I have a dataset with a bunch of entities (patients) and for each of these entities I have:

1.  A binary outcome specific to each entity (ie outcome does not vary in time)
2.  Some static predictors specific to each entity (e.g. gender, age)
3.  A single, time-varying measurement taken hourly for each entity, over some number of hours that is not necessarily the same for each (ie the timeseries for this measurement have different lengths)

I also suspect that the time-varying measurement has an effect on the outcome only when below a certain level.  In other words, doing something as simple as just taking the mean measurement over all time points does not accomplish what I want.

What I would like to do would be to have a "change point" in the time-based measurement below which it's effect on the outcome can differ from its effect above that point, or in other words, I want two coefficients for that one predictor.  I'm familiar with basic change point models but what I don't understand here is how I should literally structure my training data.  

I **don't** want to do this, because it repeats the static covariates for each measurement:

    Entity  Hour Gender  Age  Measurement  Outcome
    1       1    Male    42   3.3          1
    1       2    Male    42   8.9          1
    1       3    Male    42   1.1          1
    ...
    2       1    Female  33   2.3          0
    2       2    Female  33   5.9          0

What other choices do I have then?  What I'd really like is just one observation per entity but I'm not sure how to summarise the timeseries values into a single value for each when **I also want the change point to be part of the estimation**.

Does anybody have ideas on how to model something like this?  Confidence or credible intervals on both the change points and coefficients are a must (and suggestions within the realm of R or python would be much appreciated).

Thanks!

----
P.S.  Also, any recommendations on how to better understand the effects of repeated covariates on estimation would be a huge help too.  I know that having repeated covariates mixed with non-repeated covariates is a bad thing, but maybe there are ways to adjust for the differences in true sample sizes?  Mixed-effects regression would be great if it was applicable here, but I don't see how it is if the outcome does not also vary in time with each hourly measurement.