that Palau has an elevated prevalence of SCZ and that cases cluster in extended multigenerational pedigrees interconnected via complex genetic relationships after centuries of endogamous, but not consanguineous, marriages. The aim of our second decade of research, which extended data collection into a third generation of young, high-risk (HR) Palauans, was to identify significant predictors of intergenerational transmission of illness. Our findings revealed that degree of familial loading and gender effects on reproductive fitness are important modifiers of risk for transmission of SCZ. Among 45 distinct multiplex families, we identified 10 high-density (HD) Palauan families, each with 7-29 SCZ cases, which contain half of Palau's 260 SCZ cases and 80% of the 113 SCZ cases with one or more affected first-degree relatives, indicating that familial loading is a major risk factor for SCZ in Palau. Cases that belong to multiply affected sibships are more common than cases with an affected parent. Furthermore, only 6/38 multiply affected sibships have an affected parent, strong evidence that many unaffected parents are obligate carriers of susceptibility genes. Although reproductive fitness is dramatically reduced in affected males, the 30% minority who do become fathers are twice as likely as affected mothers to transmit SCZ to an offspring. As they evolve, these HD families can help to elucidate the genetic mechanisms that predict intergenerational transmission of SCZ.

Effective sample size: Quick estimation of the effect of related samples in genetic case-control association analyses

Affected relatives are essential for pedigree linkage analysis, however, they cause a violation of the independent sample assumption in case-control association studies. To avoid the correlation between samples, a common practice is to take only one affected sample per pedigree in association analysis. Although several methods exist in handling correlated samples, they are still not widely used in part because these are not easily implemented, or because they are not widely known. We advocate the effective sample size method as a simple and accessible approach for case-control association analysis with correlated samples. This method modifies the chi-square test statistic, p-value, and 95% confidence interval of the odds-ratio by replacing the apparent number of allele or genotype counts with the effective ones in the standard formula, without the need for specialized computer programs. We present a simple formula for calculating effective sample size for many types of relative pairs and relative sets. For allele frequency estimation, the effective sample size method captures the variance inflation exactly. For genotype frequency, simulations showed that effective sample size provides a satisfactory approximation. A gene which is previously identified as a type 1 diabetes susceptibility locus, the interferon-induced helicase gene (IFIH1), is shown to be significantly associated with rheumatoid arthritis when the effective sample size method is applied. This significant association is not established if only one affected sib per pedigree were used in the association analysis. Relationship between the effective sample size method and other methods - the generalized estimation equation, variance of eigenvalues for correlation matrices, and genomic controls - are discussed.

Power comparisons between similarity-based multilocus association methods, logistic regression, and score tests for haplotypes

Recently, a genomic distance-based regression for multilocus associations was proposed (Wessel and Schork [2006] Am. J. Hum. Genet. 79:792-806) in which either locus or haplotype scoring can be used to measure genetic distance. Although it allows various measures of genomic similarity and simultaneous analyses of multiple phenotypes, its power relative to other methods for case-control analyses is not well known. We compare the power of traditional methods with this new distance-based approach, for both locus-scoring and haplotype-scoring strategies. We discuss the relative power of these association methods with respect to five properties: (1) the marker informativity; (2) the number of markers; (3) the causal allele frequency; (4) the preponderance of the most common high-risk haplotype; (5) the correlation between the causal single-nucleotide polymorphism (SNP) and its flanking markers. We found that locus-based logistic regression and the global score test for haplotypes suffered from power loss when many markers were included in the analyses, due to many degrees of freedom. In contrast, the distance-based approach was not as vulnerable to more markers or more haplotypes. A genotype counting measure was more sensitive to the marker informativity and the correlation between the causal SNP and its flanking markers. After examining the impact of the five properties on power, we found that on average, the genomic distance-based regression that uses a matching measure for diplotypes was the most powerful and robust method among the seven methods we compared.

Genetic liability to schizophrenia in Oceanic Palau: a search in the affected and maternal generation

While liability to schizophrenia (Scz) is due to genetic and environmental factors, specific factors are largely unknown. We postulate a two-hit model for Scz, in which initial liability is generated during fetal brain development: this "hit" is precipitated by environmental stressors biologically interacting with maternal genetic vulnerability to the stress. Additional liability to Scz is generated by individual genetic vulnerability. To evaluate these putative levels of vulnerability, we search in the genome of both affected individuals and their mothers for variation that differs, statistically, from that in the general population. For parental analyses, mothers were treated as "affected," rather than their offspring, and the fathers were treated as "controls". We used a sample from the Palauan population: 175 individuals diagnosed with Scz, broadly defined; 87 mothers and 45 fathers of affected individuals. Pedigree and diagnostic data were available on 2,953 living and deceased subjects. DNA from 553 individuals was genotyped for short tandem repeats (STR) spaced approximately every 10 cM across the genome. We tested for association between affection status and STR alleles; such an approach was reasonable, despite the widely spaced markers, because this population has far-ranging linkage disequilibrium (LD). Results for the truly affected individuals were modest, whereas results from the maternal generation were promising. For a recessive model and a test for excess allele matching across mothers, significant findings occurred for D20S481, D10S1221, D6S1021, D13S317, and D18S976. Regions in which at least two adjacent markers produced substantial association statistics include 2p12-11.2, 2q24.1-32.1, 6q12-14.1, 10q23.2-24.21, 12q23.2-24.21 and 17q23.2-23.3.