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 self-controlled case series approach,
The case report follows a woman who was self-administering 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:
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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.
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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, placebo-control 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:
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From the Binomial bootstrap method, I’ve estimated the likelihood that the lack of depression while taking the supplement is due to simple chance
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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