Order-restricted inference for ordered gene expression (ORIOGEN) data under heteroscedastic variances

An Inference Methodology for Selecting and Clustering Genes Based on Likelihood Ratio Test

Peddada et al. (Gene selected and clustering for time-course and close-response microarray experiments using order-restricted inference, Bioinformatics 19 (2003): 834–841) proposed a new method for selecting and clustering genes according to their time-course or dose-response profiles. Their method necessitates the assumption of a constant variance through time or among dosages. This homoscedasticity assumption is, however, seldom satisfied in practice. In this paper, via the application of Shi’s algorithms and a modified bootstrap procedure (N. Z. Shi, Maximum likelihood estimation of means and variances from normal populations under simulations order restrictions (J. Multivariate Anal. 50 (1994) 282–293), we proposed a generalized order-restricted inference method which releases the homoscedasticity restriction. Simulation results show that procedures considered in this paper as well as those by Peddada et al. (Gene selected and clustering for time-course and close-response microarray experiments using order-restricted inference, Bioinformatics 19 (2003) 834–841) are generally comparable in terms of Type I error rate while our proposed algorithms are usually more powerful.

Classification of samples into two or more ordered populations with application to a cancer trial

In many applications, especially in cancer treatment and diagnosis, investigators are interested in classifying patients into various diagnosis groups on the basis of molecular data such as gene expression or proteomic data. Often, some of the diagnosis groups are known to be related to higher or lower values of some of the predictors. The standard methods of classifying patients into various groups do not take into account the underlying order. This could potentially result in high misclassification rates, especially when the number of groups is larger than two. In this article, we develop classification procedures that exploit the underlying order among the mean values of the predictor variables and the diagnostic groups by using ideas from order-restricted inference. We generalize the existing methodology on discrimination under restrictions and provide empirical evidence to demonstrate that the proposed methodology improves over the existing unrestricted methodology. The proposed methodology is applied to a bladder cancer data set where the researchers are interested in classifying patients into various groups.

Analysis of Correlated Gene Expression Data on Ordered Categories

A bootstrap based methodology is introduced for analyzing repeated measures/longitudinal microarray gene expression data over ordered categories. The proposed non-parametric procedure uses order-restricted inference to compare gene expressions among ordered experimental conditions. The null distribution for determining significance is derived by suitably bootstrapping the residuals. The procedure addresses two potential sources of correlation in the data, namely, (a) correlations among genes within a chip ("intra-chip" correlation), and (b) correlation within subject due to repeated/longitudinal measurements ("temporal" correlation). To make the procedure computationally efficient, the adaptive bootstrap methodology of Guo and Peddada (2008) is implemented such that the resulting procedure controls the false discovery rate (FDR) at the desired nominal level.