Friday, December 11, 2009
Letters Math
Posted By Brandon Burt on December 11, 2009, 9:13 AM
I was particularly bugged by some mathematical sloppiness contained in one of the letters in this week's Friday Letters Round-up.
The writer states that "you have X number of doctors taking care of X number of patients which takes X amount of time" and, from this, concludes that it's best to minimize the number of patience receiving health care.---
However, given that there are x doctors and x patients, then the health-care system is operating at a one-to-one doctor/patient ratio. There's no reason to conclude, as the writer does, that the amount of time doctors spend treating patience keeps pace as x increases -- the math doesn't work out.
If we let d = the total number of doctors, p = the total number of patients, and c = the average amount of time each doctor spends doing clinical work, then the average amount of time t each patient may spend being treated may be expressed as t = dc / p
The writer is trying to say that, if c and d remain constant, t is inversely proportional to p, which is a reasonable statement.
However, he neglects to recognize that there is another variable q: the average time per patient each doctor must spend dealing with random insurance forms. Then, t = d(c - qp) / p.
Expanding the quotient, we find that t = d(c/p - q)
Then, as q approaches 0, t increases uniformly.
This shows that, by eliminating complicated insurance forms, a single-payer system would actually increase the average amount of time doctors could spend with their patients, or increase the average number of patients a doctor could see in one day.
Bottom line: Don't pick up your math tips in the letters section.
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