A robust and fast two-sample test of equal correlations with an application to differential co-expression.

A robust and fast two-sample test for equal Pearson correlation coefficients (PCCs) is important in solving many biological problems, including, for example, analysis of differential co-expression. However, few existing methods for this test can achieve robustness against deviation from normal distributions, accuracy under small sample sizes, and computational efficiency simultaneously. Here, we propose a new method for testing differential correlation using a saddlepoint approximation of the residual bootstrap (DICOSAR). To achieve robustness, accuracy, and efficiency, DICOSAR combines the ideas underlying the pooled residual bootstrap, the signed root of a likelihood ratio statistic, and a multivariate saddlepoint approximation. Through a comprehensive simulation study and a real data analysis of gene co-expression, we demonstrate that DICOSAR is accurate and robust in controlling the type I error rate for detecting differential correlation and provides a faster alternative to the bootstrap and permutation methods. We further show that DICOSAR can also be used for testing differential correlation matrices. These results suggest that DICOSAR provides an analytical approach to facilitate rapid testing for the equality of PCCs in large-scale analysis.

Inter- and intra-chromosomal modulators of the APOE ɛ2 and ɛ4 effects on the Alzheimer's disease risk.

The mechanisms of incomplete penetrance of risk-modifying impacts of apolipoprotein E (APOE) ε2 and ε4 alleles on Alzheimer's disease (AD) have not been fully understood. We performed genome-wide analysis of differences in linkage disequilibrium (LD) patterns between 6,136 AD-affected and 10,555 AD-unaffected subjects from five independent studies to explore whether the association of the APOE ε2 allele (encoded by rs7412 polymorphism) and ε4 allele (encoded by rs429358 polymorphism) with AD was modulated by autosomal polymorphisms. The LD analysis identified 24 (mostly inter-chromosomal) and 57 (primarily intra-chromosomal) autosomal polymorphisms with significant differences in LD with either rs7412 or rs429358, respectively, between AD-affected and AD-unaffected subjects, indicating their potential modulatory roles. Our Cox regression analysis showed that minor alleles of four inter-chromosomal and ten intra-chromosomal polymorphisms exerted significant modulating effects on the ε2- and ε4-associated AD risks, respectively, and identified ε2-independent (rs2884183 polymorphism, 11q22.3) and ε4-independent (rs483082 polymorphism, 19q13.32) associations with AD. Our functional analysis highlighted ε2- and/or ε4-linked processes affecting the lipid and lipoprotein metabolism and cell junction organization which may contribute to AD pathogenesis. These findings provide insights into the ε2- and ε4-associated mechanisms of AD pathogenesis, underlying their incomplete penetrance.

APOE ɛ4 allele and TOMM40-APOC1 variants jointly contribute to survival to older ages.

Age-related diseases characteristic of post-reproductive life, aging, and life span are the examples of polygenic non-Mendelian traits with intricate genetic architectures. Polygenicity of these traits implies that multiple variants can impact their risks independently or jointly as combinations of specific variants. Here, we examined chances to live to older ages, 85 years and older, for carriers of compound genotypes comprised of combinations of genotypes of rs429358 (APOE ɛ4 encoding polymorphism), rs2075650 (TOMM40), and rs12721046 (APOC1) polymorphisms using data from four human studies. The choice of these polymorphisms was motivated by our prior results showing that the ɛ4 carriers having minor alleles of the other two polymorphisms were at exceptionally high risk of Alzheimer's disease (AD), compared with non-carriers of the minor alleles. Consistent with our prior findings for AD, we show here that the adverse effect of the ɛ4 allele on survival to older ages is significantly higher in carriers of minor alleles of rs2075650 and/or rs12721046 polymorphisms compared with their non-carriers. The exclusion of AD cases made this effect stronger. Our results provide compelling evidence that AD does not mediate the associations of the same compound genotypes with chances to survive until older ages, indicating the existence of genetically heterogeneous mechanisms. The survival chances can be mainly associated with lipid- and immunity-related mechanisms, whereas the AD risk, can be driven by the AD-biomarker-related mechanism, among others. Targeting heterogeneous polygenic profiles of individuals at high risks of complex traits is promising for the translation of genetic discoveries to health care.

Definitive roles of TOMM40-APOE-APOC1 variants in the Alzheimer's risk.

Despite advances, the roles of genetic variants from the APOE-harboring 19q13.32 region in Alzheimer's disease (AD) remain controversial. We leverage a comprehensive approach to gain insights into a more homogeneous genetic architecture of AD in this region. We use a sample of 2,673 AD-affected and 16,246 unaffected subjects from 4 studies and validate our main findings in the landmark Alzheimer's Disease Genetics Consortium cohort (3,662 AD-cases and 1,541 controls). We report the remarkably high excesses of the AD risk for carriers of the ε4 allele who also carry minor alleles of rs2075650 (TOMM40) and rs12721046 (APOC1) polymorphisms compared to carriers of their major alleles. The exceptionally high 4.37-fold (p=1.34 × 10-3) excess was particularly identified for the minor allele homozygotes. The beneficial and adverse variants were significantly depleted and enriched, respectively, in the AD-affected families. This study provides compelling evidence for the definitive roles of the APOE-TOMM40-APOC1 variants in the AD risk.

Protective association of the ε2/ε3 heterozygote with Alzheimer's disease is strengthened by TOMM40-APOE variants in men.

INTRODUCTION: Despite advances, understanding the protective role of the apolipoprotein E (APOE) ε2 allele in Alzheimer's disease (AD) remains elusive. METHODS: We examined associations of variants comprised of the TOMM40 rs8106922 and APOE rs405509, rs440446, and ε2-encoding rs7412 polymorphisms with AD in a sample of 2862 AD-affected and 169,516 AD-unaffected non-carriers of the ε4 allele. RESULTS: Association of the ε2/ε3 heterozygote of men with AD is 38% (P = 1.65 × 10-2 ) more beneficial when it is accompanied by rs8106922 major allele homozygote and rs405509 and rs440446 heterozygotes than by rs8106922 heterozygote and rs405509 and rs440446 major allele homozygotes. No difference in the beneficial associations of these two most common ε2/ε3-bearing variants with AD was identified in women. The role of ε2/ε3 heterozygote may be affected by different immunomodulation functions of rs8106922, rs405509, and rs440446 variants in a sex-specific manner. DISCUSSION: Combination of TOMM40 and APOE variants defines a more homogeneous AD-protective ε2/ε3-bearing profile in men.

Haplotype architecture of the Alzheimer's risk in the APOE region via co-skewness.

INTRODUCTION: As a multifactorial polygenic disorder, Alzheimer's disease (AD) can be associated with complex haplotypes or compound genotypes. METHODS: We examined associations of 4960 single nucleotide polymorphism (SNP) triples, comprising 32 SNPs from five genes in the apolipoprotein E gene (APOE) region with AD in a sample of 2789 AD-affected and 16,334 unaffected subjects. RESULTS: We identified a large number of 1127 AD-associated triples, comprising SNPs from all five genes, in support of definitive roles of complex haplotypes in predisposition to AD. These haplotypes may not include the APOE ε4 and ε2 alleles. For triples with rs429358 or rs7412, which encode these alleles, AD is characterized mainly by strengthening connections of the ε4 allele and weakening connections of the ε2 allele with the other alleles in this region. DISCUSSION: Dissecting heterogeneity attributed to AD-associated complex haplotypes in the APOE region will target more homogeneous polygenic profiles of people at high risk of AD.