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This thought experiment I came up with has been bugging me. Let's say I want to test the effectiveness of Drug A vs Drug B on reading speed (no placebo necessary). I KNOW for a fact that the effects of both drugs end after exactly 24 hours. No exception. No variation in human biochemistry.

Why couldn't I just administer both drugs to all participants over a two day period, but randomize the order (i.e. half get Drug A on day 1 and half get Drug B on day 2)? Like, what bias would be introduced by not having two treatment groups?

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  • $\begingroup$ If you are testing effectiveness of drug A vs drug B, Why don’t you give half the participants in the clinical trial drug A and give drug B to the other half? You don’t have to have placebo group for this type of study. This is done commonly and is called as “Head to Head” clinical trial. $\endgroup$
    – forecaster
    Commented Jun 19, 2020 at 23:55
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    $\begingroup$ If everyone In the trial is taking both drugs in a different sequence then it’s called “cross over design” see this article en.m.wikipedia.org/wiki/Crossover_study $\endgroup$
    – forecaster
    Commented Jun 19, 2020 at 23:57
  • $\begingroup$ I can do that, but I am asking why I need to. What bias would come from just giving the entire sample both, given my assumptions? To clarify, this isn't a practical question. If I actually ran this study, I would do as you suggested. Instead, I am asking a thought experiment to understand why your process is better. Like what's wrong with my scenario? What bias would be introduced? $\endgroup$
    – Hutchins
    Commented Jun 19, 2020 at 23:57
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    $\begingroup$ See referenced Wikipedia article if your goal is repeated measurement, it’s commonly done. A potential bias is Drug A effectiveness will spillover to next day. So you might not know if Drug A or Drug B was effective. A potential way to avoid this bias is to have Washout period, so in effect Drug A effects clears from the system during washout period. $\endgroup$
    – forecaster
    Commented Jun 20, 2020 at 0:00
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    $\begingroup$ @forecaster Ahh, thanks. So it seems like my initial intuition is right. Given my hypothetical example, and the assumptions of no carry-over, then my design is experimental and causal. Thanks! $\endgroup$
    – Hutchins
    Commented Jun 20, 2020 at 0:02

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One reason to randomize is that the treatment can alter behavior, which can change subsequent health outcomes through a non-pharmaceutical channel.

Let's say drug A works better at lifting mood, so more of the folks who get drug A on Day 1 go out drinking because they feel so much better after taking it. As a consequence of that changed behavior, when they get Drug B on Day 2 they are extra gloomy because they are hungover, which will make Drug A seem overly effective. This will even be true if there are no lingering effects of drug A itself.

Even a crossover design will not help. The folks who get Drug B on Day 1 are more likely to stay at home, so they don't have the pounding temples and nausea reducing their wellbeing under Drug A on Day 2 to offset the bias. Their Day 3 mood may altered, but by that point the are buying beers with their guinea pig earnings and the study is over.

Obviously, getting drunk is a silly example, but you might imagine other types of behavior (diet, exercise, risk taking, attrition from the study, self-medication), that can alter potential outcomes or create selection through non-pharmaceutical channels in between the two treatments.

This sort of behavior response is not applicable in all settings, so you do have to spend some time worrying whether you are making an apples to apples comparison (other than the treatment).

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