Order restricted inference for oscillatory systems for detecting rhythmic signals

Motivation Many biological processes, such as cell cycle, circadian clock, menstrual cycles, are governed by oscillatory systems consisting of numerous components that exhibit rhythmic patterns over time. It is not always easy to identify such rhythmic components. For example, it is a challenging problem to identify circadian genes in a given tissue using time-course gene expression data. There is a great potential for misclassifying non-rhythmic as rhythmic genes and vice versa. This has been a problem of considerable interest in recent years. In this article we develop a constrained inference based methodology called Order Restricted Inference for Oscillatory Systems (ORIOS) to detect rhythmic signals. Instead of using mathematical functions (e.g. sinusoidal) to describe shape of rhythmic signals, ORIOS uses mathematical inequalities. Consequently, it is robust and not limited by the biologist's choice of the mathematical model. We studied the performance of ORIOS using simulated as well as real data obtained from mouse liver, pituitary gland and data from NIH3T3, U2OS cell lines. Our results suggest that, for a broad collection of patterns of gene expression, ORIOS has substantially higher power to detect true rhythmic genes in comparison to some popular methods, while also declaring substantially fewer non-rhythmic genes as rhythmic. Availability and Implementation A user friendly code implemented in R language can be downloaded from http://www.niehs.nih.gov/research/atniehs/labs/bb/staff/peddada/index.cfm. Contact [email protected]

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.