Perhaps these articles will be of interest:

Linden, A., & Yarnold, P.R. (2016). Using machine learning to identify structural breaks in single-group interrupted time series designs. Journal of Evaluation in Clinical Practice, 22, 855-859. DOI: 10.1111/jep.12544

Linden, A., & Yarnold, P.R. (2018). Using machine learning to evaluate treatment effects in multiple-group interrupted time series analysis. Journal of Evaluation in Clinical Practice, 24, 740-744 DOI: 10.1111/jep.12966

ODA maximizes (weighted) AUC. Open access articles are available at www.ODAJournal.com. For example,

Article The Australian Gun Buyback Program and Rate of Suicide by Firearm

Article UniODA vs. ROC Analysis: Computing the "Optimal" Cut-Point

It just occurred to me that another possibility is conducting a maximum-accuracy (optimal) little-jiffy Markov analysis.

Here is a brief open-access article which demonstrates “standard” analysis for a single outcome:

https://odajournal.com/2019/02/07/confirming-the-efficacy-of-weighting-in-optimal-markov-analysis-modeling-serial-symptom-ratings

And, here is a brief open-access article which demonstrates this methodology for two time-lagged outcomes:

https://odajournal.com/2019/02/18/optimal-markov-model-relating-two-time-lagged-outcomes

In your study a hybrid variation of both of these optimal Markov approaches would be used. While you are studying a single outcome (first paper), you are interested in identifying the behavior of the modeled outcome as a function of a time-lag (second paper). This would be a little-jiffy simulation: first study a time-lag of x days (x is minimum justifiably-studied time lag), then x+1 days (or whatever the context-specific justifiable time-frame happens to be), then x+2 days, and so forth, until statistically motivated judgment suggests greater lags fall out-of-range of the alternative hypothesis.

Optimal analyses perform well in backward (and forward) little-jiffy applications.

https://odajournal.com/2013/11/24/determining-when-annual-crude-mortality-rate-most-recently-began-increasing-in-north-dakota-counties-i-backward-stepping-little-jiffy

https://odajournal.com/2013/11/01/the-most-recent-earliest-and-kth-significant-changes-in-an-ordered-series-traveling-backwards-in-time-to-assess-when-annual-crude-mortality-rate-most-recently-began-increasing-in-mclean-county-nor

And, of course, ODA enables evaluation of the stationarity of a Markov process, as well as of the number of processes underlying the Markov process.

https://odajournal.com/2018/11/14/using-oda-to-confirm-a-first-order-markov-steady-state-process

https://odajournal.com/2018/11/14/using-oda-to-determine-if-a-markov-transition-process-is-second-order