BOOKS OF RtfiDIfGS - PAHO/WHO

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REISMIAN, DEAN, ESOOBUE, AGOARWAL, KAUJALGI, LEWY & ORAVENSTEN ;._
nation and the state. Since our work was confined to supply predictions for Cuyahoga
County, two translateral prediction approaches were possible. One could either relate
national figures first to the state and then to the county or relate the state figures
directly to the county. A basic hypothesis in this study was that a relationship exists
between the numbers of anesthesiologists, surgeons, and physicians in general.
A. Model I
This model considered population and per capita income as the most important
factors which affect the number of physicians in a given region. Iistorical data on
the number of anesthesiologists in Cuyahoga County wvere not available. However,
the ratio of the number of anesthesiologists to the number of physicians was approximately
constant lor the state of Ohio frorn 1963 to 1069. 'The average ratio was 0.038,
with a range from 0.036 to 0.040. We therefore accepted 0.038 as a reasoxiable ratio
for our projections and treated Cuyalioga County as a microcosm of the state. In
Nlhdel I the nutnber of phlysciauiis ini an. year was assumed to be related to per capita
inicome and population exponentially. Specifically, if P(t) = number of physicians
in year t, S(t) = population of the county in year l and 1(t) = per capita income of
the county in year 1 then P (t) = AS (t)"'I(t)cL, where t = X-1900 (X = 1960, 1961,
1962, ... ) and Al, B", C, are equation constants. Note that both population and
per capita income were assumed to be related to year 1. Choice of base year as 1960
is irrelevant and does not change the results. S(t) = aIbl and l() = ab' where
al, b1, a2, b2.are equation constants.
D. AModel I (A )
This model predicts the supply of physicians; assuming an exponexntial relation between
the ratio of per capita income of the county anud the per capita income of the
nation. If
P(t) = number of physicians/1000 population,
I(t) = (t)/(),
I.(t) = per capita income of the county in year t,
1. (t) = per capita income of the nation in year t,
then P(t) = Aj2l(¿)B, A 2, B2 are equation constants. It was assumcd that I (t) is
exponentially related to ycar t, I(t) = A 4tb ' .
Now if D (t) = number of physicians iii the county in year t, and A (1) = (population
of the county) X 10 a then D () = P(t).'A(t).
The population of the county vwas assumed to be linearly related to year t, as
A (l) = a 3t + b3, where a3, b 3 are equation constants.
C. AfMoel II(B)
A similar model can be built wherc the estimation of the supply of physicians was
from the state to the county which is called Model II (B). If
P (t) = number of physicians/1000 population,
I(I) = I()/,(),
I1 (1) = per capita income of the county in year 1,
I.(t) = per capita income of the state in year 1,
thien, P (t) = AI (l)''"' :Ld D (t) = 1, ( (). l).11
The remaining symbols are similar to those used in Model II (A).
D. Model III
In this model the supply of pliysiciaiis was assumed to grow expollc,,tially with
year t. If P(t) = number of physicians in the county in year t aud 1 = X-1900 (where