Commentary: A structural approach to Berkson’s fallacy and a guide to a history of opinions about it

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In 1946, the physician and statistician Joseph Berkson (1899–1982) pointed out that two diseases that are independent in the general population may become ‘spuriously associated’ in hospital-based case-control studies.1 This spurious association was later referred to, often in lively debates,2–14 as Berkson’s fallacy, Berkson’s paradox or Berkson’s bias. Some authors restricted the interpretation of Berkson’s fallacy to disease-disease associations,2,5,7,8 whereas others thought that the fallacy would also apply to exposure-disease associations in hospital-based case-control studies.10–15 In this article we use directed acyclic graphs (DAGs) to describe the structure of Berkson’s fallacy, first for disease-disease associations and then for exposure-disease associations. This permits us to understand the contentious debates and strongly differing opinions about Berkson’s fallacy, and has practical implications for study design and interpretation (see Box 1). Box 1. Practical implications of Berkson’s fallacy The fallacy that became eponymous for Berkson caused controversy from its initial formulation onwards. Some held that it biased all case-control studies in hospitals; others maintained that it was only pertinent for associations between prevalent diseases, and did not exist for exposure-disease associations. The DAG analyses in this paper show that Berkson’s fallacy can exist when studying exposure-disease associations, be it only in an ‘indirect’ form and in exceptional circumstances: when in a hospital-based case-control study persons with a prevalent diagnosis are enrolled who were hospitalized for another disease that is associated with this exposure. The DAG of the problem that Berkson originally described has the same structure of all biases due to conditioning on a collider, but cannot be endowed with a causal interpretation since it was formulated and worked out as a problem of the association of prevalent diseases. When using incident cases in hospital-based case-control studies, Berkson’s fallacy becomes highly unlikely for exposure-disease associations, unless there are many people who have developed two different new diseases more or less at the same time and are hospitalized for the other disease, i.e. the disease that is not the subject of the case-control study. When incident cases in a case-control study consist only of people who have been hospitalized for that disease, Berkson’s fallacy is not possible. It is likely that Berkson’s fallacy has had very limited, if any, impact on the findings of epidemiological studies.