When describing experiments involving people, researchers focus more on data than on individuals who are the source of those data. Science is primarily objective, not subjective—hence the infrequent use of the personal pronouns I and We, and a preference for the passive voice, in research papers.
Perhaps it is this tendency to avoid referring to individuals and using such terms as cases, subjects, and even data points that led the AMA Manual of Style to include specific guidance on this topic as part of general guidance on correct and preferred usage of common words and phrases. The manual maintains  that the ‘use of case is dehumanizing when referring to a specific person.’
I find two trends to be relevant to this discussion. The first relates to lawsuits against doctors about violating privacy. Even when the text contains no identifying information, patients may file lawsuits against the physician-authors. Such possibilities encourage medical authors to be as impersonal as possible. The other trend relates to what is sometimes referred to as ‘political correctness,’ which is seen in such practices as using visually challenged for the blind and differently abled for the handicapped. Some people find even the term subject, when used to denote a person, as indicative of a lower status. In response to these considerations, which make medical writing especially challenging, we have networks such as the EQUATOR Network, short for Enhancing the QUAlity and Transparency Of health Research, which offers toolkits for authors of research papers .
Researchers in the field of medicine may feel overwhelmed by the sheer quantity of guidance available to them. However, in choosing between case and patient, it is useful to remember that case goes with the abstract whereas patient goes with the concrete: a case of hepatitis is a statistic that excludes everything else about the event but a patient suffering from hepatitis not only has hepatitis but many other attributes as well including gender, age, and dietary habits that have a bearing on the case. Each word has its uses, and a skilled writer chooses between them with discretion.
 AMA. 2007. AMA Manual of Style: a guide for authors and editors, 10th edn., p. 388. New York: Oxford University Press [and American Medical Association]. 1010 pp.
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