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What is the ‘correct’ way to compare the effect of a drug in different conditions? For example, if I have conditions a, b, c and d, where there are different numbers of ‘control’ and ‘drug’ cells in each condition and a single parameter has been measured in control and drug-treated cell (different cells).

Of course I can easily calculate the % effect of the drug for each condition, and determine whether the effect is significant (eg unpaired Student’s t-test or non-parametric equivalent). However, how do I appropriately determine whether the effect of the drug is different in each condition?

Comparing p-values across groups is not valid (e.g. Gelman, A., & Stern, H. (2006). The Difference Between “Significant” and ‘Not Significant’ is not Itself Statistically Significant. The American Statistician, 60(4), 328–331 or Nieuwenhuis, S., Forstmann, B. U., & Wagenmakers, E.-J. (2011). Erroneous analyses of interactions in neuroscience: a problem of significance. Nature Neuroscience, 14(9), 1105–1107).

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  • $\begingroup$ Are conditions different diseases or symptoms (outcomes), or are they explanatory variables that interact with treatment (like smoking would be in a study of alcohol consumption and cirrhosis)? $\endgroup$
    – dimitriy
    Commented Apr 16, 2012 at 18:27
  • $\begingroup$ This question is a little hard to follow. Can you spell out a little more thoroughly what you are measuring and the design of the study? $\endgroup$
    – gung - Reinstate Monica
    Commented Apr 16, 2012 at 19:05
  • $\begingroup$ Sorry for the lack of clarity. 'Conditions' (a, b, c, d) are different subtypes of a protein expressed in heterologous cells. One electrophysiological measurement is made form each of several individual cells in each group. In other cells, expressing the same four receptor subtypes, the measurements are made after exposure to a drug - so there are groups: a(no drug), a(drug), b(no drug), b(drug) etc. Each of these groups is made up of a number of different cells. $\endgroup$
    – user441706
    Commented Apr 17, 2012 at 7:36

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If you perform a linear regression, you could then use an interaction term condition:treatment. This would tell you if there is any effect of the combination between the two variables. This would also allow you, using post-hoc analysis (eg. emmeans, that would allow you to further look into pairwise comparisons within groups.

For example, you can look if drug Vs Ctrl is different in Condition A, B and C in separate.

Take a look at some examples here: https://cran.r-project.org/web/packages/emmeans/vignettes/basics.html

Hope this helps!

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The effect of a drug is non-linearly related to the concentration of the drug and the sensitivity of the cells in which the effect is being measured. The most appropriate way to compare the effect of a drug in different conditions is therefore to compare drug concentration-response curves in those different conditions.

Construct log-concentration response curves and then compare the logEC50 and maxima and, perhaps, the slopes of those curves. The curves will almost certainly be sigmoidal and should not be analysed by linear regression.

Do not fall into the folly of trying to make any inferences about a drug and conditions on the basis of any tests of single drug concentrations.

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