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 themore general functionalmixed-effects model (Rice andWu, 2001;Guo, 2002) and, to the best of our knowledge, we are the first to show how to derive the maximumlikelihood estimators, EM-algorithm, confidence intervals and smoother matrix with more than one fixed-effects function. We weremotivated by a real data set 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. It may also prove worthwhile performing a comparative analysis with Eady et al. (2005), which is another, similar longitudinal study taken over a shorter period of five weeks.