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Suppose in a randomized control study, we assigned each individual to one of two interventions (A or B) with equal probability. And suppose for the sake of argument, there is complete balance in characteristics in the two groups after randomization, so individuals are indeed exchangeable for all intents and purposes.

Suppose after randomization, and for no reason, we switch the labels of the individuals - those receiving A instead receive B, and vice-versa. Are there any concerns after switching?

Now let's say after randomization, perhaps the one factor that isn't balanced is location of the individuals - those randomized to B all live closer to the factory producing A, and those randomized to A live closer to the factory containing B. We therefore switch the randomization to save on transport costs. Would this switch be allowed if we believe (or, let's say we can prove) that location is not associated with our outcome of interest? Certainly, if location is related, I can see that it should not be allowed.

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Manual intervention of switching the randomization labels would typically be frowned upon, but should have no statistical effect. A statistically valid randomization between two groups is no less valid by switching the group labels. A "good" randomization depends on how it was done and the characteristics of the selected groups - neither of those change in the slightest by re-naming the groups. It doesn't matter if you arbitrarily call the first group "Group A" or "Group B". Whether or not the randomization is good depends on whether Group A and Group B are comparable, but it doesn't matter which one is called Group A.

Switching group labels dependent on some external factor should also have no effect if there is indeed zero relationship between the study outcome and the factor. Geographic location can have a subtle influence on many, many things, though, so you may inadvertently reverse an effect by switching groups based on location. That said, this change would require that you didn't adequately randomize for location in the first place - the swapped labels are no less valid than the original ones, but the original ones might not have been very good if you didn't randomize a potentially important factor.

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    $\begingroup$ This answer may be a bit misleading in light of what OP seems to be asking. Specifically, OP states "We therefore switch the randomization to save on transport costs". This makes me think that OP is not just wanting to switch the labels, but in fact, wanting to switch the labels conditional on observed imbalance $\endgroup$
    – stats_model
    Commented Jun 21, 2022 at 21:12
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    $\begingroup$ Specifically, it's no longer just the case that the relabeling is just a matter of convention. It's that the experimenter, having seen an imbalance (which one imagine shows up originally due to sampling error) adapts their treatment plan to that imbalance. In OP's example, this would bias inference as if you repeated the same experimental procedure over and again, your treatment group will tend to be geographically closer systematic because of this intentional label switching $\endgroup$
    – stats_model
    Commented Jun 21, 2022 at 21:17
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    $\begingroup$ @stats_model I agree there is certainly a potential for bias here in practical settings where we can't rule out associations. But if the factor you're switching indeed truly has no effect on any of the variables you're interested in, modifying it won't introduce bias. In the example, the treatment group would indeed be geographically closer than it otherwise would be without the label switching, but we're starting with the premise that distance is truly irrelevant - we defined the scenario such that minimizing distance has no effect at all other than reducing travel cost. $\endgroup$
    – Nuclear Hoagie
    Commented Jun 22, 2022 at 17:28
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    $\begingroup$ @NuclearHoagie You almost never know that it truly has no effect until after you've done lots of (properly-controlled) studies. While technically correct, I think this answer is worse than unhelpful. It's like saying "if the sky is bright orange, it's the same colour as some citrus fruits". (Usually the sky is a shade of blue.) $\endgroup$
    – wizzwizz4
    Commented Jun 22, 2022 at 18:20
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Don't.

The whole point of randomization is that it removes the need to make assumptions like assuming location isn't associated with the outcome. Yes, certainly, you can do it, but your confidence in your results depends on your confidence in that assumption. What's more, since geographical location will be associated with all kinds of other potential confounds, income in particular, you also need to assume that none of these factors are related to the outcome, which is generally totally unreasonable.

Another way of looking at this is that it's a case of the design and analysis of the study being contaminated by the data itself. It would be fine to switch labels if you just decided to do so at random, but not if this analysis decision is based on the data itself. More generally, many common analyses are invalidated if the analysis is tweaked based on the data as it comes in.

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