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)
  • $\begingroup$ 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

1 Answer 1


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)


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.