# How can I compute cross-correlation and auto-correlation in R using pooled data?

I'm trying to perform a lagged linear regression on time series data sourced from ~10,000 hospital patients, for the purpose of estimating causal relationships between administration of a drug and a certain physiological response. For example: Do non-steroidal anti inflammatory drugs cause hypertension?

Basically, the linear model I'm trying to fit is like this:

This assumes a maximum of 30 lags. $y$ represents hypertension, $x$ is taking the drug, and $h$ is whether the patient is admitted or not (a covariate).

My question is this: Given a unique time series for each patient (all truncated to the same length of 30 time points), how can I pool all of the time series data together to estimate things like the cross-correlation (e.g., using ccf) and auto-correlation (acf) over the entire data set? If I were just trying to fit a linear model, this can be done relatively easily using something like the plm library, but I haven't been able to find anything similar for single functions.

For reference, here is a very small example of what my data set looks like (note that I only retained 6 of the 30 total time points for each patient, for brevity):

   patient_id            time     nsaid hypertension admission
1           1               1 0.4427955    0.0000000 0.0000000
2           1               2 1.0000000    0.2097246 0.0000000
3           1               3 0.0000000    0.4916697 0.0000000
4           1               4 0.0000000    1.0000000 0.0000000
5           1               5 0.0000000    0.7902754 0.0000000
6           1               6 0.0000000    0.0000000 0.0000000
7           2               1 0.0000000    0.0000000 0.0000000
8           2               2 0.4104132    0.0000000 0.0000000
9           2               3 0.8236088    0.0000000 1.0000000
10          2               4 1.0000000    0.0000000 0.6994038
11          2               5 0.5895868    0.0000000 0.0000000
12          2               6 0.1763912    0.0000000 0.0000000