## 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 don’t really have enough observations to estimate this covariance matrix.

Try a correlation structure like

•  $\gamma \rho^ s-t$ where $s$ and $t$ are the two time-points
• (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.