Abstract
An observational study has multiple control groups if it has several distinct groups of subjects who did not receive the treatment. In a randomized experiment, every control is denied the treatment for the same reason, namely, the toss of a coin. In an observational study, there may be several distinct ways that the treatment is denied to a subject. If these several control groups have outcomes that differ substantially and significantly, then this cannot reflect an effect of the treatment, since no control subject received the treatment. It must reflect, instead, some form of bias.
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Rosenbaum, P.R. (1995). Multiple Control Groups. In: Observational Studies. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2443-1_7
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DOI: https://doi.org/10.1007/978-1-4757-2443-1_7
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