Band 17, Heft 2

Gene-environment (G×E) interaction plays a pivotal role in understanding the genetic basis of complex disease. When environmental factors are measured continuously, one can assess the genetic sensitivity over different environmental conditions on a disease trait. Motivated by the increasing awareness of gene set based association analysis over single variant based approaches, we proposed an additive varying-coefficient model to jointly model variants in a genetic system. The model allows us to examine how variants in a gene set are moderated by an environment factor to affect a disease phenotype. We approached the problem from a variable selection perspective. In particular, we select variants with varying, constant and zero coefficients, which correspond to cases of G×E interaction, no G×E interaction and no genetic effect, respectively. The procedure was implemented through a two-stage iterative estimation algorithm via the smoothly clipped absolute deviation penalty function. Under certain regularity conditions, we established the consistency property in variable selection as well as effect separation of the two stage iterative estimators, and showed the optimal convergence rates of the estimates for varying effects. In addition, we showed that the estimate of non-zero constant coefficients enjoy the oracle property. The utility of our procedure was demonstrated through simulation studies and real data analysis.

Arrays based on single nucleotide polymorphisms (SNPs) have been successful for the large scale discovery of copy number variants (CNVs). However, current CNV calling algorithms still have limitations in detecting CNVs with high specificity and sensitivity, especially in case of small (<100 kb) CNVs. Therefore, this study presents a simple statistical analysis to evaluate CNV calls from SNP arrays in order to improve the noise-robustness of existing CNV calling algorithms. The proposed approach estimates local noise of log R ratios and returns the probability that a certain observation is different from this log R ratio noise level. This probability can be triggered at different thresholds to tailor specificity and/or sensitivity in a flexible way. Moreover, a comparison based on qPCR experiments showed that the proposed noise-robust CNV calls outperformed original ones for multiple threshold values.

Zhang, Z. and Zheng, L. (2015): “A mutual information estimator with exponentially decaying bias,” Stat. Appl. Genet. Mol. Biol., 14, 243–252, proposed a nonparametric estimator of mutual information developed in entropic perspective, and demonstrated that it has much smaller bias than the plugin estimator yet with the same asymptotic normality under certain conditions. However it is incorrectly suggested in their article that the asymptotic normality could be used for testing independence between two random elements on a joint alphabet. When two random elements are independent, the asymptotic distribution of $\sqrt{n}$n-normed estimator degenerates and therefore the claimed normality does not hold. This article complements Zhang and Zheng by establishing a new chi-square test using the same entropic statistics for mutual information being zero. The three examples in Zhang and Zheng are re-worked using the new test. The results turn out to be much more sensible and further illustrate the advantage of the entropic perspective in statistical inference on alphabets. More specifically in Example 2, when a positive mutual information is known to exist, the new test detects it but the log likelihood ratio test fails to do so.