Hi All,
I am searching for the correct statistical method to test if 2 continuous variables measured repeatedly (5 timepoints) in n = 20 subjects are associated with each other. The question to be answered would be along the lines of "Do the two variables show similar temporal dynamics?" or "Does variable 1 explain the change of variable 2 across time points?".
Further info: One variable is a MRI metric, one is a hormone level, see the attached plot. The hormone variable was log-transformed. Time is binned into 5 timepoints with constant time intervals, but could also be expressed as a continuous measure if needed. On visual inspection, the variables show comparable dynamics. The development across time looks non-linear.
Ideas: One can obviously correlate the differences between T0 and T1/T2/... between the two variables but I feel that information and power would get lost here. There is the "Repeated measurement correlation" method (Article Repeated Measures Correlation
fully ) but I am not fully convinced by this as, for one, it assumes a constant regression slope across subjects. There will surely be a way to model this in custom linear model framework - here, I would be thankful for suggestions as I am not too confident with this. Also, I could imagine to come up with a permutation-based method, modelling the development in each subject, averaging outcome metrics, and assessing significance based on randomized data under the null hypothesis of random temporal development.Does anyone have a good idea how to approach this theoretically and in practice? (python or R, python preferred).
Thanks a lot!
I'm wondering whether a latent transition analysis would meet your needs. The Depmix package in R does this. You can include covariates into your transition model. It is not the equivalent of a correlation, however.
If you are looking for temporal correlations specifically, the TSclust package has a function for this. Reference is: Pablo Montero, José A. Vilar (2014). TSclust: An R Package for Time Series Clustering. Journal of Statistical Software, 62(1), 1-43. URL http://www.jstatsoft.org/v62/i01/.
Lastly, see the following page for some additional ideas: https://bbolker.github.io/mixedmodels-misc/notes/corr_braindump.html
Based on your description, it sounds like you want to assess the relationship between two continuous variables measured repeatedly over time in the same individuals. You also mention that the relationship between the two variables may be non-linear, which suggests that a simple correlation analysis may not be appropriate. In this case, a common approach is to use a linear mixed-effects model (LMM) or generalized linear mixed-effects model (GLMM) to account for the repeated measures and individual differences in the relationship between the two variables.
Here's an outline of how you could approach this using R and the lme4 package:
Here's an example of the syntax for fitting an LMM in R:
==================================================
library(lme4)
model
I think you can use Principle Component Analysis (PCA), or Patial Least Square Regression.
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