# Find the difference in treatment and control groups during segments of time series data

I have time-series data for a control group and treatment group. I would like to measure the change in current flowing through a cell membrane before and after drug treatment. Each cell is treated with either a control substance or a drug (e.g. Verapamil). Ideally, the control group should show no change in current, while the treatment group should show a change during a few brief time periods. I would like to determine the brief time periods when the change in current in the treatment group is different from the control group.

The figure below shows the average change in current (bottom panels) for cells treated with the control substance (n=6) and Verapamil (n=9). I zoomed in on a segment (right) where I expect to see a difference between the control and drug groups. The red box (right top panel) indicates where p<.05 when comparing the two groups with a t-test at every timepoint.

I'm quite happy with the segments that the t-test identified, as a modeling study produced similar results. I've read that running t-tests at every timepoint is not a valid approach for time-series data. According to this post, it may be appropriate to fit a Gaussian mixture model to the data, and then use parametric bootstrapping to compare the groups.

Fitting Gaussian mixture models and parametric bootstrapping are new concepts to me, so I was hoping for some feedback before I started down that path. Specifically, I was hoping someone could help me understand:

• Is the Gaussian mixture models + parametric bootstrapping a valid approach for this problem? Are there assumptions I need to consider if I pursue this approach?
• Most of the examples I've seen online have a multiple orders of magnitude fewer timepoints than my dataset. Will this affect my ability to fit the data?
• My data has occasional jumps in ∆I when stepping to new voltage values (right panel, at ~1972ms). My guess is that these jumps will be difficult to fit. Because of this, I was wondering if it is valid to approach each segment separately, fitting Gaussian models from 1ms after each voltage "discontinuity" to the end of that segment?