AES Consulting meeting on 02 May 2017
Cyclical correlation structure
An RNAseq experiment is run with two genotypes with 4 pigs per genotype and samples are collected at times 0, 2, 6, and 24 hours after injection of a pathogen.
The question is about what correlation structure to use when we expect that gene response will likely be related at times 0 and 24 hours due to the circadian rhythm.
Thoughts
Try an unstructured covariance matrix, but we donâ€™t really have enough observations to estimate this covariance matrix.
Try a correlation structure like

$\gamma \rho^ st $ where $s$ and $t$ are the two timepoints  (0,24): $\gamma$, (0,2): $\rho^2$, (2,24): $\gamma\rho^2$
 $\gamma \rho^u,v$ where $u$ and $v$ are 0 for 24 hours and 1 for 6 hours, but 0 and 2 hours are optimized by maximizing over all possible choices amongst all genes
Obviously a consulting solution is to eliminate the temporal structure by taking an average or taking differences, etc.