I have collected `metabolomics`

data from cancer patients in 3 time
points (1st, 2nd and 3rd week) but `from different patients`

meaning 1st
week data is collected from some patients, 2nd week's data from different
patients and the same for 3rd week.
if I had data for all 3 weeks from the same patients, I could model
the data and see if there is any association between 3 weeks or not
which is my goal.
so the question is considering the fact that I have data from
different groups of patients for each week, is it still possible to
reach my goal which is finding the association (correlation) between 3 weeks using data
of 3 weeks but from different patients?
is there any statistical method or analysis for my goal?

Do you have data from some patients at multiple time points (i.e. some patients are represented at more than one time point) or are all the patients entirely different at each time point? In the first case, you have incomplete time series and you should treat this as a missing value problem. In the second case, this could be considered as independent sampling of a population at different time points so there's no missing value. I am not quite sure I understand what you're trying to do but for the second case, there are methods to compute measures of association between two data tables.

@ Jean-Karim Heriche: the 2nd is similar to what I meant. every time point has different patients.