Bayes factors based on robust TDT-type tests for family trio design
-
Min Yuan
,
Xiaoqing Pan
Abstract
Adaptive transmission disequilibrium test (aTDT) and MAX3 test are two robust-efficient association tests for case-parent family trio data. Both tests incorporate information of common genetic models including recessive, additive and dominant models and are efficient in power and robust to genetic model specifications. The aTDT uses information of departure from Hardy-Weinberg disequilibrium to identify the potential genetic model underlying the data and then applies the corresponding TDT-type test, and the MAX3 test is defined as the maximum of the absolute value of three TDT-type tests under the three common genetic models. In this article, we propose three robust Bayes procedures, the aTDT based Bayes factor, MAX3 based Bayes factor and Bayes model averaging (BMA), for association analysis with case-parent trio design. The asymptotic distributions of aTDT under the null and alternative hypothesis are derived in order to calculate its Bayes factor. Extensive simulations show that the Bayes factors and the p-values of the corresponding tests are generally consistent and these Bayes factors are robust to genetic model specifications, especially so when the priors on the genetic models are equal. When equal priors are used for the underlying genetic models, the Bayes factor method based on aTDT is more powerful than those based on MAX3 and Bayes model averaging. When the prior placed a small (large) probability on the true model, the Bayes factor based on aTDT (BMA) is more powerful. Analysis of a simulation data about RA from GAW15 is presented to illustrate applications of the proposed methods.
Acknowledgments
Dr. Min Yuan is supported by the National Science Foundation of China (NSFC), Grant No. 11201452, 11271346 and 11401558. Dr. Xiaoqing Pan is supported by the Fundamental Research Funds for the Central Universities (No. WK2040160010) and China Postdoctoral Science Foundation (No. 2014M561823).
Conflict of interest statement: We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled “Bayes Factors Based on robust TDT-type Tests for Family Trio Design.”
Appendix A
Using the facts that
the expectation of Zθ can be shown to be
and the variance of Zθ is
Therefore, Zθ is asymptotically distributed as
Appendix B
Let f(x)=n2x+n4x2. Making Taylor expansion of
The variance of
where
Therefore,
Appendix C
Denote
and
The covariance between Zθ and Zhwd can be shown to be
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©2015 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Research Articles
- A novel method to prioritize RNAseq data for post-hoc analysis based on absolute changes in transcript abundance
- A mutual information estimator with exponentially decaying bias
- Bayes factors based on robust TDT-type tests for family trio design
- Modeling gene-covariate interactions in sparse regression with group structure for genome-wide association studies
- Weighted Kolmogorov Smirnov testing: an alternative for Gene Set Enrichment Analysis
- Application of the fractional-stable distributions for approximation of the gene expression profiles
- Software and Application Notes
- CSI: a nonparametric Bayesian approach to network inference from multiple perturbed time series gene expression data
- TopKLists: a comprehensive R package for statistical inference, stochastic aggregation, and visualization of multiple omics ranked lists
Artikel in diesem Heft
- Frontmatter
- Research Articles
- A novel method to prioritize RNAseq data for post-hoc analysis based on absolute changes in transcript abundance
- A mutual information estimator with exponentially decaying bias
- Bayes factors based on robust TDT-type tests for family trio design
- Modeling gene-covariate interactions in sparse regression with group structure for genome-wide association studies
- Weighted Kolmogorov Smirnov testing: an alternative for Gene Set Enrichment Analysis
- Application of the fractional-stable distributions for approximation of the gene expression profiles
- Software and Application Notes
- CSI: a nonparametric Bayesian approach to network inference from multiple perturbed time series gene expression data
- TopKLists: a comprehensive R package for statistical inference, stochastic aggregation, and visualization of multiple omics ranked lists
