Distance-Based Regression Analysis for Measuring Associations

Distance-based regression model, as a nonparametric multivariate method, has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic association studies, genomic analyses, and many other research areas. Based on it, a pseudo-F statistic which partitions the variation in distance matrices is often constructed to achieve the aim. To the best of our knowledge, the statistical properties of the pseudo-F statistic has not yet been well established in the literature. To fill this gap, the authors study the asymptotic null distribution of the pseudo-F statistic and show that it is asymptotically equivalent to a mixture of chi-squared random variables. Given that the pseudo-F test statistic has unsatisfactory power when the correlations of the response variables are large, the authors propose a square-root F-type test statistic which replaces the similarity matrix with its square root. The asymptotic null distribution of the new test statistic and power of both tests are also investigated. Simulation studies are conducted to validate the asymptotic distributions of the tests and demonstrate that the proposed test has more robust power than the pseudo-F test. Both test statistics are exemplified with a gene expression dataset for a prostate cancer pathway.

     

Summation of absolute value test for multiple outcome comparison with moderate effect

In biomedical research, in order to evaluate the effect of a drug, investigators often need to compare the differences between one treatment group and another one by using multiple outcomes. The rank-sum tests can handle the case where the outcome differences between two groups are in the same direction. If they are not, MAX can handle it and is very useful when one/some of the differences is/are relatively larger than the others. When the individual outcome difference between two groups is moderate, a new method, summation of the absolute value of rank-based test for each outcome, is proposed in this work. Power comparison with the existing methods based on simulation studies and a real example show that the proposed test is a robust test, and works well when the difference for each outcome is moderate. The authors also derive some theoretical results for comparing the power between MAX and the the proposed method.     

A model-embedded trend test with incorporating Hardy-Weinberg equilibrium information

The genetic models are greatly important in the analysis of genetic epidemiologic studies and many of the studies are conducted using the trend test under the additive model. However, for many complex diseases and traits, the underlying genetic model for a genetic locus is usually uncertain. So a robust test free of genetic model is appropriate. In this paper, the authors propose a model-embedded trend test by incorporating Hardy-Weinberg equilibrium information and obtain the explicit formula to calculate its statistical significance. Extensive simulation studies show the proposed test is more robust than the existing procedures. Finally, a real application is further analyzed to show the performance of the proposed test.