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In this paper we have demonstrated a complete framework for the analysis ofmicroarray time series data. The unique characteristics of microarry data lendthemselves well to a functional data analysis approach and we have shown howthis naturally extends to the inclusion of covariates such as age and sex. Ourmodel presented here is a specialisation of the more general functionalmixed-effects model and, to the best of our knowledge, we are the first to showhow to derive the maximum-likelihood estimators, EM-algorithm, confidenceintervals and smoother matrix with more than one fixed-effects function.  We were motivated by a real data set characterising healthy human geneexpression levels over time and we have aimed to improve upon the existingresults with a more flexible model. By taking a roughness penalty approach,this is achieved while avoiding overfitting, allowing for a departure from theoriginal linear mixed-effects model when the data permits it. A deeperbiological interpretation is required to fully assess our success here, but theresults we have highlighted in this paper suggest that we can easily attachmeaning to our findings.

Functional modelling of microarray time series with covariate curves