Single individual measured 30 times in one of two conditions, how do I compare?

#1
Hi thanks in advance for the help.

We have 60 datapoints from a single individual measured repeatedly.

30 of them are from one condition (on Oral contraceptive, OC) and 30 are from a different condition (not on oral contraceptive, non-OC). Each set of 30 was collected on 30 consecutive days, one year apart.

Currently we have aligned the days by menstrual cycle day and performed a paired t-test where the "pairs" are menstrual cycle days and the conditions are OC and non-OC.

However, this may not be valid because the delta for cycle day 1 and the delta for cycle day 2 may be more similar than the delta for cycle day 1 and the delta for cycle day 30, maybe. i.e. the data from each cycle day are not independent. This may not be the case but I don't know how to test for that, and are there other assumptions that might be being violated with this approach?

We have also considered a GLM where we look at (measure~condition + 1|cycle-day), would this be valid?

All analyses are performed in R.

The dataset is available here : https://openneuro.org/datasets/ds002674/versions/1.0.3

From the dataset: In this set of dense-sampling, deep phenotyping studies, we determined whether day-to-day variation in sex hormone concentrations impacts connectivity states across major intrinsic brain networks. In Study 1 (sessions 1-30, 2018), the participant was naturally cycling; in Study 2 (sessions 31-60, 2019), the participant was placed on an oral hormonal regimen.

Thanks,
Pneumaethylamine