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Longitudinal genomics data and survival outcome are common in biomedical studies, where the genomics data are often of high dimension. It is of great interest to select informative longitudinal biomarkers (e.g. genes) related to the survival outcome. In this paper, we develop a computationally efficient tool, LCox, for selecting informative biomarkers related to the survival outcome using the longitudinal genomics data. LCox is powerful to detect different forms of dependence between the longitudinal biomarkers and the survival outcome. We show that LCox has improved performance compared to existing methods through extensive simulation studies. In addition, by applying LCox to a dataset of patients with idiopathic pulmonary fibrosis, we are able to identify biologically meaningful genes while all other methods fail to make any discovery. An R package to perform LCox is freely available at https://CRAN.R-project.org/package=LCox.

Response selective sampling design is commonly adopted in genetic epidemiologic study because it can substantially reduce time cost and increase power of identifying deleterious genetic variants predispose to human complex disease comparing with prospective design. The proportional odds model (POM) can be used to fit data obtained by this design. Unlike the logistic regression model, the estimated genetic effect based on POM by taking data as being enrolled prospectively is inconsistent. So the power of resulted Wald test is not satisfactory. The modified POM is suitable to fit this type of data, however, the corresponding Wald test is not optimal when the genetic effect is small. Here, we propose a new association test to handle this issue. Simulation studies show that the proposed test can control the type I error rate correctly and is more powerful than two existing methods. Finally, we applied three tests to Anticyclic Citrullinated Protein Antibody data from Genetic Workshop 16.

A way to enhance our understanding of the development and progression of complex diseases is to investigate the influence of cellular environments on gene co-expression (i.e. gene-pair correlations). Often, changes in gene co-expression are investigated across two or more biological conditions defined by categorizing a continuous covariate. However, the selection of arbitrary cut-off points may have an influence on the results of an analysis. To address this issue, we use a general linear model (GLM) for correlated data to study the relationship between gene-module co-expression and a covariate like metabolite concentration. The GLM specifies the gene-pair correlations as a function of the continuous covariate. The use of the GLM allows for investigating different (linear and non-linear) patterns of co-expression. Furthermore, the modeling approach offers a formal framework for testing hypotheses about possible patterns of co-expression. In our paper, a simulation study is used to assess the performance of the GLM. The performance is compared with that of a previously proposed GLM that utilizes categorized covariates. The versatility of the model is illustrated by using a real-life example. We discuss the theoretical issues related to the construction of the test statistics and the computational challenges related to fitting of the proposed model.

In recent years, alignment-free methods have been widely applied in comparing genome sequences, as these methods compute efficiently and provide desirable phylogenetic analysis results. These methods have been successfully combined with hierarchical clustering methods for finding phylogenetic trees. However, it may not be suitable to apply these alignment-free methods directly to existing statistical classification methods, because an appropriate statistical classification theory for integrating with the alignment-free representation methods is still lacking. In this article, we propose a discriminant analysis method which uses the discrete wavelet packet transform to classify whole genome sequences. The proposed alignment-free representation statistics of features follow a joint normal distribution asymptotically. The data analysis results indicate that the proposed method provides satisfactory classification results in real time.