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I want to estimate the effect of some treatments on an outcome. I am interested in the effect of treatment A, the effect of treatment B, and the effect of applying both treatments simultaneously.

I have data on who received which treatment and who received both. Would it be ok to run a regression with:

  • An indicator variable for having received only treatment A
  • and an indicator variable for having received only treatment B
  • and an indicator variable for having received both

Having this "both" category smells like parameter dependency or something to me, so I thought I should ask...

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    $\begingroup$ If the indicators are $0$ or $1$, with $1$ having received the treatment, then the indicator for both will be the product of the indicators for the individual treatments. Or you $\endgroup$
    – Henry
    Commented Jul 6, 2021 at 10:44

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You shouldn't need the indicator variable for having received both, otherwise you're good.

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    $\begingroup$ You need both if allowing for interaction/synergism/non-additivity of the treatments. Then you can make multiple contrasts. $\endgroup$
    – Frank Harrell
    Commented Jul 6, 2021 at 11:05
  • $\begingroup$ @FrankHarrell given your credentials, I believe you, but I don't understand. Could you point me to somewhere where I can read up on this some more? $\endgroup$
    – Porter
    Commented Jul 10, 2021 at 20:08
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    $\begingroup$ As was said earlier you include a product variable capturing interaction if you don't believe the two treatment effects are additive. $\endgroup$
    – Frank Harrell
    Commented Jul 10, 2021 at 21:12

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