Order restricted inference for oscillatory systems for detecting rhythmic signals

Abstract

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: peddada@niehs.nih.gov

A Bootstrap Based Measure Robust to the Choice of Normalization Methods for Detecting Rhythmic Features in High Dimensional Data

“…The vertical axis (Dim2) may be interpreted as the axis drawing distinctions between ORIOS and RAIN algorithms. Lastly, it is clear from the MCA plot that ORIOS normalization methods are less separated than JTK or RAIN, i.e., rhythmic (and non-rhythmic) groups are more compact when using ORIOS, which is one more reason, in addition to the results provided in Larriba et al ( 2016 ), to prefer ORIOS as the algorithm for detecting rhythmic genes.…”

“…The mouse liver data consisted of 45,101 probe sets (genes) at 48 time points representing two periods. Taking M g ( n, a ) ≥ 0.99 as the criterion to declare a gene to be rhythmic (the choice of this criterion is motivated by the findings of Larriba et al, 2016 ), in Table 1 we summarize the results of three rhythmicity detection algorithms, namely ORIOS, JTK, and RAIN using unnormalized data and seven normalization methods ( 0.-Unnormalized, 1.-Quantile, 2.-(Cyclic) Loess, 3.-Contrast, 4.-Constant, 5.-Invariant Set, 6.-Qspline, 7.-VSN ). The number of rhythmic genes identified varies vastly among the normalization methods within each rhythmicity detection algorithm (Table 1 ).…”

“…This is in sharp contrast to ORIOS which almost always produced p -values subject to smaller variability than the expected p -values. This is one more reason, in addition to the results provided in Larriba et al ( 2016 ), to prefer ORIOS as the method for detecting rhythmic genes.…”

“…All statistical decision rules require a user-supplied threshold when making inferences and the proposed methodology is no exception. The threshold of 0.99 used in our criterion for rhythmicity corresponds to 1% level of significance and is largely motivated by the specificity and sensitivity findings of Larriba et al ( 2016 ).…”

“…There are several algorithms available in the literature to determine whether a gene is rhythmic or not. Some recent examples include JTK_Cycle (from now on JTK) (Hughes et al, 2010 ), RAIN (Thaben and Westermark, 2014 ), and ORIOS (Larriba et al, 2016 ). The performance of such algorithms potentially depends upon, among other factors, the normalization methods used.…”