Data-adaptive multi-locus association testing in subjects with arbitrary genealogical relationships
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Gail Gong
Abstract
Genome-wide sequencing enables evaluation of associations between traits and combinations of variants in genes and pathways. But such evaluation requires multi-locus association tests with good power, regardless of the variant and trait characteristics. And since analyzing families may yield more power than analyzing unrelated individuals, we need multi-locus tests applicable to both related and unrelated individuals. Here we describe such tests, and we introduce SKAT-X, a new test statistic that uses genome-wide data obtained from related or unrelated subjects to optimize power for the specific data at hand. Simulations show that: a) SKAT-X performs well regardless of variant and trait characteristics; and b) for binary traits, analyzing affected relatives brings more power than analyzing unrelated individuals, consistent with previous findings for single-locus tests. We illustrate the methods by application to rare unclassified missense variants in the tumor suppressor gene BRCA2, as applied to combined data from prostate cancer families and unrelated prostate cancer cases and controls in the Multi-ethnic Cohort (MEC). The methods can be implemented using open-source code for public use as the R-package GATARS (Genetic Association Tests for Arbitrarily Related Subjects) <https://gailg.github.io/gatars/>.
Funding source: NIH
Award Identifier / Grant number: R01CA179011 and R01CA094069
Funding statement: This work was supported by NIH Funder Id: http://dx.doi.org/10.13039/100000002, grants R01CA179011 and R01CA094069.
Acknowledgment
We are grateful to the Multi-ethnic Cohort (MEC) investigators who made the MEC prostate cancer data available for analysis.
Appendices
A Alternate definitions of QB, QS and QT
Straightforward matrix multiplication based on equations (4–6) gives the following expressions for the three basic test statistics:
These expressions show that QB sums phenotype-genotype products over markers before squaring the summations. Thus, as is well-known (e.g. Schaid et al., 2013), QB is vulnerable to power loss for target sets containing both positively and negatively trait-associated markers. Moreover, QB and QS contrast genotype similarities in pairs of subjects who share positive (or negative) trait residuals yn – μn against similarities in residual-discordant pairs. Thus they are vulnerable to power loss when applied to marker sets whose trait-associated variants are all associated in the same direction. For example, for a binary trait with phenotypes yn = 1 for affected subjects and yn = 0 for unaffected subjects, expressions (11) show that QB and QS contrast genotype similarities in pairs of concordantly affected and concordantly unaffected subjects against genotype similarities in phenotype-discordant pairs. Thus they are vulnerable to power loss by genotype sharing in pairs of unaffected subjects, a particular problem for rare deleterious variants, when many pairs of controls share the wild-type allele. In contrast, QT compares observed genotype sharing by pairs of affected subjects with its null value based on the null predicted phenotypes μn, and can assume either positive or negative values. Simulations (data not shown) support these heuristic power comparisons by suggesting that when all trait-associated variants are positively associated, QT outperforms or matches both QB and QS for both binary and quantitative traits. However, when the trait-associated markers are both positively- and negatively-associated and the trait is binary, QS outperforms QT, which in turn outperforms QB.
B Optimizing the data-adaptive statistics
Here we describe the procedure used to determine the vector α* = (α*B, α*S, α*T) that maximizes the value Xα (G) = –log10P(α;G), where P(α;G) is the nominal p-value of Qα(G). The three pair-wise statistics QBS, QBT and QST (which lie along the three edges of the triangle
C Null distribution of statistics Qα for fixed α
Under the null hypothesis, when α is fixed and the test statistic Qα of (4) is conditioned on subjects’ phenotypes and covariates, it is asymptotically equivalent to a quadratic form in a Gaussian vector. The distribution of such quadratic forms is known and can be described as follows. Dropping the subscript α and focusing on the automsome, we rewrite (4) as
with
where U is the (2M)×(2M) orthonormal matrix of eigenvectors of
where
D Selecting the null marker sets
In the kth of K iterations, we construct a set of null markers by randomly sampling one marker from each of M sampling sets S1, …, SM containing diallelic autosomal markers. Each sampling set Sm is chosen to contain at least 200 markers with empirical MAFs “matching” that of target marker m, i.e. lying in the interval (πm(1 – ε), πm(1 + ε)) for some user-specified value of ε, with 0 < ε ≪ 1 (we chose ε = 0.01). In addition, Sm contains no target markers or markers known to be associated with the trait. To construct these M sampling sets, GATARS uses the recombination hotspots identified by Myers et al. (2005) to partition the human autosome into 12,327 chromosome segments, with linkage equilibrium between pairs of markers in distinct segments. GATARS then deletes all segments containing target markers or markers known to be associated with the trait. The sampling sets Sm are obtained by choosing all markers on the remaining segments with frequencies matching the frequency πm of marker m, m = 1, …, M.
For the data application, we identified 8515 chromosome segments without target markers or markers known to be associated with prostate cancer, and containing at least one marker with frequency matching one or more of the M = 24 target markers. These segments yielded potential sampling sets ranging in size from 225 to 31,562 markers; but for computational efficiency we limited their sizes to at most 1000 markers. For a given replication of a given simulation, we created a sampling set for each of the M = 20 target markers by randomly selecting 200 markers with matching MAFs from the simulated chromosomal segments without target markers.
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Articles in the same Issue
- netprioR: a probabilistic model for integrative hit prioritisation of genetic screens
- Combining gene expression data and prior knowledge for inferring gene regulatory networks via Bayesian networks using structural restrictions
- Reproducibility of biomarker identifications from mass spectrometry proteomic data in cancer studies
- Data-adaptive multi-locus association testing in subjects with arbitrary genealogical relationships
Articles in the same Issue
- netprioR: a probabilistic model for integrative hit prioritisation of genetic screens
- Combining gene expression data and prior knowledge for inferring gene regulatory networks via Bayesian networks using structural restrictions
- Reproducibility of biomarker identifications from mass spectrometry proteomic data in cancer studies
- Data-adaptive multi-locus association testing in subjects with arbitrary genealogical relationships
