A Back of the Envelope Calculation Regarding Communities and Physicians (and a Recommendation)

I came across a statistic in A Study of Rural Society (Kolb, Brummer, and Ogburn, 1946).* From the chapter, “Rural Health and Medical Services”:

“The American Medical Associates estimates that a critical level is reached when there is one physician for every 1500 people. Below that, health and productivity are endangered.”

Two questions come to mind. First, what is the physician population ratio today? Second, how could one physician possibly care for a community of 1500 people? We’ll take on the latter first, and begin with some assumptions.

Let us assume that the population of 1500 is uniformly distributed, that is, there are just as many kids in the 0-10 age group as old folks in the 71-80 group. (This is a false assumption, as mortality rates are not constant across all age groups, but it does allow us to calculate how one physician could care for 1500 people. I’ll have more to justify the assumption below.) Defining an age group as 10 years, there are eight groups-- ages 0 to 80 years-- each with 187.5 individuals. (We’ll treat the 80+ folks as outliers. Maybe a mistake, but it doesn’t affect the numbers.) Let us assume this hypothetical population is fundamentally healthy, and does not suffer from “made up” ailments (which may be very real for a small segment of the population, but are marketed such that you, too, suffer from restless leg syndrome). Further, let us assume that individuals in this population age gracefully-- that is individuals do not desire to be able to look or preform at age 70 as they had at age 25. (You watch TV, you know what I’m talking about.) Finally, let us assume that the community is comprised of folks who are self-reliant under normal circumstances, e.g., parents do not take their children to the doctor when the kids pass around the common cold; rather, they give the kids some hot tea, tuck ‘em in bed, and let them sweat it out.

We want to next ask how often each individual in a given age group might really need to go to the doctor each year. Based on 50 years of living, raising three children, and having parents, here’s what I came up with:

Age group: number of doctor visits per individual per year (typical reasons for visit)

0-10: 2 (childhood illness & injury)
11-20: 1 (injury)
21-30: 2 (childbirth)
31-40: 1 (injury, onset of early manifesting genetic illness)
41-50: 2 (onset of menopause, injury)
51-60: 1 (injury, onset of later manifesting genetic illness, etc.)
61-70: 2 (falls, & just getting older!)
71-80: 2 (ditto)

Recall the first assumption of uniform age distribution. Certainly, an infant is going to be taken to the doctor more than twice a year. But some children and adolescents, absent a broken limb, will not need to go to the doctor at all in any given year ( in the ‘40s, boys “worked through” sports injuries, and girls’ “mood swings” were attributed to a visit from some distant “Aunt”), same goes for men in their 20s, and many folks in their 20s through 60s. So I contend that, at least for this back of the envelope calculation, my assumptions stand for this hypothetical community of the mid-1940s.

Let’s say our physician is committed to spending one full hour with each of his patients. Yes, yes, it takes more than an hour to set a broken bone, but it may take only 15 minutes to pronounce that Little Junior is doing just fine. So again, it all washes out on the back of the envelope. How much time does he spend addressing the medical needs of this community? 1940 hours. [(2x187.5) + (1 x 187.5) ... = 1940 office visits per year.]

Lo and Behold! A 40 hour work week, including a two week vacation, totals 2000 work hours per year. Imagine that! The AMA, circa 1945, got it right. Remove any of the assumptions-- not all folks are perfectly healthy-- factor in 60 year old medical technology and facilities, not to mention travel time-- and a community of 1500 people is probably the upper limit of what a country doctor could handle.

What is the physician population ratio today in the US? That depends on how you want to calculate it. According to the 2000 US census, the population was 281,421,906. According to the ASMs Physician Characteristics and Distribution in the US, 2004 Edition there 853,187 physicians. Of those, 674,824 were engaged in “Patient care,” the reminder were (in decreasing order) inactive, unclassifiable, engaged in administrative medicine, research, teaching, or “other.” I can make an argument for using the greater number to calculate how many physicians are attending to the medical needs of 1500 people, but I won’t at this time. So using the lesser number, it turns out that it now takes 3.5 doctors to tend to the needs of the same sized population our one country doctor could handle. (If using the total number of physicians, add a-whole-nother doctor.)

Several things could account for this 350% increase from the AMAs 1945 “critical” doctor population ratio to today’s. First, the 1945 AMA recommendations could have been wildly wrong to begin with. But since my guesstimate about doctors’ office visits cohere nicely with the number of hours in a country doctor’s day, shall we say, and the minimal needs of a community of 1500, it seems to me that the 1945 AMA “critical level,” is justifiable

It is more likely the case that the assumptions do not apply to today’s population. Recall, the community is: fundamentally healthy; has not been exposed to “made up” ailments; ages gracefully; features a strong self-reliance streak.

There are reasons to think this three and one-half fold increase is a good thing. Increased specialization, beyond that of a country doctor, will hopefully restore the perfect vision of someone close to my family. Tomorrow. (Think good thoughts for him.) No doubt advances in medical technology, tools, and understanding of the cardio-vascular system allowed my father, one of the first 1000 by-pass recipients, who had three subsequent by-pass surgeries, to live a happy-- albeit with all the dietary sacrifices Mom could impose-- and productive life well into his 70s, and to share his life with five grand-daughters. And it’s highly unlikely that I’d be planning the next 30 or 40 years of my life with someone if that someone had been shooting himself up with pig insulin for the last 30.

1:1500 isn’t necessarily good, but isn’t necessarily bad. So I would argue, that there are valuable lessons to be learned from our hypothetical population. And I’ll conclude by suggesting that health care reform begins at home. Reform your behavior such that you are the primary provider for your health, and if you are a parent, your children’s. On optimistic days, I have great faith that those of us cut out of the “don’t tread on me” piece of cloth will prevail. On pessimistic days, I see that we have failed miserably already. The one and only way to keep yourself out of whatever “health care system” emerges is to stay healthy. Eat your veggies. Grow your own veggies. Take some Red Cross courses to learn how to deal with common “emergencies.” Age gracefully. Rely on yourselves.


* Although I am an old book lover, I do not recommend that you all beat a path to grab the four copies of A Study of Rural Society available at Amazon, unless you are curious to read a book written by the intellectual ancestors of today’s bi-coastal elitists.