Functional modelling of microarray time series with covariate curves

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.