Functional modelling of microarray time series with covariate curves

TL;DR

This paper introduces a comprehensive functional data analysis framework for microarray time series, incorporating covariates like age and sex, and extends existing models with new estimation and inference methods.

Contribution

It presents the first derivation of maximum-likelihood estimators, EM-algorithm, confidence intervals, and smoother matrix for models with multiple fixed-effects functions in this context.

Findings

Enhanced model flexibility with roughness penalties

Successful application to human gene expression data

Potential for improved biological interpretation

Abstract

In this paper we have demonstrated a complete framework for the analysis of microarray time series data. The unique characteristics of microarry data lend themselves well to a functional data analysis approach and we have shown how this naturally extends to the inclusion of covariates such as age and sex. Our model presented here is a specialisation of the more general functional mixed-effects model and, to the best of our knowledge, we are the first to show how to derive the maximum-likelihood estimators, EM-algorithm, confidence intervals and smoother matrix with more than one fixed-effects function. We were motivated by a real data set characterising healthy human gene expression levels over time and we have aimed to improve upon the existing results with a more flexible model. By taking a roughness penalty approach, this is achieved while avoiding overfitting, allowing for a departure from the original linear mixed-effects model when the data permits it. A deeper biological interpretation is required to fully assess our success here, but the results we have highlighted in this paper suggest that we can easily attach meaning to our findings.