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Suppose I have data that looks something like the following for a single subject:

Treatments: amount of a shot they receive, such as 5cc, 10cc, 15cc, 20cc Outcome of interest: energy level

Question of interest: do increases in the amount of the shot received cause increased energy levels.

And then assume that the above is done with multiple subjects (i.e. $n$ subjects face all possible treatments).

Can someone point me in the direction of tests that work for such a situation? Or perhaps point me to a book/chapter that discusses this topic?


Some thoughts: What if we looked at two treatments at a time.

For example, consider the 5cc and 10cc treatment.

  • Average the "energy level" of each subject for the 5cc treatment, and call this $e_{5cc}$.
  • Average the "energy level" of each subject for the 10cc treatment, and call this $e_{10cc}$
  • test if $e_{10cc} \geq e_{5cc}$ with two-sample t-test or something?

or, alternatively, just compute the sign (+ or -) of the difference in energy levels, for each subject, between the 10cc and 5cc treament, and do a Sign test?

However, if we look at two treatments at a time, how would we deal with the possibility that sometimes we see an increase and sometimes we see a decrease?

  • For example, what if we see a significant increase from 5 to 10cc, a decrease from 10 to 15cc, and an increase from 15-20 cc.
  • Somehow we would need to test if the increases outweigh the decreases... (i.e., we would need a way to find out which pairwise comparisons matter most)
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  • $\begingroup$ Would it make sense to have the cc of the treatment be a continuous variable? Then you could test the beta coefficient related to the cc variable (or some sort of transformation of cc such as cc$^2$ $\endgroup$ Feb 29, 2020 at 0:45
  • $\begingroup$ @DavidVeitch Is what you are suggesting the following: Let $cc$ be continuous. Then just make a panel dataset of the data and use standard estimating techniques for panel data? Also, to directly answer your question: yes it makes sense for cc to be a continuous variable, but in any observable dataset the data will have it in discrete increments. $\endgroup$
    – user106860
    Feb 29, 2020 at 0:52

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You can analyze this via a dose–response curve (wiki), which shows the magnitude of response (in this case energy levels) for different levels of drug concentration. There is a package in R (called "drc"), you can read more about it in Ritz C, Baty F, Streibig JC, Gerhard D (2015) Dose-Response Analysis Using R. PLoS ONE 10(12). (journal link)

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