Correlations between two variables repeatedly measured

[Sergio Serrano]

Hi,

I have a panel data of 30 subjects with 8 longitudinal observations each. I have measured 10 plasma biomarkers as continuous outcomes that I would like to correlate with the abundance of two bacterial families in their gut microbiome, also longitudinally measured at the same 8 timepoints. Since the sample size is small, I am seeking to optimize the power to detect statistically significant associations:

The simpler option would be to calculate Spearman's correlations at each timepoint. However, with this strategy, the total number of available observations is divided by the number of timepoints (8) and implies 80 (8 timepoints x10 biomarkers) correlation analyses.

In this situation, I have noticed in the literature that a popular solution i is to simply merge all the measurements over time (i.e., 10 correlation analyses using 240 observations [8 timepoints x 30 individuals]. I assume that this is incorrect, since different measurements belong to the same individual and, hence, are intrinsically correlated.

I wonder if linear mixed models would be a more efficient and valid approach:

xtset id_subject week
mixed biomarker_A bacterial_A week || id_subject:, covariance(independent)

I understand that using this code, the computed coefficient would represent the magnitude of the association over time between both continuous variables. For example, a coefficient = 2 with P value <0.05 should be interpreted as "for every unit of increase of bacteria_A there is a significant increase of 2 units of biomarker_A".

Any comments will be very appreciated.

Thanks in advance,
Sergio

[Clyde Schechter]

Your reasoning is generally correct, and I support the use of the mixed model here. We can quibble over whether the inclusion of week as a linear continuous term is appropriate--but that depends on the science here which you understand and I don't. One other detail in the model: if you are treating these biomarker assessments as repeated measures, -cov(exchangeable)- would usually be more appropriate than -cov(independent)-.

I am one of those people who wholeheartedly endorse the American Statistical Association's recommendation that the concept of statistical significance be abandoned, and I urge others here to move to a world beyond p < 0.05. See https://www.tandfonline.com/doi/full...5.2019.1583913 for the "executive summary" and
https://www.tandfonline.com/toc/utas20/73/sup1 for all 43 supporting articles. Or https://www.nature.com/articles/d41586-019-00857-9 for the tl;dr. That said, yes, a coefficient = 2 would be interpreted as a unit of increase of bacteria_A is associated with a 2 unit increase of biomarker_A.

[Sergio Serrano]

Thank you very much for your reply. I enjoyed and learnt reading through the ASA recommendations.