Longitudinal Impact of Intervention on Continuous Outcome Variable

Question

I am working on a research project to determine the impact of several different interventions on a dependent variable. Over the last couple days, I have been reading about possible ways to approach the problem, but I haven't found anything that exactly fits how I have conceptualized the problem (though perhaps I'm thinking about it in the wrong way).

The easiest way to explain the question is with an example. Suppose I want to determine the longitudinal effectiveness of two new procedures intended to lower blood pressure. I want to know not only whether they're effective, but also which is most effective and if other factors impact the outcome (e.g. covariates like age). Considering the following:

1. Each patient undergoes only one intervention.
2. I have 5-10 blood pressure measurements for each patient pre- and post-intervention at uneven time periods.
3. Since blood pressure fluctuates naturally based on a variety of environmental factors (which I can't control for), I would like to take all of my measurements into consideration rather than using a simple point estimate (e.g. mean, median, etc.).

So far, I have investigated these options, but none of them seem to take into account everything I would like to:

1. Mixed-design ANOVA:

  In this case, I would use the intervention (and potentially, some other elements like patient sex, age, etc.) as the between-subjects factors and time as the within-subjects factor. The issue here is that I would not be able to take all of my measurements into account, I would have to use 1-2 point estimates at different time periods.

2. Interrupted Time Series:

  In this method, the measurements from each individual could be view as a time series. I could use interrupted time series analysis to test if there is a change at or close to the time of intervention. The problem is that this can only be used on a single time series (or possibly one time series from each intervention group), so it would be an incomplete picture of the data.

3. Multiple Analyses:

  I could perform multiple analyses to answer the different portions of my question. In this method, I could potentially use a t-test or non-parametric test (e.g. Wilcoxon) to determine separately if there is a difference pre- and post-intervention for each treatment. I could then use ANCOVA on the post-treatment data (with the pre-treatment mean/median of each sample as a covariate) to determine which of the two treatments was most successful. However, both of these would fail to take into account the variation within each of the subjects.

Note:

Previous literature on this subject has just used point estimates (e.g. median of 3 measurements) for pre-intervention and difference at pre-determined time points (e.g. 1 day, 1 week, 4 weeks, etc.) post-intervention

Is there some other type of analysis/model/test that I haven't found that could answer these questions? Am I thinking about the problem in the wrong way? Perhaps it is okay to use the point estimates and I am just overly worried about the natural fluctuation in the measurement?

Update - here's an example of the kind of data I am dealing with:

╔═══════════╦════════════╦══════════════╦═══════════╦══════════╗
║  Subject  ║ Treatment  ║ Measurement  ║   Date    ║ Pre/Post ║
╠═══════════╬════════════╬══════════════╬═══════════╬══════════╣
║ Patient 1 ║ A          ║           12 ║ 1/1/2018  ║ Pre      ║
║ Patient 1 ║ A          ║           16 ║ 1/23/2018 ║ Pre      ║
║ Patient 1 ║ A          ║           13 ║ 2/4/2018  ║ Pre      ║
║ Patient 1 ║ A          ║           14 ║ 2/7/2018  ║ Pre      ║
║ Patient 1 ║ A          ║           12 ║ 2/21/2018 ║ Post     ║
║ Patient 1 ║ A          ║           10 ║ 3/5/2018  ║ Post     ║
║ Patient 1 ║ A          ║            8 ║ 3/12/2018 ║ Post     ║
║ Patient 1 ║ A          ║            9 ║ 4/15/2018 ║ Post     ║
║ Patient 1 ║ A          ║            7 ║ 5/12/2018 ║ Post     ║
║ Patient 2 ║ B          ║           21 ║ 1/1/2018  ║ Pre      ║
║ Patient 2 ║ B          ║           22 ║ 1/23/2018 ║ Pre      ║
║ Patient 2 ║ B          ║           19 ║ 2/4/2018  ║ Pre      ║
║ Patient 2 ║ B          ║           17 ║ 2/7/2018  ║ Pre      ║
║ Patient 2 ║ B          ║           24 ║ 2/21/2018 ║ Pre      ║
║ Patient 2 ║ B          ║           21 ║ 3/5/2018  ║ Pre      ║
║ Patient 2 ║ B          ║           10 ║ 3/12/2018 ║ Post     ║
║ Patient 2 ║ B          ║           15 ║ 4/15/2018 ║ Post     ║
║ Patient 2 ║ B          ║           13 ║ 5/12/2018 ║ Post     ║
╚═══════════╩════════════╩══════════════╩═══════════╩══════════╝

Answer 1

I don't agree with your reflection about Interrupted Time Series as there may be multiple time point of Intervention and multiple ( waiting to be discovered) time points of intervention via Intervention Detection schemes here https://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html