A Linear Mixed Model Spline Framework for Analysing Time Course ‘Omics’ Data

Abstract

Time course ‘omics’ experiments are becoming increasingly important to study system-wide dynamic regulation. Despite their high information content, analysis remains challenging. ‘Omics’ technologies capture quantitative measurements on tens of thousands of molecules. Therefore, in a time course ‘omics’ experiment molecules are measured for multiple subjects over multiple time points. This results in a large, high-dimensional dataset, which requires computationally efficient approaches for statistical analysis. Moreover, methods need to be able to handle missing values and various levels of noise. We present a novel, robust and powerful framework to analyze time course ‘omics’ data that consists of three stages: quality assessment and filtering, profile modelling, and analysis. The first step consists of removing molecules for which expression or abundance is highly variable over time. The second step models each molecular expression profile in a linear mixed model framework which takes into account subject-specific variability. The best model is selected through a serial model selection approach and results in dimension reduction of the time course data. The final step includes two types of analysis of the modelled trajectories, namely, clustering analysis to identify groups of correlated profiles over time, and differential expression analysis to identify profiles which differ over time and/or between treatment groups. Through simulation studies we demonstrate the high sensitivity and specificity of our approach for differential expression analysis. We then illustrate how our framework can bring novel insights on two time course ‘omics’ studies in breast cancer and kidney rejection. The methods are publicly available, implemented in the R CRAN package .

Development of statistical tools for integrating time course ‘omics’ data

“…Such modelling can be performed by calculating the mean or the median of the expression values across all subjects for each time point, but that naive approach is sensitive to outliers and missing data. We propose instead to model expression trajectories as a smooth function of time, using linear mixed model splines (LMMS) that we previously developed [128]. LMMS is advantageous as it can handle unbalanced designs -when the number of observations per time point is unequal, and missing data.…”

“…Description of the study The study of Dong et al modelling approach developed previously [128] was used to obtain representative trajectories over 14 equally spaced time points between embryo day 12 and postnatal day 30. In addition to allowing interpolation to even out spacing between time points, LMMS can handle unbalanced designs -when the number of observations per time point is unequal, or if there are missing data.…”

“…Smoothing prior to analysis will also help reducing the noise in the data and will prevent the detection of high-frequency random noise. We further filtered the data to retain only miRNAs and mRNAs declared as differentially expressed over time using lmmsDE [128] (FDR ≤ 0.05). The final dataset analysed with DynOmics included 105 miRNAs and 11, 326 mRNAs.…”

“…In a previous study we showed that quality filtering and modelling of the molecule trajectories prior to clustering and differential expression (DE) analysis improves the robustness of the biological results [128]. Researchers are in need of user-friendly applications to answer their biological questions, but current supported tools that provide easy to use time course 'omics' data analysis methods via a graphical user interface (GUI) have limitations.…”

“…These methods perform differential expression analysis using spline fitting [38,128], Bayesian methods [63,57,138,139], Gaussian processes [58,59,60], and a two-step regression approach (maSigPro [61]). Other methods focus on clustering expression profiles to identify co-expressed trajectories, e.g., a subset of molecules for which expression changes occur simultaneously across time [24,37,46,140,128,139,141]. Targeted co-expression analysis can also be performed using various model-based applications to retrieve data sets from databases given specific query data [142,143,144].…”