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I am looking at the effects of resistance to a drug intended to increase serotonin levels on the course of depression. Basically, every participant (N=20) takes a pre measurement of serotonin levels (concentration) and does a questionnaire to assess for depression levels (scored out of 50). Then, every participant is given the drug intended to increase serotonin levels. We then measure both their serotonin levels and depression score on the questionnaire after 15 weeks of taking the drug. We want to see if the change in depression scores (either worsened or improved depression) depends on their response to the drug (response would be whether their serotonin levels is increased, decreased, or stays the same) after the 15 weeks. Overall, our hypothesis would be that resistance to the drug (meaning it doesn’t effect their serotonin levels or even decreases serotonin levels) results in worsened depression (meaning higher depression scores after the 15 weeks) and that a positive response to the drug (meaning increased serotonin levels) improves depression scores.

The problem is I cannot find any statistical test to answer this research question.

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    $\begingroup$ The title question presumes there is no such test; unless there's a better reason for that than "I'm not aware of one", it would be better not to make that presumption in the title. $\endgroup$
    – Glen_b
    Commented Mar 2, 2020 at 2:04

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It sounds you want a "difference-in-difference" model? Basically you would just regress the change in score on the change in serotonin, and interpret the regression intercept as the average change over time, and the slope as the effect of sensitivity to the drug on depression.

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  • $\begingroup$ Thanks for the answer, so I would treat change in serotonin as the independent variable and change in depression as the dependent? And then just find a regression model that satisfies the assumption for the differences? $\endgroup$
    – Ryan
    Commented Mar 1, 2020 at 20:21
  • $\begingroup$ Yes, that's what I would do. $\endgroup$
    – Neal Fultz
    Commented Mar 1, 2020 at 21:19
  • $\begingroup$ You said the intercept of the regression as the average change over time? The average change of what over time? $\endgroup$
    – Ryan
    Commented Mar 2, 2020 at 3:16
  • $\begingroup$ The time between pre/post test. $\endgroup$
    – Neal Fultz
    Commented Mar 2, 2020 at 19:33
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There are two levels of the response here, increased or decreased depression. The serotonin have three levels. This gives 2x3=6 different possible outcomes for each patient. If you create a grid, 2x3, you can count the number of each possible outcome.

Meaning, in the first row, you have patients with decreased depression, in the second-row people with increased depression.

In the first column, decreased serotonin, in the middle column, no change, in the third column, with smaller serotonin. From this you perform a Pearson chi-squared test

https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test.

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