Hi! I’m new to the forum and hope to get some feedback on a report I’m publishing. I’ll describe it below and if it helps, I can link to the draft paper. Please let me know if I can make this question any more clear.
The goal of the methods is to estimate the likelihood that a particular treatment caused a given outcome for a single individual, and that this event was not due to placebo. It takes inspiration from the selfcontrolled case series approach,
The case report follows a woman who was selfadministering a supplement to treat episodic depression. Her depression would happen reliably about every 2 months, lasting about 3 days at a time. She claims that she never had a depressive episode during her periodic use of a supplement, which lasted about 20 days consecutively once every 3 months over a 2 year period.
So, here’s what I did:

I simulated random dates for a window to see how often a randomly assigned period of 20 days (the treatment) would overlap with the episodic depression (3 days). I ran this simulation 15,000 times to get a probability of overlap.

To see the likelihood that there would be zero overlap over a 2 year period, I plan on counting the number of times in 15,000 simulations that there were 8 consecutive periods with no overlap (8 periods of 3 months = 2 years). I believe this estimates the probability that overlap is due to chance over the 2 year period.
The second part is as follows: this particular supplement is under intense scrutiny as a possible placebo effect. An actual randomized, placebocontrol study was done to determine how often people taking the supplement wrongly attribute a positive outcome to a placebo.
So, I’m using Bayes rule to look at the proportion of users in the randomized study who wrongly attribute a positive effect to a placebo pill.
Together, I combine the estimates for the case report:

From the Binomial bootstrap method, I’ve estimated the likelihood that the lack of depression while taking the supplement is due to simple chance

the prior distribution from the randomized study to estimate how likely it is this particular case study is suffering from a placebo effect.
I’d love feedback on this approach. I’m happy to link to my code/the paper or clarify this post.
thank you!
Greg