  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.
