Volume 11, Issue 6

Gene expression profiles from microarray time course experiments provide a unique opportunity to examine genome-wide signal processing and gene responses. A fundamental issue in microarray experiments is that the treatment condition can only be controlled at the cell level rather than at the gene level. The treatment condition does not affect all genes equally. Some genes depend on other genes to detect external changes. The dependency between genes is not fully deterministic and may vary with treatment condition. Thus the expression of each gene is potentially affected by two confounding effects: the treatment effect and the gene context effect arising from the regulatory interactions among genes. This gene context effect is hard to isolate. Neither can it be simply ignored. Instead, this gene context information which may be different under different treatment conditions is of primary biological interest. We introduce an approach which deals with the confounding effects and takes into account the uncontrollable gene context effect. Our method is based on the estimation of the number of hidden states, which, in our development, corresponds to the order of a hidden Markov model (HMM). For each gene, its observed expression is modeled by a gamma distribution determined by the corresponding hidden state at each time point. Those genes showing evidence for more than one hidden state can be categorized as the signalling genes, or in a wider sense, as the response genes which are coordinated by a cell system in reaction to a specific external condition. These response genes can be used in the comparison of different treatment conditions, to investigate the gene context effect under different treatments. Microarray time course data are also analyzed to demonstrate our method.

Genetic and other scientific studies routinely generate very many predictor variables, which can be naturally grouped, with predictors in the same groups being highly correlated. It is desirable to incorporate the hierarchical structure of the predictor variables into generalized linear models for simultaneous variable selection and coefficient estimation. We propose two prior distributions: hierarchical Cauchy and double-exponential distributions, on coefficients in generalized linear models. The hierarchical priors include both variable-specific and group-specific tuning parameters, thereby not only adopting different shrinkage for different coefficients and different groups but also providing a way to pool the information within groups. We fit generalized linear models with the proposed hierarchical priors by incorporating flexible expectation-maximization (EM) algorithms into the standard iteratively weighted least squares as implemented in the general statistical package R. The methods are illustrated with data from an experiment to identify genetic polymorphisms for survival of mice following infection with Listeria monocytogenes. The performance of the proposed procedures is further assessed via simulation studies. The methods are implemented in a freely available R package BhGLM (http://www.ssg.uab.edu/bhglm/).

Despite their importance in biology and biomedicine, genetic mapping of binary traits that change over time has not been well explored. In this article, we develop a statistical model for mapping quantitative trait loci (QTLs) that govern longitudinal responses of binary traits. The model is constructed within the maximum likelihood framework by which the association between binary responses is modeled in terms of conditional log odds-ratios. With this parameterization, the maximum likelihood estimates (MLEs) of marginal mean parameters are robust to the misspecification of time dependence. We implement an iterative procedures to obtain the MLEs of QTL genotype-specific parameters that define longitudinal binary responses. The usefulness of the model was validated by analyzing a real example in rice. Simulation studies were performed to investigate the statistical properties of the model, showing that the model has power to identify and map specific QTLs responsible for the temporal pattern of binary traits.

Microarray data can be used to identify prognostic signatures based on time-to-event data. The analysis of microarrays is often associated with overfitting and many papers have dealt with this issue. However, little attention has been paid to incomplete time-to-event data (truncated and censored follow-up). We have adapted the 0.632+ bootstrap estimator for the evaluation of time-dependent ROC curves. The interpretation of ROC-based results is well-established among the scientific and medical community. Moreover, the results do not depend on the incidence of the event, as opposed to many other prognostic statistics. Here, we have tested this methodology by simulations. We have illustrated its utility by analyzing a data set of diffuse large-B-cell lymphoma patients. Our results demonstrate the well-adapted properties of the 0.632+ ROC-based approach to evaluate the true prognostic capacity of a microarray-based signature. This method has been implemented in an R package ROCt632.