Occam's razor vs Hickam's dictum

Relating it to the field of medicine, a physicist should strive to look for the fewest possible causes that will account for all the symptoms. This is portrayed through the TV series House, in which Dr Gregory always treats his patients based on one disease. If the symptoms worsen, then the unknown disease must have been mistreated. The cause of the symptoms, though difficult to envisage, can actually be the simplest and most likely of those that are considered, thus conforming to Occam's Razor. Yeah, I know, more like turning the patient into a guinea pig put into a medical experiment that can cost the patient his/her life. But hey, if the patient dies, the doctor in charge can be convicted of negligence that leads to death; which immediately takes away the doctor's permit.
On the other hand, Hickam's dictum states that patients can have as many diseases as they damn well please. Yeah, those were the exact words from John Hickam, MD. The argument given by him is that it is often statistically more likely that a patient has several common diseases, rather than having a single rarer disease which explains the myriad of their symptoms. Another key reason is that, independently of statistical likelihood, some patients do in fact turn out to have multiple diseases. In such cases multiple categories of diagnosis may indeed have independent causes rather than a single source, i.e. may be due to separate events or combinations of events to which the patient may have been subjected or exposed. Thus Hickam's dictum provides physicians with a counterbalancing principle to the unfettered use of Occam's razor in diagnosis.
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I'm bored. Can't help it.