# Multiple correlated outcomes in a randomized experiment with two groups and two time points: How to analyze?

In a randomized trial, subjects are randomized into two groups, a control group and an intervention group. There are multiple outcomes (15 in total), namely miRNA (microRNA) which are measured before (baseline) and after the intervention period (follow-up). These miRNA are highly correlated. We don't have specific hypotheses concerning the change of individual miRNAs, i.e. we don't have hypotheses of the sort "miRNA1 is expected to change in the intervention group but not miRNA2".

Usually, I would analyze such a design using an ANCOVA, with the measurement at follow-up as dependent variable and the baseline measurements and a group indicator as predictors (see Vickers et al. (2001)). We could do separate ANCOVAs for each miRNA, but I suspect it would be beneficial to take the correlation among the miRNAs into account. Also, with so many tests we'd need to make some multiplicity adjustments.

Specifically, I can think of three possible analyses that seem reasonable to me:

1. Indiviual ANCOVAs for each miRNA.
2. Summarize the miRNA using a PCA (principal component analysis) and use the components (e.g. the first one) in the ANCOVA as described above.
3. A MANVOA on the change scores of the miRNA.

Which analysis would you recommend?