# how to measure the causal impact of interventions which happen at different times on different time series?

My data consists of a bunch of time series of daily clicks on some merchandises on a website, a portion of which have an intervention (only 1 intervention per time series), others don't. The intervention happens at different timing at different time series in the past. I want to measure the causal effect of the intervention on the treated group collectively (ideally with some confidence interval).

added sample data:

day item clicks timeperiod
1.   'A'  20.    'before intervention'
2.   'A'  18.    'before intervention'
3.   'A'  22.    'before intervention'
...
100. 'A'  26.    'after intervention' <-intervention event happened on day-100
101. 'A'  32.    'after intervention'
102. 'A'  30.    'after intervention'
103. 'A'  38.    'after intervention'
1.   'B'  30.    'before intervention'
2.   'B'  38.    'before intervention'
3.   'B'  32.    'before intervention'
...
50. 'B'  56.    'after intervention' <-intervention event happened on day-50
51. 'B'  52.    'after intervention'
52. 'B'  40.    'after intervention'
53. 'B'  58.    'after intervention'
...


And for items that did not receive the intervention, it's similar except the last col doesn't exist

I have some questions:

• How can I aggregate the treated time series despite the different timing of the interventions? Assuming there are other cofounders that make the traffic vary. I was trying to find some implementation to refer to but haven't found any yet.
• would it make sense to measure the effect on individual treated time series and report the distribution of effects instead? is it better to approach it at a collective level or individual level?
• When is it better to use matching vs synthetic data for choosing controls?

Thanks in advance for any answers!

• Welcome to CV! Is your outcome clicks per individual, per day? And how is the intervention assigned? Are individuals randomized to treatment and control conditions upon visiting the website? Please clarify or show us a small subset of your data. Dec 29 '20 at 0:48
• @ThomasBilach that's right. the outcome could be on them individually or collectively. the intervention was done previously on some pre-selected items (not by me). it's not a randomized treatment/control setting but there are plenty of potential controls. I'm adding some sample data above Dec 29 '20 at 3:08