I´m trying to undertake a meta-analysis of change-from-base-line longitudinal data. My idea is to code an Heterogenous autoregressive covariance matrix (HAR1), and then fit a multiple splines model for each study, which will be pooled in a second stage with a Random Effect Model.

My data frame corresponds to the mean and SD of a variable through multiple time points in multiple studies (not all studies share the same time points).

#Chunck of data in long format extracted with dput()
structure(list(study = c("Chan et al. (2007)", "Chan et al. (2007)", 
"Chan et al. (2007)", "Chan et al. (2007)", "Miyamoto et al, (2014)", 
"Miyamoto et al, (2014)", "Miyamoto et al, (2014)", "Miyamoto et al, (2014)", 
"Miyamoto et al, (2014)", "Miyamoto et al, (2014)"), n = c(11, 
11, 11, 11, 15, 15, 15, 15, 15, 15), time_point = c(0, 24, 48, 
72, 0, 8, 16, 24, 32, 40), value = c(108.955, 219.403, 359.701, 
223.881, 193.8, 274.7, 294.1, 289, 294.6, 291.7), SD = c(82.09, 
105, 194.03, 113.432, 70.1, 70.7, 78.1, 88.1, 68.2, 72.7)), row.names = c(NA, 
-10L), class = c("tbl_df", "tbl", "data.frame"))

Although I have found some papers on the topic, they are difficult to generalize. Can you help me on how to code an HAR1 for the change from baseline data?
Do I need to arbitrarily set a correlation coefficient? If so, what would be a good approximation?

This GitHub includes code for an HAR1 given 4 fixed time-points