Motivated by questions arising from the field of statistical genetics, we consider the problem of testing main, nested, and interaction effects in unbalanced factorial designs. Based on the concept...

Background: Microarray experiments examine the change in transcript levels of tens of thousands of genes simultaneously. To derive meaningful data, biologists investigate the response of genes within specific pathways. Pathways are comprised of genes that interact to carry out a particular biological function. Existing methods for analyzing pathways focus on detecting changes in the mean or over-representation of the number of differentially expressed genes relative to the total of genes within the pathway. The issue of how to incorporate the influence of correlation among the genes is not generally addressed. Results: In this paper, we propose a non-parametric rank test for analyzing pathways that takes into account the correlation among the genes and compared two existing methods, Global and Gene Set Enrichment Analysis (GSEA), using two publicly available data sets. A simulation study was conducted to demonstrate the advantage of the rank test method. Conclusions: The data indicate the advantages of the rank test. The method can distinguish significant changes in pathways due to either correlations or changes in the mean or both. From the simulation study the rank test out performed Global and GSEA. The greatest gain in performance was for the sample size case which makes the application of the rank test ideal for microarray experiments.

In the parametric setting, the notion of a likelihood function forms the basis for the development of tests of hypotheses and estimation of parameters. Tests in connection with the analysis of variance stem entirely from considerations of the likelihood function. On the other hand, non parametric procedures have generally been derived without any formal mechanism and are often the result of clever intuition. In the present article, we propose a more formal approach for deriving tests involving the use of ranks. Specifically, we define a likelihood function motivated by characteristics of the ranks of the data and demonstrate that this leads to well-known tests of hypotheses. We also point to various areas of further exploration such as how co-variates may be incorporated.

Since December 2019, many statistical spatial–temporal methods have been developed to track and predict the spread of the COVID-19 pandemic. In this paper, we analyzed the COVID-19 dataset which includes the number of biweekly infected cases registered in Ontario from March 2020 to the end of June 2021. We made use of Bayesian Spatial–temporal models and Area-to-point (ATP) and Area-to-area (ATA) Poisson Kriging models. With the Bayesian models, spatial–temporal effects and government intervention effects on infection risk are considered while the ATP Poisson Kriging models are used to display the spread of the pandemic over space.

A general method is proposed for constructing nonparametric tests of trend for proportions. Such alternatives arise in situations where it is of interest to test for monotonicity in rates of growth. The class of tests is based on the ranks of the observations. The general approach consists of defining two sets of rankings: the first describes the time and the other the binary data itself. The test tatistic measures the similarity between the two sets. The asymptotic null distributions are determined for similarity measures due to Spearman, Kendall and Hamming. A limited simulation study shows that the Spearman test has greater power.