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CHAPTER 3
PhysPops --- The Doses in Some Massive Studies of Dose-Response
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Part 1.
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Purpose and Data for Our Dose-Response Studies
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Part 2.
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Some Reasons for Expecting Our Dose-Response Concept to Fail
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Part 3.
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PhysPop Data for the Nine Census Divisions, 1921-1992
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Part 4.
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Designation of the "High-5" and "Low-4" Census Divisions
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Part 5.
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Dose-Differences: What Does the Evidence Show?
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Part 6.
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"Lockstep" --- Ideal Retention of the 1921 Proportions
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Part 7.
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"Lockstep" --- Reality-Checks by Regression Analysis
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Part 8.
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Two Crucial Aspects of PhysPop History
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Box 1.
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Summary of PhysPop Values by Decades, and Their Ranking by Census Divisions.
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Figure 3-A.
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Behavior of High-5 and Low-4 PhysPops through Time.
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Figure 3-B.
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Complete "Lockstepping" of PhysPop Proportions over Time.
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Figure 3-C.
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Imperfect Retention of PhysPop Proportions over Time.
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Figure 3-D.
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Comparison of Four Types of PhysPop Values.
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Table 3-A.
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Universal PhysPop Table.
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Table 3-B.
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Population-Sizes of the Census Divisions, by Decades, 1910-1990.
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Table 3-C.
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How Sets of PhysPops Correlate through Time.
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Definition of PhysPop
"PhysPop"
is our abbreviation for "Number of Physicians per 100,000 Population." When
pressed for space: PP. When really pressed for space: pp.
*
Part
1. Purpose and Data for Our Dose-Response Studies
The
titles of this chapter and of the book itself both emphasize the term "dose-response study."
Such studies address questions like, "When all other things are equal, does the cancer mortality-rate
rise as exposure from ionizing radiation rises?" Yes. That fact has been established for decades
(Chapter 2, Part 4c). Additional proof, that ionizing radiation is a cause of Cancer, is not needed.
Then
what is our interest in additional dose-response studies?
Our
interest is in exploring Hypothesis-1, that specifically medical radiation --- which is
readily controllable by humans --- is a highly important cause of Twentieth Century cancer-mortality
in the United States. The new set of dose-response studies, contemplated for this monograph, might be
able provide a basis for estimating the magnitude of that causal role. Is the role trivial, as so often
claimed, or is it highly important? We decided to attempt dose-response studies based on the input
described below.
1a. The
Input-Data for Our Dose-Response Studies
The
minimum requirements for a dose-response study include data on responses and doses, of
course.
Cancer
is the relevant response for testing our Hypothesis-1. Cancer mortality-rates per
100,000 population are available for the United States, by states and by the Nine Census Divisions.
These rates provide our input-data on response (details in Chapter 4).
And
what about input-data on dose? A fundamental premise of our studies is that the more
physicians per 100,000 population, the more radiation procedures per 100,000 population will be
ordered. Such procedures are initiated by a physician, even if someone else actually performs a
procedure. Thus, we arrive at the premise that average radiation dose per capita
from medical procedures during a specific year,
is approximately proportional to the number of physicians per
100,000 population during the same year.
This
common-sense premise is supported by the numerous authors of the 1988 and 1993 reports
of the United Nations Committee on the Effects of Atomic Radiation. In their 1993 report, in Annex C
on medical radiation exposures worldwide, they state (UNSCEAR 1993, pp.223-224/Para.10): "In the
UNSCEAR 1988 Report, a good correlation was shown to exist between the number of xray
examinations per unit of population and the number of physicians per unit of population." And they
depict a linear correlation in Figure 1 (UNSCEAR 1993, p.347). The premise is also supported by the
evidence already provided specifically for the USA in our
Chapter 2, Part 3c,
Point 1. The substantial
increases, described there, in xray procedures per 1,000 population and in per capita sales of medical
xray film, occurred during the period of a rapid increase in the number of physicians per 1,000 (or
per 100,000) population --- namely, following federal enactment of medical entitlements in the
mid-1960s.
Our
input-data on dose will be numbers of physicians per 100,000 population, by Census
Divisions (USA), as explained in Part 1b below. At the outset, we did not know at what year such
records began to be kept, relative to the discovery of xrays in 1895. We were able to obtain data
starting in 1921.
1b. PhysPop
as a Surrogate for Medical Radiation Dose, by Census Divisions
Using
the premise from Part 1a, we can state:
Average
radiation dose (in rads) per capita from medical procedures = (k)(PhysPop), where k is
a conversion-factor from physicians per 100,000 population into average number of rads received per
capita during the same year. ("Rad" is defined in Appendix A.) We approximate that k has the same
value nationwide at any one time. There is no requirement for the value of k to remain the same,
decade after decade.
At
any one time, in each of the Nine Census Divisions, the magnitude of average per capita
dose from medical radiation is proportional to (k) times (PhysPop for that particular Census Division).
Thus, we can (and we do) use the PhysPop values for individual Census Divisions as a surrogate for
average per capita doses received in such Census Divisions. If a PhysPop value in the First Census
Division is 1.43 times bigger than the PhysPop value in the Ninth Census Division, then the resulting
average dose per person is 1.43 times higher in Census Region One than in Census Region Nine --- as
a good approximation. PhysPop values reveal the relative size of average per capita doses in the
Nine Census Divisions.
Our
studies never require the quantification of k. Thus, our studies permit the possibility that
average per capita dose could decrease in every Census Division, during a period when PhysPop values
could simultaneously increase. For example, if PhysPop rose 2-fold while average dose-level of
radiation per procedure fell 3-fold, then the average per capita dose would decrease to 2/3 of its earlier
level: Dose = (k/3)(2PhysPop) = (2/3)(k)(PhysPop).
1c. Two
Special Merits of Using PhysPop Values as Dose-Surrogates
Dose-response
studies, based on the relative size of doses, of course can be fully as valid as
studies based on absolute dose-values. Because the absolute doses from medical radiation in the past
and present are highly uncertain and forever debatable (Chapter 2, Part 3), studies based on a
reasonable approximation of the relative size of doses (PhysPop values) can be the most reliable.
Indeed, one of the major scientific strengths of this monograph is its independence from anyone's
estimates of absolute doses.
A
second strength of the PhysPop method deserves some discussion:
Epidemiologic
research on the health effects of ionizing radiation is sometimes characterized by
input-data which are vulnerable to potentially biased, after-the-fact adjustments of dosage and
responses, and after-the-fact exclusion of selected groups or cases as "unqualified" for retention in a
study, or after-the-fact inclusion of "reserve" samples. Even retroactive shuffling of dose-cohorts ---
after they have produced a dose-response --- is now a chronic practice in one of the world's most
important radiation databases, the Atomic-Bomb Survivor Database (discussion in Chapter 2, Part 5c).
Such
practices, as well as the fact that so much radiation research is funded by governments
which are far from neutral about the hazards of ionizing radiation, necessarily create doubt about the
trustworthiness of the raw databases themselves. The first obligation of objective scientists is to seek
assurance that they do not work with biased data which will produce misleading results. For example,
few objective analysts on the smoking-issue would rely on data from a database sponsored by, and thus
controlled by, the tobacco industry.
So,
in the world of radiation epidemiology, the radiation studies which are presented in this
monograph have a special foundation of credibility: The inputs for both dose (PhysPops) and response
(Mortality-Rates) are data collected over decades by people with no conceivable intent or ability to bias
the outcome of a radiation study. The data are public and not vulnerable to successful alteration.
*
Part
2. Some Reasons for Expecting Our Dose-Response Concept to Fail
We
were aware, at the outset, that the merits described in Part 1c could not eliminate the
several reasons to bet against detecting any dose-response in such data. But researchers who
demand a guarantee before they begin, rarely begin. Pessimism is paralytic. And sometimes
irrational. It can be unreasonable to assume that all imaginable obstacles, to obtaining useful
information, will actually materialize.
"Whatever
you want to do, if you overanalyze it --- if you start looking for all the pluses and
all the minuses --- you might never start." So spoke Dr. Herb Boyer, molecular biologist, and
co-founder of Genentech Inc., a pioneering enterprise in the biotechnology world. The occasion: An
interview on Genentech's 20th anniversary in 1996 (Boyer 1996).
Nonetheless,
Part 2 will briefly describe some of the potential obstacles, as a guide to whether
or not they materialized, and as a guide to some of our decisions.
2a. Inconsistent
Studies on Natural Background Radiation
What
made us ever imagine that a dose-response from medical irradiation might be
detectable by geographical regions, when numerous attempts to find a dose-response from
geographical differences in natural background radiation have been conflicting and non-definitive?
The
idea probably occurred to us because of our 1981 analysis of the Frigerio paper, described
in Chapter 2, Part 9b. Moreover, as a result of our work on the 1995 breast-cancer book, we had
learned how much medical irradiation has been used. So we thought that the average per capita dose
per year from medical radiation might exceed the annual dose from natural background sources by
enough to "show up." This thinking was related to the fact that medical x-rays are 2-fold to 4-fold
more harmful (biologically) than the gamma rays from natural background sources, as discussed in
Chapter 2, Part 7. So we decided to take the next step, and to examine the PhysPop data.
2b. The
Necessity of differences in PhysPop Values by Census Divisions
Of
course we did not know, until we obtained and studied the data in this chapter, that sufficient
differences would exist in the doses (PhysPops) on a geographical basis. It is impossible to do a
very useful dose-response study without appreciable differences in doses! Medical irradiation could be
the paramount cause of the cancer-problem, and still we would obtain no hint of such a fact from our
proposed dose-response study --- if the doses were about the same in all Nine Census Divisions.
A
dose-response study typically plots, on a graph, a proposed cause on the horizontal x-axis,
versus a proposed consequence on the vertical y-axis. If real-world evidence shows that a series of
increments in the proposed cause, goes with a series of increments in the proposed consequence, the
causal presumption is reasonable unless a better explanation can be demonstrated. The causal
presumption is especially reasonable when the proposed cause (ionizing radiation) is already a
proven cause of the effect (excess cancer-mortality).
So
our very first task was to find out if there would be any appreciable differences in the
dose-input (PhysPops in the Nine Census Divisions) for our proposed study. In Part 5 of this chapter,
we will discuss the range of differences we found in PhysPops, and how the range changed over the
1921-1992 period.
2c. Annual
Radiation Dose versus Accumulated Radiation Dose
The
chance, that a cell acquires a new (non-inherited) carcinogenic mutation due to ionizing
radiation, is proportional to the cell's accumulated radiation dose. We knew at the outset that a
PhysPop value for a single year would not be proportional to the average accumulated total dose
in one census region, versus all other regions --- unless the regional PhysPop values retained their
proportionality with each other over time. This aspect of our studies is explored in Parts 6 and 7
(below).
PhysPops,
as informative surrogates for accumulated doses, were threatened in yet
another way. Even if PhysPop rankings in the various Census Divisions happened to remain stable
long enough to produce some discernible differences in the radiation consequences, we needed to worry
about the impact of the population's mobility.
The Potential Problem from Migration between Census Divisions
Whenever
people move from a Census Division of higher PhysPop value to a Census Division
of lower PhysPop value, they carry their cancer-risk with them. Because they mix their higher
accumulated dose (and their higher risk of radiation-induced Cancer) with the new population's lower
accumulated dose (and lower risk of radiation-induced Cancer), such migration necessarily degrades
PhysPop as a measure of the relative magnitude of accumulated dose received by people dying within
those two Census Divisions. And the same potential problem applies to migration from low PhysPop
to high PhysPop Census Divisions. The concern would essentially vanish if all radiation-induced
Cancers were delivered within 2 or 3 years after irradiation. The potential problem occurs because
latency periods (delivery times) for radiation-induced Cancers are spread over decades, as discussed in
Chapter 2, Part 8. As more decades pass, more people migrate between Census Divisions. By
contrast, the migration which occurs within single Census Divisions creates no problem at all for our
proposed dose-response studies.
2d. Distribution
of the Combined Impact from Other Carcinogens
We
knew at the outset, of course, that a dose-response to medical
irradiation could be obscured in our proposed studies, if the
combined force of carcinogens other than medical irradiation
were to have an unequal impact on the cancer mortality-rates
of the Nine Census Divisions. This is a nearly universal hazard
in epidemiology. For example, in the Atomic-Bomb Survivor Study,
one can (and must) assure that the groups receiving different doses
of bomb-radiation are comparable in age-and-sex distribution. But
there is no way to force the dose-cohorts to be comparable in their
lifetime exposures to all non-bomb carcinogens (known and unknown)
before and after August 1945. And in our own studies, there is no
way to force the nine populations in the Nine Census Divisions to
be comparable in their lifetime exposures to all non-xray carcinogens
(known and unknown). In such studies (and many others), one hopes
that providence has distributed the extraneous non-comparabilities in
such a way that their combined carcinogenic force is nearly equal
("matched") in all dose-cohorts. Otherwise, these unequal impacts
can distort the true dose-response between the two variables under
study (Chapter 5,
Part 7, and Chapter 48).
*
Part
3. PhysPop Data for the Nine Census Divisions, 1921-1992
Overlapping
sources exist for data on the number of physicians per 100,000 population in the
USA. They include the U.S. Government, the American Medical Association, and the American
Hospital Association. (We did not happen to use any AHA publications.) We have found data back as
far as 1921.
3a. The
"Universal" PhysPop Table: Table 3-A (Four Pages)
Table
3-A is located, of course, after the text of this
chapter. It is the Universal PhysPop
Table covering the years 1921-1993, for the Nine Census Divisions of the USA. The word "universal"
calls attention to the fact that the PhysPops are the same no matter what cause of death is compared
with them. Thus, this single table is the origin of x-axis data for numerous chapters of this book.
The
table covers general practitioners and specialists combined. The details are provided in
Parts 3c and 3d. We did not find data for every calendar year between 1921 and 1992. The years for
which we have found data are flagged "+" in the Universal PhysPop Table 3-A. The years for which
we obtained values by interpolation, are unflagged.
The
data on PhysPops are often presented state-by-state in various sources. In combining data
from various states, to obtain the average PhysPop value for an entire Census Divisions, we weighted
each state's PhysPop value by the contemporaneous size of the state's population (details in Part 3d).
3b. Which
States Belong to Which Census Divisions?
Because
we were searching for data on the Nine Census Divisions from 1895 onward, the fact
that Alaska and Hawaii did not become states until after World War Two seemed like a probable
complication. In view of their small populations, we decided at the outset to exclude Alaska and
Hawaii from consideration. For consistency, we also excluded the District of Columbia, which is not a
state and whose population has always been small, too. So, these three entities are omitted from our
Universal PhysPop Table 3-A. Below, we list the states (total = 48) in each of the Nine Census
Divisions (from PHS 1995, p.302, for example). Populations of each Census Division, by decades, are
shown in our Table 3-B.
o East
North Central: Illinois, Indiana, Michigan, Ohio, Wisconsin. 5 states.
o East
South Central: Alabama, Kentucky, Mississippi, Tennessee. 4 states.
o Middle
Atlantic: New Jersey, New York, Pennsylvania. 3 states.
o Mountain:
Arizona, Colorado, Idaho, Montana, Nevada, New Mexico, Utah,
Wyoming. 8 states.
o New
England: Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island,
Vermont. 6 states.
o Pacific:
California, Oregon, Washington. 3 states.
o South
Atlantic: Delaware, Florida, Georgia, Maryland, North Carolina, South
Carolina, Virginia, West Virginia. 8 states.
o West
North Central: Iowa, Kansas, Minnesota, Missouri, Nebraska, North
Dakota, South Dakota. 7 states.
o West
South Central: Arkansas, Louisiana, Oklahoma, Texas. 4 states.
3c. Evolution
of Four Categories of PhysPops
Over
the years, the reports of PhysPop values gradually developed multiple categories. For
instance, distinction is made between federal and nonfederal physicians. Federal physicians are those
on active duty with the armed forces, the Public Health Service, the Veterans' Administration, the
Indian Service, and other federal agencies (Pennell 1952, p.10). Some of the distinctions developed
due to "manpower" forecasts, for wartime and for new federal programs such as Medicare and
Medicaid, which were enacted in 1965. By 1965, PhysPop values came in four varieties, based on:
1. o Total
physicians --- active + inactive, federal + nonfederal, in the USA and its
possessions (Canal Zone prior to 1980, Pacific islands, Puerto Rico, Virgin
Islands). Specified in AMA 1993,
Table A-16, p.32.
2. o Total
patient-care physicians, federal and nonfederal. Not available until
1965 (AMA 1993, Table A-16, p.32).
3. o Total
nonfederal physicians --- active + inactive --- in the 50 states and
D.C. Specified in AMA 1993,
Table A-17, p.33.
4. o Nonfederal
patient-care physicians, 50 states and D.C.
The
relative sizes of these four types of PhysPops --- for the years
1965, 1970, 1975, 1980, 1985, and 1992 --- are graphed in
AMA 1993, Figure 4, p.15. We
have reproduced the AMA graph at the end of this chapter, as
Figure 3-D. It is evident that the four
types are very tightly correlated with each other.
3d. Sources
Used for PhysPop Values from 1921 Onwards
Our
choices for the Universal PhysPop Table 3-A were determined by what was available to us
in the literature either by states or by Census Divisions. By states, the AMA tables offer only one
"choice": Total nonfederal PhysPops. As of 1949, only a very small share of the total was inactive
(see below). The fraction was low also in 1975, 1985, 1990 (see Part 3e).
PhysPops for 1921-1949
PhysPop
data from 1921 through 1949 are from Pennell 1952 in our Reference List. This is
Public Health Service Publication 263, Section 1, prepared by Maryland Y. Pennell and Marion E.
Altenderfer, and entitled "The Health Manpower Source Book Section 1. Physicians." Its Table 2 (at
page 14) is Physician-Population Ratios in the United States, by Region and State: 1921-1949. Pennell
and Altenderfer based their table on the following sources
in our Reference List: AMA 1950,
Census Bureau 1951, and
Linder 1947.
Pennell's
Table 2 does not specify any subset of physicians. By comparing numbers in
Pennell's Table 2 with numbers in Pennell's Tables 1 and 4, we can establish that the PhysPops in
Table 2 are for total physicians (active + inactive, federal + nonfederal).
Separately,
and only for the year 1949, Pennell provides the composition of the total 201,277
physicians: 179,041 active nonfederal + 12,536 federal + 9,700 retired.
PhysPops for 1959
PhysPop
data for 1959 are from Stewart
1960 in our Reference List. This
is Public Health Service Publication 263, Section 10, prepared by
William H. Stewart and Maryland Y. Pennell, and entitled "The Health
Manpower Source Book Section 10. Physicians' Age, Type of Practice, and
Location." On page 26 is its table, Physician-Population Ratio in
Each State, and Age of Physicians: Non-Federal Physicians per 100,000
Civilian Population, 1959. Stewart 1960 (p.1) bases the number and
location of physicians (mid-1959) on data supplied to the Public
Health Service by the American Medical Association, and rates per
100,000 population, by states, on mid-1959 population data from
the Census Bureau (1959). We used
1959 population data from
Grove 1968 (Table 74) in order to
obtain population-weighted PhysPop values for the Nine Census Divisions.
PhysPops for 1963, 1965, 1970, 1975, 1980, 1981
PhysPop
data for 1963, 1965, 1970, 1975, 1980, and 1981 all are taken from
AMA 1982 in our
Reference List, Table A-7, Non-Federal
Physicians, Civilian Population, Physician-Population Ratios for
Selected Years 1963-1981. That table provides all the data we need
to calculate population-weighted PhysPop values for the Nine Census
Divisions.
PhysPops for 1983
PhysPop
data for 1983 are taken from AMA 1986
in our Reference List, Table A-9,
Non-Federal Physicians, Civilian Population, and Physician/Population
Ratios for Selected Years 1963-1985. That table provides all the data
we need to calculate population-weighted PhysPop values for the Nine
Census Divisions.
PhysPops for 1985, 1990, 1993
PhysPop
data for 1985, 1990, and the start of 1993 are taken from
AMA 1994 in our
Reference List, Table A-18, Non-Federal
Physicians, Civilian Population, Physician/Population Ratios for
Selected Years 1970-1993. That table provides all the data we need
to calculate population-weighted PhysPop values for the Nine Census
Divisions.
3e. Difference
between PhysPops from Table 3-A and from
PHS 1995
In
"Health, United States, 1995 (PHS 1995,
pp.218-219), there is Table 97 which presents PhysPops for 1975, 1985,
1990, and 1994 by Census Divisions and by states. We note the word
"active" in Table 97's title: Active Nonfederal Physicians and Doctors
of Medicine in Patient Care per 10,000 Civilian Population ... 1975,
1985, 1990, and 1994. Of course, we multiply PhysPop values in Table
97 by ten, in order to convert them to the more customary "per 100,000"
population. In our Universal PhysPop Table 3-A,
the PhysPop values come from the combination of active plus inactive
physicians. Not surprisingly, our PhysPops for 1975, 1985, and 1990
are higher than those presented in PHS 1995, Table 97.
Would
analysts reach the same conclusions that we do, about the relationship
of PhysPops with biological phenomena (such as cancer mortality-rates),
if they used the ratios from Table 97, instead of the ratios from our
Universal PhysPop Table 3-A?
The
answer is yes. They would reach the same conclusions, because the
correlations between the two sets of data are so very high. We
demonstrate this by the three regression analyses which follow and
which produce correlation coefficients (R) of 0.9916, 0.9855, and
0.9863. Our studies rely on the relative magnitudes rather
than absolute magnitudes of the nine PhysPop values (Parts
1b and 1c), and such high
correlations between Table 97 and Table 3-A
mean that the relative magnitudes among the PhysPop values are
extremely similar in Table 97 and Table 3-A. (Readers who are
unfamiliar with linear regression analysis will find an introduction
to the topic in Part 7 of this chapter, and more
explanation in Chapter 5, Part 5).
Below,
listed by the Nine Census Divisions, are the PhysPop values per
100,000 population from PHS 1995,
Table 97 (including active doctors of osteopathy), and to the right
of them, the values for the matching Census Divisions from our
Universal PhysPop Table 3-A.
YEAR = 1975 Tab 97 Tab 3-A YEAR = 1975
Pacific 179 208 Regression Output:
New England 191 215 Constant -11.5257
West North Central 133 141 Std Err of Y Est 5.2312
Mid-Atlantic 195 213 R Squared 0.9832
East North Central 139 146 No. of Observations 9
Mountain 143 156 Degrees of Freedom 7
West South Central 119 128
East South Central 105 117 X Coefficient(s) 1.1784
South Atlantic 140 156 Std Err of Coef. 0.0582
Unweighted Avg. 149.3 164.4 R = 0.9916
Ratio (Tab3A/Tab97) = 1.10
YEAR = 1985 Tab 97 Tab 3-A YEAR = 1985
Pacific 225 256 Regression Output:
New England 267 293 Constant -13.6604
West North Central 183 186 Std Err of Y Est 8.5884
Mid-Atlantic 261 276 R Squared 0.9712
East North Central 193 195 No. of Observations 9
Mountain 178 193 Degrees of Freedom 7
West South Central 164 171
East South Central 150 162 X Coefficient(s) 1.1391
South Atlantic 197 216 Std Err of Coef. 0.0741
Unweighted Avg. 202.0 216.4 R = 0.9855
Ratio (Tab3A/Tab97) = 1.07
YEAR = 1990 Tab 97 Tab 3-A YEAR = 1990
Pacific 234 265 Regression Output:
New England 290 320 Constant -14.3549
West North Central 198 203 Std Err of Y Est 8.7876
Mid-Atlantic 284 298 R Squared 0.9729
East North Central 206 209 No. of Observations 9
Mountain 193 208 Degrees of Freedom 7
West South Central 178 184
East South Central 168 182 X Coefficient(s) 1.1342
South Atlantic 217 234 Std Err of Coef. 0.0716
Unweighted Avg. 218.7 233.7 R = 0.9863
Ratio (Tab3A/Tab97) = 1.07
*
Part
4. Designation of the "High-5" and "Low-4" Census Divisions
In
the Universal PhysPop Table 3-A, the PhysPop values for 1921 are presented in order of
size, from the highest value in the Pacific Division (165.11 physicians per 100,000 population) to the
lowest value in the South Atlantic Division (110.32 physicians per 100,000 population).
We
can (and do) retain the 1921 sequence of the Census Divisions, even though the PhysPop
values do not remain ranked in that order during all subsequent years. Use of the 1921 sequence leads
to two terms used in Table 3-A (and used also in our tables of mortality rates): High-5 and Low-4.
Definition of "High-Five" and "Low-Four" Census Divisions
o The
term "High-5" always refers to the first Five Census Divisions listed
in the Universal PhysPop Table for 1921: Pacific, New England, West
North Central, Mid-Atlantic, East North Central. Since PhysPop values
are surrogates for average per capita dose from medical radiation
(Part 1b), the term High-5 refers to the Census
Divisions with the highest average doses per capita from
medical irradiation in 1921. Our shortest abbreviation is Hi5.
o The
term "Low-4" always refers to the last Four Census Divisions listed
in the Universal PhysPop Table for 1921: Mountain, West South
Central, East South Central, South Atlantic. Since PhysPop values
are surrogates for average per capita dose from medical radiation
(Part 1b), the term Low-4 refers to the Census
Divisions with the lowest average doses per capita from medical
irradiation in 1921. Our shortest abbreviation is Lo4.
A Point to Keep in Mind, and the Next Question
A
point to keep in mind is that High-5 and Low-4 are two Census-Division sets whose members
were determined by their physpop rankings in 1921, not by their cancer mortality-rates in 1921.
What happens to High-5 and Low-4 PhysPop values, as the interval after 1921 grows ever longer? We
will explore that issue in Part 5, below.
*
Part
5. Dose-Differences: What Does the Evidence Show?
For
PhysPop, which is the dose-surrogate in our dose-response studies,
there are pages of entries in the Universal Table.
Do these entries reflect sufficient differences in dose among the
Nine Census Divisions --- and are differences maintained long enough in
their rank order --- to produce detectable differences in cancer consequences?
To
facilitate getting a grasp on the issue of PhysPop differences and their duration, we
calculated average values for the High-5 and Low-4 Divisions in each column. In the Universal
PhysPop Table 3-A, the nine main entries for the Nine Census Division are weighted averages
(Part 3a), but the High-5 and Low-4 averages (located beneath the main entries) are not
population-weighted. They are provided just as approximations which can supply an overview for each
particular year, and for changes over time. Table 3-A also shows the ratio of Hi5/Lo4.
5a. Revelations
about PhysPop Behavior, 1921 through 1990: Figure 3-A
Figure
3-A presents two graphs which plot annual PhysPop behavior from 1921 through 1990,
in terms of High-5 and Low-4 groupings. These graphs provide a visual overview. No values from
the graphs are ever used in calculations. Therefore, readers need not worry at all about some minor
differences between the graphs and Table 3-A. The graphs reflect our early exploration --- before we
had every final PhysPop value of Table 3-A --- of a question which would determine whether or not
to proceed with the project: Was there a persistent dose-difference between the Census Divisions?
The
upper graph plots the annual High-5 and Low-4 averages, separately, 1921-1990. It is
clear that they are relatively flat until almost 1970, when both of them take off like rockets to much
higher values. The steep rise in PhysPop values occurred after the 1965 enactment of Medicare and
other federal programs.
The
lower graph plots the annual ratios of average High-5 PhysPop over average Low-4
PhysPop. The ratio tells us how many-fold larger High-5 PhysPop is, compared with Low-4. At a
value of 1.0, of course, their magnitudes would be equal. The graph produces some very important
information.
First,
because the ratios never fall to 1.0, it immediately assures us that average annual High-5
doses always remained higher than the average annual Low-4 doses. So there has been an annual
dose-difference, from 1921 to 1990.
Second,
the graph of Hi5/Lo4 PhysPop ratios shows us that there was an extended period of
relative PhysPop stability from about 1933 through 1968. From Table 3-A (which has the final
PhysPop values), we know that the ratio of High-5 PhysPop over Low-4 PhysPop was 1.37 in 1933;
then the ratio rose to a maximum value of 1.46 in 1940; by 1968 the ratio had returned to 1.37. In
other words, between 1933 and 1968, the range for the Hi5/Lo4 ratio stayed within the limits of 1.37
and 1.46.
5b. What
the Ratios Fail to Show
The
Hi5/Lo4 ratios obscure the full magnitude of the differences between PhysPops. Although
the maximum Hi5/Lo4 ratio is 1.46, the ratio comes from averages. Two examples illustrate the point.
In 1921, when the Hi5/Lo4 ratio was only 1.18, the ratio of Pacific Division over South Atlantic was
(165.11 / 110.32), or 1.50. In 1950, when the Hi5/Lo4 ratio was 1.44, the ratio of the Mid-Atlantic
Division over East South Central was (168.81 / 83.25) = 2.03.
In
addition, the Hi5/Lo4 ratios are crude enough to obscure shifts of PhysPop rank within
both the High-5 and the Low-4 groups. Therefore, Box 1 provides a separate study of changes in
PhysPop ranking for the 1921-1990 period. What emerges
from Part 2 of Box 1 is that there is
remarkable stability in PhysPop ranking, when the Nine Census Divisions are viewed as three "Trios":
TopTrio, MidTrio, LowTrio. For example, in the 1931-1990 period, only two of the Nine Divisions
(West North Central and South Atlantic) ever "migrate" from their 1940 Trio into another Trio.
(Details in Box 1.)
*
Part
6. "Lockstep" --- The Ideal Relation among All Sets of PhysPops
The
formal definition of "lockstep" is: A method of marching in such close file that the
corresponding legs of the marchers must keep step precisely.
We
are going to bend the term, so that "lockstep" refers to a set of proportions (ratios)
whose values persist unchanged through time. For example, PhysPop "lockstep" would mean that the
proportions observed among the nine PhysPop values in 1921, and the proportions observed in every
subsequent year, are the same. PhysPop "lockstep" would mean that the relative magnitudes are
constant among the nine PhysPop values, even when the absolute values rise or fall. Part 6b will
provide an illustration.
Box
1 already demonstrates that perfect "lockstep" for PhysPop values does not occur, for
perfection would tolerate no changes in Hi5/Lo4 ratios over time (see Part 7d) and no changes in rank
order of the Divisions over time.
6a. The
Ideal Data for Our Proposed Study
Researchers
always wish for "better data." Under ideal circumstances for our inquiry, no
migration of populations from one Census Division to another would have occurred after 1895, and for
the entire century, the PhysPops of the Nine Census Divisions would have retained a fixed
proportionality with each other: "Lockstep."
Under
such circumstances, the nine average doses of medical radiation, accumulated by any
particular year, would always be in that fixed proportion to each other --- regardless of their absolute
values in rads. And the nine irradiated populations would gradually deliver the consequent
radiation-induced cancers in the same Census Division where they were irradiated --- in proportion to
dose (Chapter 5, Part 5d). The changing age-distribution of the population since 1895 would not
distort that expectation because cancer mortality-rates, by Census Divisions, are age-adjusted to a
fixed year (Chapter 4).
A Note about "Ideal" Data
In
this chapter, and later, we sometimes refer to "ideal" data or circumstances. We feel
impelled to emphasize, for students who may not have done any research yet themselves, that the term
"ideal" does not imply any bias or passion. To imagine conditions "exactly as one would desire" (see
below), unclouded by real-world perturbations, can be so crucial to elucidating a topic that it is a
regular feature of science.
For
example, chemists and physicists refer to "an ideal gas," "ideal conditions," and "the
perfect gas law." We quote from Mahan's "University Chemistry" text (Mahan 1975, p.43-44): "The
expression PV = nRT is obeyed by all gases in the limit of low densities and high temperatures ---
`ideal' conditions under which the forces between molecules are of minimum importance.
Consequently, [PV = nRT] is known as the perfect gas law, or the ideal gas equation of state."
In
other words, the law is valid under ideal conditions, but does not make perfect predictions
under real-world conditions. This use of the word "ideal" is in full harmony with the dictionary
definition which says that "ideal" means: "Existing as an idea, model, or archetype ...; thought of as
perfect or a perfect model; exactly as one would desire ...; having the nature of an idea or conception;
identifying or illustrating an idea or conception" (Webster 1954, p.720).
6b. Figure
3-B: Retention of Perfect Proportionality ("Lockstep")
With
respect to evaluating retention (or non-retention) of PhysPop proportionalities through
time, we will use Figures 3-B and 3-C as illustrations. (The term "linear regression," in the titles of
these two figures, may be unfamiliar to some readers. But the point of Part 6b can be understood
without any understanding of linear regression.) Figures 3-B and 3-C each compare the set of 1921
PhysPops with the set of 1940 PhysPops, but in different ways. When readers understand the two
figures, they will understand our Table 3-C, which shows with great simplicity how 21 sets of
PhysPops, from 1921 through 1993, compare with every other set of PhysPops through most of
this century.
In
Figure 3-B, Column B presents the 1921 PhysPop values and Column C presents the 1940
PhysPop values, from the Universal PhysPop Table 3-A. The numerical values for South Atlantic
changed from 110.32 to 100.74. The ratio (1940 / 1921) is 100.74 / 110.32, or 0.9131617.
If
the nine PhysPops had the same proportions with each other in 1940 as they had with each
other in 1921, we could multiply every 1921 PhysPop value by 0.9131617 to discover what the
values would have been in 1940. We put these "ideal" values in Column D of Figure 3-B. Column
D entries = (Column B entries times 0.9131617).
Some Consequences of Retaining perfect Proportionality
The
D-Column values in Figure 3-B are the "ideal" values which we would have preferred to
find in 1940. We would have preferred them to the real values in Column C, because every value in
Column D still stands in the same proportion to every other value in Column D, as every value in
Column B stands to every other value in Column B. We can demonstrate this "lockstepping" for any
two Census Divisions. For example:
- (WNoCent 1940 Ideal / Mountain 1940 Ideal) = (128.69 / 123.62) = 1.041.
- (WNoCent 1921 / Mountain 1921) = (140.93 / 135.38) = 1.041.
And
because the sets of real 1921 data and ideal 1940 data have the same internal
proportionalities, it is also true that cross-ratios for every pair must be the same. Example:
- (NewEngl 1940 Ideal / NewEngl 1921 Real) = (129.89 / 142.24) = 0.913.
- (WSoCentral 1940 Ideal / WSoCentral 1921 Real) = (114.28 / 125.15) = 0.913.
And
because the sets of real 1921 data and ideal 1940 data have the same internal
proportionalities (we have created perfect "lockstep"), the two sets of data have a perfect linear
correlation with each other. Part 7 discusses "perfect linear correlation" and linear regression
analysis, for readers who are unfamiliar with these terms.
*
Part
7. "Lockstep" --- Reality-Checks by Regression Analysis
The
technique of data regression is a branch of mathematics which can evaluate the correlation
between two sets of values (for example, a set called "x" and a set called "y"). Regression analysis
will be covered in considerably more detail
in Chapter 5 (Parts 5, 6, 7). For now, we need touch on
only a few aspects of regression analysis.
7a. Equation
of Best Fit, Line of Best Fit, and the R-Squared Value
In
linear regression analysis, the input data are a finite set of x-values and the corresponding
y-values --- as shown in Columns B and D of Figure 3-B. The output includes three values of
interest to us here: The X-Coefficient, the Constant, and the R-squared value.
Equation of Best Fit: How It Relates to Part 6b
In
linear regression analysis, the equation of best fit is the equation for a straight line: (y) = (m
* x) + (c). Note: * is the symbol for multiplication in this book. The regression output (boxed in
Figure 3-B) provides the values for "m" (the X-Coefficient) and for "c" (the Constant). Users of the
equation can then specify additional values for "x" (values additional to the regression's input values )
and calculate what the corresponding values for "y" would be if (repeat, if) there were a perfect
correlation between the x-values and the y-values.
Example:
If x = 80 (a value not in Col.B), what would the matching y-value be? We use the
equation for a straight line: y = (X-Coefficient * x) + (Constant). The boxed output in Figure 3-B
tells us the X-Coefficient = 0.91316 --- a number already seen in Part 6b. And the output tells us that
the Constant = zero. So, when x = 80, y = 73, because: y = (0.91316 * 73) + zero.
This
example is only what we already demonstrated in Part 6b --- except 80 is an
additional value of x not used in Part 6b. The X-Coefficient in Part 6b is 0.91316 --- we just
didn't give it the formal name there. And because we made x and y directly proportional in Part 6b
--- when we said (y = 0.91316 * x) --- then zero is the only possible value for the Constant. Thus, it
is no surprise at all that the regression output produced zero as the value of the Constant.
Line of Best Fit, and Graphing
In
making x,y graphs, it is customary to measure the x-values along the horizontal axis, and to
measure the y-values along the vertical axis.
The
line of best fit (the straight line seen in Figure 3-B) simply depicts a long series of x,y
pairs, calculated by using the equation of best fit. The point, which depicts y=73 when x=80, is part
of the straight line in Figure 3-B.
The R-Squared Value: A Key Measure of Correlation
Regression
output also provides a value for R-squared, which is the output of real interest in
this chapter. The R-squared value is a measure of how closely the x-input and the y-input are
correlated. Only a perfect correlation has an R-squared value of 1.00. Imperfect correlations
produce R-squared values between 1.00 and zero. The value "R" --- also called the correlation
coefficient (Part 3e) --- is the square root of R-squared.
Since
we insured in Part 6b that our x,y pairs are perfectly proportional to each other, they are
also perfectly correlated with each other. And thus it is no surprise at all that the regression output in
Figure 3-B produces an R-squared value of 1.00. When R-squared = 1.00, every pair of x,y values
sits right upon the line of best fit, with no scatter. In Figure 3-B, the nine boxy symbols are indeed
upon the line of best fit.
7b. Figure
3-C: Degradation of Perfect Proportionality
Figure
3-C moves from the "ideal" world, depicted in Figure 3-B, into the real world. Figure
3-C shows no "ideal" values. It shows only real-world input-data: The PhysPop set of 1921 and the
PhysPop set of 1940.
The
two graphs in Figure 3-C look quite different from the graph in Figure 3-B. The nine
boxy symbols show some scatter around the lines of best fit. The scatter reflects the inferior
correlation compared with the "ideal" correlation (R-sq = 0.58 here, compared with 1.00 in Figure
3-B).
Thus,
R-squared is an evaluation of how much the 1940 PhysPop values have strayed from the
proportions which they had with each other in 1921. Quite obviously, the 1921 and 1940 sets of
PhysPops are not in perfect "lockstep."
A Point about Correlations
If
regression analysis is employed to study a cause-effect relationship, it is customary to
designate the proposed cause as the x-axis variable. However, the correlation between two sets of
numbers is whatever it is, independent of human choices to call one set "x" and the other set "y."
Figure 3-C demonstrates this point by reversing the designations of the two sets of PhysPops. The
R-squared values in both figures turn out the same, as they must. However, other things have changed
--- such as the Constant (the value of the y-intercept) and the X-Coefficient (the slope of the best-fit
line).
7c. Table
3-C: How Sets of PhysPops Correlate through Time
Table
3-C is "How Sets of PhysPops Correlate through Time." At its top are 21 sets of
PhysPop values. They are the input data for approximately 200 separate regression analyses, whose
R-squared values are reported in the body of Table 3-C.
Because
Table 3-C (like Figure 3-A) was part of our early exploration, we had not yet obtained
all the PhysPop sources which we subsequently obtained. So, not every PhysPop value in Table 3-C is
an exact match for the corresponding final value in Table 3-A. The differences often come from a
mixture in Table 3-C of the four different types of PhysPop values described in Part 3c. The purpose
of Table 3-C was to ascertain if PhysPops were hopelessly deviant from "lockstepping" --- and since
the four types of PhysPop values are so highly correlated with each other, Table 3-C is not misleading.
When we undertook our subsequent dose-response studies, we used PhysPop values only from Table
3-A --- as readers can verify for themselves.
Due
to Table 3-C's early origin, it does not put the Census Divisions in the same sequence as
Table 3-A. Of course, the sequence has no impact whatsoever on the regression output, as long as the
x and y sets of PhysPops are in the same sequence with respect to Census Divisions.
The Grid of R-Squared Values
Beneath
the raw PhysPop data is a grid of R-squared values. For instance, where the
column for 1980 intersects the row for 1934, the R-squared value of 0.72 comes from the
regression output when the 1980 PhysPops (directly above) are regressed on the 1934 PhysPops (in a
column far to the right). The R-squared value would be the same if we had regressed the 1934
PhysPops (as the y-set) on the 1980 PhysPops (as the x-set), as pointed out in Part 7b.
Readers
can quickly orient themselves in Table 3-C by knowing that, when the PhysPops of
1921 are regressed upon the PhysPops of 1921, there has to be a perfect correlation --- and it
shows up as an R-squared value of 1.00 where the column for 1921 intersects the row for 1921.
Because
Table 3-C describes every comparison between two sets of PhysPops by an R-squared
value, everyone can readily see the decrement in "lockstepping" over any chosen interval of time. The
approximately 200 regression analyses are not shown.
7d. Consistency
between Figure 3-A and Table 3-C
If
successive PhysPop sets had retained a fixed proportionality ("lockstep") over time, the
Hi5/Lo4 ratio depicted in Figure 3-A would be perfectly flat. The ratio would be the same, year after
year. We can illustrate this quickly.
The
Hi5/Lo4 PhysPop ratio for 1921 is 1.18 --- provided in the Universal Table 3-A. The
"ideal" 1940 values from Figure 3-B (Column D) reflect perfect "lockstep" with the 1921 values. We
compute the Hi5 average PhysPop as 131.792. The Lo4 average PhysPop is 112.00. The Hi5/Lo4
PhysPop ratio is (131.792 / 112.00), or 1.18 for the "ideal" entries too. Change in Hi5/Lo4 PhysPop
ratios, over time, reflects deviation from "lockstep."
In
Figure 3-A and in the text (Part 5a), we pointed to the period of 1933 through 1968 as a
period when the Hi5/Lo4 PhysPop ratio was relatively constant. This means that Table 3-C should
show high R-squared values during this same period, in the vertical column for 1967. It does. The
lowest R-squared value is 0.82, at the intersect of the 1967 column with the 1934 row.
*
Part
8. Two Crucial Aspects of PhysPop History
Earlier
in this chapter (Part 2b), we pointed out that our proposed dose-response studies require
the existence of appreciable differences in PhysPops (our dose-surrogates) among the Nine
Census Divisions. PhysPop history might not have delivered differences. It is just happenstance that
such differences occurred (Parts 5a and 5b).
It
is also happenstance that, during the years after the introduction of medical radiation, chaos
did not characterize the relationships between successive sets of PhysPops. Chaos would have
prevented PhysPops from representing relative accumulated dose-differences in the Nine Census
Divisions. Although the R-squared value (in Table 3-C) of 0.58 between the 1921 PhysPops and the
1940 PhysPops is not "great," it's far from being a value of 0.02. By 1927-1929, the correlations with
1940 become very respectable. And for the entire stretch from 1933-1967, successive sets of
PhysPops were close to retaining "lockstep" proportionality with each other (Table 3-C, Figure 3-A).
If
PhysPop history had not met the requirements for dose-response studies, it might have been
forever impossible for anyone to detect the particular consequences which are uncovered in this book
from the introduction of radiation into medicine.
>>>>>>>>>>
Box 1 of Chap. 3
Summary of PhysPop Values by Decades, and Their Ranking by Census Divisiions.
o Part 1. Census Divisions,
in our permanent order, with corresponding PhysPop values.
1921 1931 1940 1950 1960 1970 1980 1990
From Table 3-A. PhysPop PhysPop PhysPop PhysPop PhysPop PhysPop PhysPop PhysPop
Pacific 165.11 159.97 159.72 148.60 158.74 183.83 235.84 265.09
New England 142.24 142.35 161.55 162.51 164.37 186.51 254.37 319.88
West North Central 140.93 126.50 123.14 120.06 111.25 123.77 165.86 202.78
Mid-Atlantic 137.29 140.82 169.76 168.71 162.65 192.00 237.41 297.79
East North Central 136.06 128.59 133.36 123.69 114.56 127.17 169.79 208.54
Mountain 135.38 118.89 119.89 119.38 112.93 137.27 177.76 208.20
West South Central 125.15 105.95 103.94 101.34 101.65 113.20 153.18 184.34
East South Central 119.76 96.73 85.83 83.05 88.00 100.89 139.51 182.42
South Atlantic 110.32 99.59 100.74 99.07 105.36 130.70 187.22 234.48
Average ALL 134.70 124.38 128.66 125.16 124.39 143.93 191.22 233.72
Average High-Five 144.33 139.65 149.51 144.71 142.31 162.66 212.65 258.82
Average Low-Four 122.65 105.29 102.60 100.71 101.99 120.52 164.42 202.36
Ratio (Hi5/Lo4) 1.18 1.33 1.46 1.44 1.40 1.35 1.29 1.28
o Part 2.
Census Divisions, in shifting order, sorted by descending PhysPop values.
1921 1931 1940 1950 1960 1970 1980 1990
PhysPop PhysPop PhysPop PhysPop PhysPop PhysPop PhysPop PhysPop
Pac Pac MidAtl MidAtl NewEng MidAtl NewEng NewEng
Top Trio NewEng NewEng NewEng NewEng MidAtl NewEng MidAtl MidAtl
WNoCen MidAtl Pac Pac Pac Pac Pac Pac
MidAtl ENoCen ENoCen ENoCen ENoCen Mtn SoAtl SoAtl
Mid Trio ENoCen WNoCen WNoCen WNoCen Mtn SoAtl Mtn ENoCen
Mtn Mtn Mtn Mtn WNoCen ENoCen ENoCen Mtn
WSoCen WSoCen WSoCen WSoCen SoAtl WNoCen WNoCen WNoCen
Low Trio ESoCen SoAtl SoAtl SoAtl WSoCen WSoCen WSoCen WSoCen
SoAtl ESoCen ESoCen ESoCen ESoCen ESoCen ESoCen ESoCen
Above, in Part 2, where the Nine Census Divisions are sorted by descending
PhysPop values, we have labeled them as three "Trios": Top, Mid, Low ---
reflecting, relatively, the highest to lowest average per capita
dosage from medical radiation.
During the 1931-1990 period, only two of the nine Divisions (West North Central
and South Atlantic) ever "migrated" from their 1931 Trio into an adjacent Trio.
Measured in terms of Trios, remarkable stability occurred for sixty years in
PhysPop ranking. When the overview includes the 1921 values, then the
Mid-Atlantic Division becomes a migrant too, and West North Central makes an
additional move.
Figure 3-A.
Behavior of Hi5 and Lo4 PhysPops through Time.
Related Text = Part 5a.
Figure 3-B.
Complete "Lockstepping" of PhysPop Proportions over Time.
Linear Regression of Two Perfectly Correlated
and Perfectly Proportional Sets of Data.
Related Text = Part 6b.
o For the regression analysis
below, the x-variable input is Col.B: Actual PhysPop values for
1921. The y-variable input is Col.D: Ideal (synthetic) PhysPop
values for 1940. Output for this regression is shown to the
right. Both input and output are depicted by the graph. For
discussion of regression analysis and its depiction, please
consult Chapter 5,
Part 5.
o The nine boxy symbols on
the graph depict the nine pairs of input from Columns B and D.
The line of best fit depicts the output for this perfect
correlation. (R-squared = 1.00). All nine boxes sit right on
the line, with no scatter. Boxes overlap when input-pairs have
similar values. Because perfect proportionality exists between
Columns B and D, the Constant = 0 in the best-fit equation. The
line of best-fit goes right through the origin (y = 0, when x = 0).
Col.A Col.B Col.C Col.D Data Regression
Real Real Ideal Regression of Ideal 1940 PhysPops (Col.D)
Census 1921 1940 1940 upon Real 1921 PhysPops (Col.B)
Division Phys Phys Phys
Pops Pops Pops Regression Output:
Pacific 165.11 159.72 150.77 Constant 0.000000000
New England 142.24 161.55 129.89 Std Err of Y Est 0.0000014617
West North Central 140.93 123.14 128.69 R Squared 1.000000
Mid Atlantic 137.29 169.76 125.37 No. of Observations 9
East North Central 136.06 133.36 124.24 Degrees of Freedom 7
Mountain 135.38 119.89 123.62
West South Central 125.15 103.94 114.28 X Coefficient 0.9131617114
East South Central 119.76 85.83 109.36 Std Err of Coefficient 0.0000000332
South Atlantic 110.32 100.74 100.74
Regression of "Ideal" PhysPop 1940 upon Real PhysPop 1921
Figure 3-C.
Imperfect Retention of PhysPop Proportions over Time.
Linear Regressions with 1921 and 1940 PhysPops from Table 3-A.
Related Text = Part 7b.
o For the first regression
analysis below, the x-variable input is the set of PhysPop
values for 1921. The y-variable input is the PhysPop set of
1940. For the second regression analysis, we switch. The
x-input is 1940 and the y-input is 1921. both
regressions produce R-squared = 0.58, because the correlation
between two fixed sets of numbers is fixed. The leftside
graph depicts the first regression, and the rightside graph
depicts the second. Because the correlation is not perfect,
the nine boxy symbols do not all sit exactly upon the line of
best fit. There is some scatter around the line.
1921 1940
Census Real Real
Division PhysPops PhysPops Data Regression
"x" "y" Regression Output:
Pacific 165.11 159.72 Constant -67.425
New England 142.24 161.55 Std Err of Y Est 20.641
West North Central 140.93 123.14 R Squared 0.579
Mid-Atlantic 137.29 169.76 No. of Observations 9
East North Central 136.06 133.36 Degrees of Freedom 7
Mountain 135.38 119.89
West South Central 125.15 103.94 X Coefficient 1.4558
East South Central 119.76 85.83 Std Err of Coef. 0.4688
South Atlantic 110.32 100.74 X-Coeff. / S.E. = 3.1050
1940 1921
Census Real Real
Division PhysPops PhysPops Data Regression
"x" "y" Regression Output:
Pacific 159.72 165.11 Constant 83.491
New England 161.55 142.24 Std Err of Y Est 10.792
West North Central 123.14 140.93 R Squared 0.579
Mid-Atlantic 169.76 137.29 No. of Observations 9
East North Central 133.36 136.06 Degrees of Freedom 7
Mountain 119.89 135.38
West South Central 103.94 125.15 X Coefficient 0.3980
East South Central 85.83 119.76 Std Err of Coef. 0.1282
South Atlantic 100.74 110.32 X-Coeff. / S.E. = 3.1050
Regression of PhysPop 1940 (Y-axis)
upon PhysPop 1921 (X-axis)
|
Regression of PhysPop 1921 (Y-axis)
upon PhysPop 1940 (X-axis)
|
Figure 3-D.
Comparison of Four Types of PhysPop Values.
Related Text = Part 3c.
This figure is reproduced from p.15 of AMA 1993 in our Reference List:
Physician Characteristics and Distribution in the U.S., 1993 Edition,
by Roback + Randolph + Seidman of the American Medical Association,
Department of Physician Data Services.
|
Table 3-A
|
Universal PhysPop Table
|
First page of four
|
Related text = Parts 3a + 3b
o PhysPop
values are numbers of physicians per 100,000
population. Entries are for general practitioners and
specialists combined --- 1921 through 1993 (details in
text). Sources of the data are provided in the text,
Part 3d. The years which are flagged with a "+" sign
present prime data. Entries for the unflagged years have
been interpolated.
o The
particular states belonging to each Census Division
are listed in the text, Part 3b. PhysPop
entries for the Nine Census Divisions have been weighted by
state populations, whereas the three rows of averages are
non-weighted. High-5 and Low-4 are defined in the text,
Part 4.
o This
single table is the source of data for numerous
chapters of this book. The term "universal" in the table's
title emphasizes that the PhysPops are the same, regardless
of which cause of death is compared with them.
Census Division 1921+ 1922 1923+ 1924 1925+ 1926 1927+ 1928 1929+ 1930
Pacific 165.11 164.09 163.06 162.36 161.67 159.75 157.83 157.24 156.64 158.30
New England 142.24 139.82 137.39 137.85 138.31 137.91 137.50 137.98 138.46 140.40
West North Central 140.93 139.62 138.31 136.11 133.92 132.73 131.54 130.13 128.72 127.61
Mid-Atlantic 137.29 138.11 138.92 136.64 134.36 136.38 138.40 138.45 138.49 139.65
East North Central 136.06 133.94 131.82 129.68 127.54 126.86 126.18 126.35 126.51 127.55
Mountain 135.38 132.95 130.51 126.40 122.30 120.52 118.75 118.72 118.68 118.79
West South Central 125.15 122.16 119.16 116.00 112.83 110.54 108.25 106.92 105.60 105.77
East South Central 119.76 116.46 113.16 110.19 107.22 104.64 102.07 100.74 99.41 98.07
South-Atlantic 110.32 108.56 106.79 105.20 103.61 102.87 102.13 101.50 100.86 100.23
Average ALL 134.70 132.85 131.01 128.94 126.86 125.80 124.74 124.22 123.71 124.04
Average High-Five 144.33 143.11 141.90 140.53 139.16 138.73 138.29 138.03 137.76 138.70
Average Low-Four 122.65 120.03 117.41 114.45 111.49 109.64 107.80 106.97 106.14 105.72
Ratio (High/Low) 1.18 1.19 1.21 1.23 1.25 1.27 1.28 1.29 1.30 1.31
Census Division 1931+ 1932 1933 1934+ 1935 1936+ 1937 1938+ 1939 1940+
Pacific 159.97 160.01 160.05 160.09 159.26 158.44 158.03 157.62 158.64 159.72
New England 142.35 144.43 146.51 148.60 149.39 150.18 152.13 154.08 157.82 161.55
West North Central 126.50 126.32 126.14 125.96 126.05 126.14 125.54 124.95 124.06 123.14
Mid-Atlantic 140.82 143.75 146.69 149.62 152.33 155.05 157.87 160.69 165.19 169.76
East North Central 128.59 128.84 129.10 129.36 129.89 130.42 131.20 131.98 132.66 133.36
Mountain 118.89 118.32 117.74 117.16 118.48 119.80 119.84 119.88 119.95 119.89
West South Central 105.95 105.53 105.11 104.68 104.10 103.52 103.15 102.79 103.37 103.94
East South Central 96.73 95.15 93.58 92.00 90.97 89.94 89.07 88.21 87.03 85.83
South-Atlantic 99.59 99.20 98.80 98.41 98.78 99.16 99.21 99.26 100.06 100.74
Average ALL 124.38 124.62 124.86 125.10 125.47 125.85 126.23 126.61 127.64 128.66
Average High-Five 139.65 140.67 141.70 142.72 143.38 144.04 144.96 145.87 147.68 149.51
Average Low-Four 105.29 104.55 103.81 103.06 103.08 103.10 102.82 102.53 102.60 102.60
Ratio (High/Low) 1.33 1.35 1.37 1.38 1.39 1.40 1.41 1.42 1.44 1.46
|
Universal PhysPop Table
|
Second page of four
|
o PhysPop
values are numbers of physicians per 100,000
population. Entries are for general practitioners and
specialists combined --- 1921 through 1993 (details in
text). Sources of the data are provided in the text,
Part 3d. The years which are
flagged with a "+" sign present prime data. Entries
for the unflagged years have been interpolated.
o The
particular states belonging to each Census
Division are listed in the text,
Part 3b. PhysPop entries for the
Nine Census Divisions have been weighted by state
populations, whereas the three rows of averages are
non-weighted. High-5 and Low-4 are defined in the
text, Part 4.
o This
single table is the source of data for numerous
chapters of this book. The term "universal" in the
table's title emphasizes that the PhysPops are the same,
regardless of which cause of death is compared with them.
Census Division 1941 1942+ 1943 1944 1945 1946 1947 1948 1949+ 1950
Pacific 152.84 145.95 146.22 146.48 146.74 147.00 147.27 147.53 147.79 148.60
New England 162.77 163.99 163.77 163.55 163.33 163.11 162.88 162.66 162.44 162.51
West North Central 125.09 127.05 126.21 125.38 124.54 123.76 122.87 122.04 121.20 120.06
Mid-Atlantic 172.19 174.63 173.93 173.23 172.53 171.83 171.13 170.43 169.73 168.71
East North Central 134.12 134.89 133.48 132.06 130.65 129.24 127.82 126.41 125.00 123.69
Mountain 118.18 116.46 117.01 117.55 118.09 118.64 119.18 119.72 120.27 119.38
West South Central 104.41 104.88 104.42 103.31 103.52 103.06 102.61 102.16 101.40 101.34
East South Central 86.16 86.49 85.94 85.39 84.84 84.29 83.74 83.19 82.64 83.05
South-Atlantic 101.71 102.68 102.10 101.53 100.95 100.38 99.80 99.22 98.65 99.07
Average ALL 128.61 128.56 128.12 127.61 127.24 126.81 126.37 125.93 125.46 125.16
Average High-Five 149.40 149.30 148.72 148.14 147.56 146.99 146.39 145.81 145.23 144.71
Average Low-Four 102.62 102.63 102.37 101.95 101.85 101.59 101.33 101.07 100.74 100.71
Ratio (High/Low) 1.46 1.45 1.45 1.45 1.45 1.45 1.44 1.44 1.44 1.44
Census Division 1951 1952 1953 1954 1955 1956 1957 1958 1959+ 1960
Pacific 149.40 150.21 151.01 151.82 152.62 153.43 154.23 155.04 155.84 158.74
New England 162.59 162.66 162.74 162.81 162.88 162.96 163.03 163.11 163.18 164.37
West North Central 118.09 117.77 116.62 115.48 114.34 113.19 112.05 110.90 109.76 111.25
Mid-Atlantic 167.68 166.66 165.81 164.62 163.59 162.57 161.55 160.52 159.50 162.65
East North Central 122.37 121.06 119.75 118.44 117.12 115.81 114.50 113.18 111.87 114.56
Mountain 118.51 117.64 116.76 115.88 115.00 114.12 113.25 112.37 111.49 112.93
West South Central 101.28 101.21 101.15 101.09 101.03 100.97 100.90 100.84 100.78 101.65
East South Central 83.46 83.86 84.27 84.68 85.09 85.50 85.90 86.31 86.72 88.00
South-Atlantic 99.49 99.91 100.33 100.75 101.16 101.58 102.00 102.42 102.84 105.36
Average ALL 124.76 124.55 124.27 123.95 123.65 123.35 123.05 122.74 122.44 124.39
Average High-Five 144.03 143.67 143.19 142.63 142.11 141.59 141.07 140.55 140.03 142.31
Average Low-Four 100.69 100.66 100.63 100.60 100.57 100.54 100.51 100.49 100.46 101.99
Ratio (High/Low) 1.43 1.43 1.42 1.42 1.41 1.41 1.40 1.40 1.39 1.40
|
Universal PhysPop Table
|
Third page of four
|
o PhysPop
values are numbers of physicians per 100,000
population. Entries are for general practitioners and
specialists combined --- 1921 through 1993 (details in
text). Sources of the data are provided in the text,
Part 3d. The years which are flagged with
a "+" sign present prime data. Entries for the unflagged
years have been interpolated.
o The
particular states belonging to each Census Division
are listed in the text, Part 3b. PhysPop
entries for the Nine Census Divisions have been weighted
by state populations, whereas the three rows of averages
are non-weighted. High-5 and Low-4 are defined in the
text, Part 4.
o This
single table is the source of data for numerous
chapters of this book. The term "universal" in the
table's title emphasizes that the PhysPops are the same,
regardless of which cause of death is compared with them.
Census Division 1961 1962 1963+ 1964 1965+ 1966 1967 1968 1969 1970+
Pacific 161.64 164.55 167.45 167.54 167.62 170.86 174.10 177.35 180.59 183.83
New England 165.56 166.75 167.94 170.52 173.09 175.77 178.46 181.14 183.83 186.51
West North Central 112.74 114.24 115.73 118.25 120.76 121.36 121.96 122.57 123.17 123.77
Mid-Atlantic 165.80 168.94 172.09 175.22 178.34 181.07 183.80 186.54 189.27 192.00
East North Central 117.25 119.94 122.63 123.16 123.69 124.39 125.08 125.78 126.47 127.17
Mountain 114.37 115.81 117.25 117.26 117.26 121.26 125.26 129.27 133.27 137.27
West South Central 102.52 103.38 104.25 104.28 104.31 106.09 107.87 109.64 111.42 113.20
East South Central 89.28 90.57 91.85 92.98 94.11 95.47 96.82 98.18 99.53 100.89
South-Atlantic 107.88 110.39 112.91 115.41 117.91 120.47 123.03 125.58 128.14 130.70
Average ALL 126.34 128.29 130.23 131.62 133.01 135.19 137.38 139.56 141.74 143.93
Average High-Five 144.60 146.88 149.17 150.93 152.70 154.69 156.68 158.67 160.66 162.66
Average Low-Four 103.51 105.04 106.57 107.48 108.40 110.82 113.24 115.67 118.09 120.52
Ratio (High/Low) 1.40 1.40 1.40 1.40 1.41 1.40 1.38 1.37 1.36 1.35
Census Division 1971 1972 1973 1974 1975+ 1976 1977 1978 1979 1980+
Pacific 188.70 193.57 198.45 203.32 208.19 213.72 219.25 224.78 230.31 235.84
New England 192.25 197.99 203.72 209.46 215.20 223.03 230.87 238.70 246.54 254.37
West North Central 127.20 130.63 134.06 137.49 140.92 145.91 150.90 155.88 160.87 165.86
Mid-Atlantic 196.24 200.47 204.71 208.94 213.18 218.03 222.87 227.72 232.56 237.41
East North Central 130.94 134.72 138.49 142.27 146.04 150.79 155.54 160.29 165.04 169.79
Mountain 141.06 144.85 148.65 152.44 156.23 160.54 164.84 169.15 173.45 177.76
West South Central 116.19 119.18 122.18 125.17 128.16 133.16 138.17 143.17 148.18 153.18
East South Central 104.18 107.47 110.75 114.04 117.33 121.77 126.20 130.64 135.07 139.51
South-Atlantic 135.78 140.86 145.94 151.02 156.10 162.32 168.55 174.77 181.00 187.22
Average ALL 148.06 152.19 156.33 160.46 164.59 169.92 175.24 180.57 185.89 191.22
Average High-Five 167.07 171.48 175.89 180.30 184.71 190.30 195.89 201.47 207.06 212.65
Average Low-Four 124.30 128.09 131.88 135.67 139.46 144.45 149.44 154.43 159.43 164.42
Ratio (High/Low) 1.34 1.34 1.33 1.33 1.32 1.32 1.31 1.30 1.30 1.29
|
Universal PhysPop Table
|
Fourth page of four
|
o PhysPop
values are numbers of physicians per 100,000
population. Entries are for general practitioners and
specialists combined --- 1921 through 1993 (details in
text). Sources of the data are provided in the text,
Part 3d. The years which are flagged with
a "+" sign present prime data. Entries for the unflagged
years have been interpolated.
o The
particular states belonging to each Census Division
are listed in the text, Part 3b. PhysPop entries
for the Nine Census Divisions have been weighted by state
populations, whereas the three rows of averages are
non-weighted. High-5 and Low-4 are defined in the text,
Part 4.
o This
single table is the source of data for numerous
chapters of this book. The term "universal" in the table's
title emphasizes that the PhysPops are the same,
regardless of which cause of death is compared with them.
Census Division 1981+ 1982 1983+ 1984 1985+ 1986 1987 1988 1989 1990+
Pacific 241.07 245.83 250.59 253.18 255.78 257.64 259.50 261.37 263.23 265.09
New England 261.79 270.07 278.35 285.44 292.52 298.00 303.47 308.94 314.41 319.88
West North Central 170.49 175.13 179.76 183.06 186.36 189.65 192.93 196.21 199.50 202.78
Mid-Atlantic 245.75 255.00 264.24 270.03 275.83 280.22 284.61 289.01 293.40 297.79
East North Central 174.96 180.94 186.91 190.82 194.72 197.49 200.25 203.01 205.78 208.54
Mountain 182.02 184.91 187.80 190.17 192.53 195.67 198.80 201.93 205.07 208.20
West South Central 156.72 160.32 163.92 167.48 171.04 173.70 176.36 179.02 181.68 184.34
East South Central 144.39 148.87 153.34 157.67 162.00 166.09 170.17 174.25 178.34 182.42
South-Atlantic 191.23 197.83 204.43 210.15 215.86 219.59 223.31 227.03 230.76 234.48
Average ALL 196.49 202.10 207.70 212.00 216.30 219.78 223.27 226.75 230.24 233.72
Average High-Five 218.81 225.39 231.97 236.51 241.04 244.60 248.15 251.71 255.26 258.82
Average Low-Four 168.59 172.98 177.37 181.37 185.36 188.76 192.16 195.56 198.96 202.36
Ratio (High/Low) 1.30 1.30 1.31 1.30 1.30 1.30 1.29 1.29 1.28 1.28
Census Division 1991 1992+ 1993+ *
Pacific 266.57 268.05 269.50
New England 327.11 334.35 343.80
West North Central 209.48 216.17 219.00
Mid-Atlantic 307.67 317.56 323.60
East North Central 215.02 221.50 225.40
Mountain 211.23 214.26 218.30
West South Central 189.43 194.53 195.40
East South Central 188.38 194.33 196.70
South-Atlantic 239.45 244.41 247.80
Average ALL 239.37 245.02 248.83
Average High-Five 265.17 271.53 276.26
Average Low-Four 207.12 211.88 214.55
Ratio (High/Low) 1.28 1.28 1.29
* 1993 entries are for January 1, 1993, from Roback 1994.
Table 3-B
Population Sizes of the Census Divisions: 1910 through 1990
Related Text = Part 3b.
1910 1910 1920 1920 1930 1930
Census Division Pop Fraction Pop Fraction Pop Fraction
Pacific 4,192,304 0.0457 5,566,851 0.0529 8,194,433 0.0670
New England 6,652,675 0.0725 7,400,909 0.0703 8,268,680 0.0676
West North Central 11,637,921 0.1269 12,544,249 0.1192 13,296,915 0.1086
MidAtlantic 19,315,892 0.2105 22,261,144 0.2115 26,260,750 0.2146
East North Central 18,250,621 0.1989 21,475,543 0.2040 25,297,185 0.2067
Mountain 2,633,517 0.0287 3,336,101 0.0317 3,702,789 0.0303
West South Central 8,784,534 0.0958 10,242,224 0.0973 12,176,830 0.0995
East South Central 8,409,901 0.0917 8,893,307 0.0845 9,887,214 0.0808
South Atlantic 11,864,826 0.1293 13,552,701 0.1287 15,306,720 0.1251
91,742,191 1.0000 105,273,029 1.0000 122,391,516 1.0000
Census Division 1940 1940 1950 1950 1960 1960
Pop Fraction Pop Fraction Pop Fraction
Pacific 9,733,262 0.0739 14,486,527 0.0961 21,198,044 0.1182
New England 8,437,290 0.0641 9,314,453 0.0618 10,509,367 0.0586
West North Central 13,516,990 0.1027 14,061,394 0.0933 15,394,115 0.0858
MidAtlantic 27,539,487 0.2092 30,163,533 0.2002 34,168,452 0.1905
East North Central 26,626,342 0.2022 30,399,368 0.2017 36,225,024 0.2020
Mountain 4,150,003 0.0315 5,074,998 0.0337 6,855,060 0.0382
West South Central 13,064,525 0.0992 14,537,572 0.0965 16,951,255 0.0945
East South Central 10,778,225 0.0819 11,477,181 0.0762 12,050,126 0.0672
South Atlantic 17,823,151 0.1354 21,182,335 0.1406 25,971,732 0.1448
131,669,275 1.0000 150,697,361 1.0000 179,323,175 1.0000
Census Division 1970 1970 1980 1980 1990 1990
Pop Fraction Pop Fraction Pop Fraction
Pacific 26,087,000 0.1293 31,523,000 0.1398 37,837,000 0.1535
New England 11,781,000 0.0584 12,322,000 0.0546 12,998,000 0.0527
West North Central 16,240,000 0.0805 17,124,000 0.0759 17,777,000 0.0721
MidAtlantic 37,149,000 0.1842 36,770,000 0.1630 37,660,000 0.1527
East North Central 40,212,000 0.1993 41,636,000 0.1846 42,232,000 0.1713
Mountain 8,230,000 0.0408 11,319,000 0.0502 13,398,000 0.0543
West South Central 19,132,000 0.0948 23,669,000 0.1049 26,797,000 0.1087
East South Central 12,723,000 0.0631 14,573,000 0.0646 15,313,000 0.0621
South Atlantic 30,169,000 0.1496 36,621,000 0.1624 42,540,000 0.1725
201,723,000 1.0000 225,557,000 1.0000 246,552,000 1.0000
Some sources provided entries to the last digit, but no one should take
seriously any such implied accuracy of census-taking. Sources: For
1910, 1920, 1930: World Almanac 1991, p.553. For 1940, 1950,
1960: Grove 1968, Table 74.
For 1970, 1980: Roback 1990.
For 1990: Roback 1994. Entries
above exclude no one by color or "race."
Table 3-C.
How Sets of Physpops Correlate through Time
Related Text = Part 7c.
Table 3-C: The 21 sets of Phys/Pop values for 1921-1993 match
Table 3-A, with some exceptions (please
see textof Part 7c). The rows of R-squared
values come from regressing our PhysPop set upon another PhysPop
set. The intersection of a column with a row reveals which two
sets produced the R-squared value.
1993 1992 1990 1985 1980 1975 1967 1965 1963 1949 1942 1940 1938 1936 1934 1931 1929 1927 1925 1923 1921
Phys/ Phys/ Phys/ Phys/ Phys/ Phys/ Phys/ Phys/ Phys/ Phys/ Phys/ Phys/ Phys/ Phys/ Phys/ Phys/ Phys/ Phys/ Phys/ Phys/ Phys/
The 9 Census Div Pop Pop Pop Pop Pop Pop Pop Pop Pop Pop Pop Pop Pop Pop Pop Pop Pop Pop Pop Pop Pop
New England 343.8 334.3 319.9 292.5 254.2 215.1 174.5 168.6 167.1 162.4 164.0 161.6 154.1 150.2 148.6 142.3 138.5 137.5 138.3 137.4 142.2
Middle Atlantic 323.6 317.6 297.8 275.8 237.3 213.1 178.2 173.1 168.7 169.7 174.6 169.8 160.7 155.1 149.6 140.8 138.5 138.4 134.5 138.9 137.3
East North Centr 225.4 221.5 208.6 194.7 169.8 145.9 124.5 121.3 118.2 125.0 134.9 133.4 132.0 130.4 129.4 128.6 126.5 126.2 127.5 131.8 136.1
West North Centr 219.0 216.2 202.8 186.4 165.8 140.8 119.1 116.2 114.0 121.2 127.1 123.1 125.0 126.1 126.0 126.5 128.7 131.5 133.9 138.3 140.9
South Atlantic 247.8 244.4 234.5 215.9 187.0 156.0 122.7 118.4 113.0 98.7 102.7 100.7 99.3 99.2 98.4 99.6 100.9 102.1 103.6 106.8 110.3
East South Centr 196.7 194.3 182.4 162.0 139.7 117.4 93.4 90.5 89.2 83.2 86.5 85.8 88.2 89.9 92.0 96.7 99.4 102.1 107.2 113.2 119.8
West South Centr 195.4 194.5 184.3 171.0 153.3 128.0 106.2 103.4 102.5 102.2 104.9 103.9 102.8 103.5 104.7 106.0 105.6 108.2 112.8 119.2 125.2
Mountain 218.3 214.3 208.2 192.5 177.5 155.9 125.1 121.0 117.8 119.7 116.1 119.9 119.9 119.8 117.2 118.9 118.7 118.7 122.3 130.5 135.4
Pacific 269.5 268.0 265.1 255.8 236.2 208.1 167.3 161.4 159.6 147.5 146.0 159.7 157.6 158.4 160.1 160.0 156.6 157.8 161.7 163.1 165.1
Correlation of Each Phys/Pop with All Other Phys/Pops (Measured in R-Squared).
Year 1993 1992 1990 1985 1980 1975 1967 1965 1963 1949 1942 1940 1938 1936 1934 1931 1929 1927 1925 1923 1921
Phys/Pop 21 0.15 0.16 0.20 0.25 0.34 0.38 0.41 0.41 0.44 0.48 0.43 0.58 0.65 0.72 0.77 0.87 0.88 0.90 0.96 0.98 1.00
Phys/Pop 23 0.20 0.21 0.25 0.31 0.40 0.45 0.49 0.49 0.52 0.56 0.51 0.67 0.78 0.83 0.84 0.91 0.94 0.95 0.98 1.00
Phys/Pop 25 0.28 0.29 0.33 0.40 0.49 0.53 0.56 0.56 0.59 0.61 0.57 0.71 0.77 0.83 0.88 0.95 0.97 0.98 1.00
Phys/Pop 27 0.38 0.39 0.43 0.49 0.58 0.62 0.67 0.67 0.69 0.72 0.69 0.81 0.87 0.92 0.95 0.98 0.99 1.00
Phys/Pop 29 0.42 0.43 0.47 0.53 0.61 0.66 0.71 0.71 0.73 0.76 0.73 0.85 0.90 0.94 0.97 0.99 1.00
Phys/Pop 31 0.45 0.46 0.50 0.57 0.65 0.69 0.74 0.74 0.76 0.79 0.76 0.88 0.92 0.96 0.98 1.00
Phys/Pop 34 0.56 0.57 0.60 0.66 0.72 0.77 0.82 0.83 0.85 0.89 0.87 0.95 0.98 0.99 1.00
Phys/Pop 36 0.60 0.61 0.63 0.69 0.74 0.79 0.85 0.86 0.87 0.93 0.91 0.98 0.99 1.00
Phys/Pop 38 0.65 0.65 0.67 0.72 0.77 0.81 0.88 0.89 0.90 0.96 0.94 0.99 1.00
Phys/Pop 40 0.71 0.72 0.73 0.78 0.81 0.85 0.91 0.92 0.93 0.98 0.96 1.00
Phys/Pop 42 0.76 0.76 0.74 0.77 0.76 0.79 0.88 0.89 0.89 0.98 1.00
Phys/Pop 49 0.77 0.78 0.78 0.81 0.82 0.85 0.92 0.93 0.93 1.00
Phys/Pop 63 0.87 0.88 0.90 0.94 0.96 0.98 1.00 1.00 1.00
Phys/Pop 65 0.87 0.88 0.91 0.94 0.96 0.98 1.00 1.00
Phys/Pop 67 0.87 0.89 0.91 0.95 0.96 0.99 1.00
Phys/Pop 75 0.88 0.89 0.93 0.96 0.99 1.00
Phys/Pop 80 0.90 0.91 0.95 0.98 1.00
Phys/Pop 85 0.96 0.97 0.99 1.00
Phys/Pop 90 0.99 0.99 1.00
Phys/Pop 92 0.99 1.00
Phys/Pop 93 1.00
Years 1993 1992 1990 1985 1980 1975 1967 1965 1963 1949 1942 1940 1938 1936 1934 1931 1929 1927 1925 1923 1921
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