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Models of Causal Relationships
Drawing upon the concepts presented earlier in the chapter, this
section introduces models of disease causation. Relationships
between suspected disease-causing factors and outcomes fall
into two general categories: not statistically associated and
statistically associated.15 Among statistical associations are
non-causal and causal associations. Possible types of
associations are formatted in Figure 9–2.
We have already considered the role of statistical significance
in evaluating an association and noted that evaluation of
statistical significance is used to rule out the operation of
chance in producing an observed association; a nonstatistically
associated (independent) relationship is shown in box A of the
diagram (left side).
FIGURE 9–2 Map of possible associations between disease-
causing factors and outcomes.
Source: Data from B MacMahon and TF Pugh, Epidemiology
Principles and Methods. Boston, MA: Little, Brown and
Company; 1970.
As shown in Figure 9–2, a statistical association may be either
noncausal or causal. What is meant by a noncausal (secondary)
association? Suppose factor C is related to disease outcome A.
The association may be due to the operation of a third factor B
that is related to both C and A. Thus, the association between C
and A is secondary to the association of C with B and C with A.
For example, periodontal disease (C) is associated with chronic
obstructive pulmonary disease (A).16 One possible explanation
for this association is the secondary association
of smoking (B) with both periodontal disease (C) and chronic
obstructive pulmonary disease (A). This model suggests that the
increased risk of chronic obstructive pulmonary disease
associated with periodontal disease is related to the role that
smoking may play as a cofactor in both conditions. Here is a
map of a secondary association: C ← B → A.1
With respect to causal associations, the relationship between
factor and outcome may be indirect or direct. An indirect causal
association involves the operation of an intervening variable,
which is a variable that falls in the chain of association between
C and A. An illustration of an indirect association is the
postulated relationship between low education levels (C) and
obesity (A) among men.17 Men who have lower education
levels tend to be more obese than those who have higher
education levels. It is plausible that the relationship between C
and A operates through the intervening variable of lack of
leisure time physical activity (B). An indirect association
involves an intervening variable in the association between C
and A. This relationship may be formatted as follows: C → B →
A.1 Note that the arrow between C and B has been reversed in
contrast with an indirect noncausal association.
Multiple Causality
The foregoing section provided models of causality that employ
more than one factor. As stated earlier in this chapter, the
measure risk difference implies multivariate causality by
isolating the effects of a single exposure from the effects of
other exposures. The example on NSAIDs examined the
difference between risk of peptic ulcer among users and
nonusers of NSAIDs, where the risk difference was 12.5 per
1,000 person-years. The risk of peptic ulcer caused by other
exposures was 4.2 per 1,000 person-years.
The issue of disease causality is exceedingly complicated. To
describe exposure–disease relationships, epidemiologists have
developed complex models of disease causality. These models
acknowledge the multifactor causality of diseases, even those
that seem to have “simple” infectious agents. Often, these
models involve an ecologic approach by relating disease to one
or more environmental factors. “The requirement that more than
one factor be present for disease to develop is referred to
as multiple causation or multifactorial etiology.”18(p
27) Examples of several influential models are the:
· •• epidemiologic triangle
· •• web of causation
· •• wheel model
· •• pie model
Web of causation
The web of causation is “… a popular METAPHOR for the
theory of sequential and linked multiple causes of diseases and
other health states.”1 The web of causation implicates broad
classes of events and represents an incomplete portrayal of
reality.15 Although the web of causation for most diseases is
complex, one may not need to understand fully the causality of
any specific disease in order to prevent it. An example of the
web of causation of avian influenza is provided in Figure 9–3.
Follow the infection of the human host from the virus reservoir
in wild birds. As of 2007, the virus had not mutated into a form
that could be spread readily from person to person.
Wheel model
The wheel model is similar to the epidemiologic triangle and
web of causation with respect to involving multiple causality
(Figure 9–4). Observe that the model explains the etiology of
disease by calling into play host and environment interactions.
Environmental components are biologic, social, and physical.
The circle designated as “host” refers to human beings or other
hosts affected by a disease. The circle called “genetic core”
acknowledges the role that genetic factors play in many
diseases. The wheel model de-emphasizes specific agent factors
and, instead, differentiates between host and environmental
factors in disease causation. The biologic environment is
relevant to infectious agents, by taking into account the
environmental dimensions that permit survival of microbial
agents of disease.
FIGURE 9–3 The web of causation for avian influenza.
A wheel model may be used to account for the occurrence of
childhood lead poisoning.18 In this example, preschool children
are typical hosts. The physical environment provides many
opportunities for lead exposure from lead-based paint in older
homes, playground equipment, candy wrappers, and other
sources. Some children ingest paint chips from peeling surfaces
as a result of pica, the predilection to eat nonfood substances.
Because lead-based paints often are located in poorer
neighborhoods that have substandard housing, the social
environment is associated with childhood poisoning. Limited
access to medical care in such communities may restrict
screening of preschool children for lead exposure. Elimination
of childhood lead poisoning requires visionary public
health leadership to advocate for detection of lead-based paints
and other sources of environmental lead exposure as well as the
implementation of screening programs. Such efforts will help to
protect vulnerable children against the sequelae of lead
poisoning.
Pie model
Another model of multiple causality (multicausality) is the
causal pie model.19 As Figure 9–5 shows, the model indicates
that a disease may be caused by more than one causal
mechanism (also called a sufficient cause), which is defined as
“a set of minimal conditions and events that inevitably produce
disease.”19(p S144) Each causal mechanism is denoted in
Figure 9–5 by the numerals I through III. An example of
different causal mechanisms for a disease is provided by the
etiology of lung cancer: lung cancer caused by smoking; lung
cancer caused by exposure to ionizing radiation; and lung
cancer caused by inhalation of carcinogenic solvents in the
workplace.
FIGURE 9–5 Three sufficient causes of disease.
Source: From KJ Rothman and S Greenland, Causation and
causal inference in epidemiology, Am J Public Health, 2005;
vol 95, p S145. Reprinted with permission from the American
Public Health Association.
Rothman and Greenland note that, “A given disease can be
caused by more than one causal mechanism, and every causal
mechanism involves the joint action of a multitude of
component causes.”19(p S145) The component causes, or
factors, are denoted by the letters shown within each pie slice.
A single letter indicates a single component cause. A single
component could be common to each causal mechanism (shown
by the letter A that appears in each pie); in
other cases, the component causes for each causal mechanism
could be different for each mechanism (shown by the letters that
differ across the pies). Returning to the lung cancer example, a
common factor that could apply to all causal mechanisms for
lung cancer is a genetic predisposition for cancer. Several other
component causes might be different for each causal mechanism
involved in the etiology of lung cancer.
In models of multicausality, most of the identified component
causes are neither necessary nor sufficient causes (defined in
the section on absolute effects). Accordingly, it is possible to
prevent disease when a specific component cause that is neither
necessary nor sufficient is removed; nevertheless, when the
effects of this component cause are removed, cases of the
disease will continue to occur.
Conclusion
This chapter covered two new measures of effect—absolute and
relative effects—that may be used as aids in the interpretation
of epidemiologic studies. In addition, the chapter presented
guidelines that should be taken into account when one is
interpreting an epidemiologic finding. Absolute effects, the first
variety of which is called risk differences, are determined by
finding the difference in measures of disease frequency between
exposed and nonexposed individuals. A second type of absolute
effect, called population risk difference, is found by computing
the difference in measures of disease frequency between the
exposed segment of the population and the total population.
Relative effects are characterized by the inclusion of an
absolute effect in the numerator and a reference group in the
denominator. One type of relative effect, the etiologic fraction,
attempts to quantify the amount of a disease that is attributable
to a given exposure. The second type of relative effect, the
population etiologic fraction, provides an estimate of the
possible impact on the population rates of disease that can be
anticipated by removal of the offending exposure. With respect
to interpretation of epidemiologic findings, one should be
cognizant of the influence of sample size upon the statistical
significance of the results. Large sample sizes may lead to
clinically unimportant, yet statistically significant, results;
small sample sizes may yield statistically nonsignificant results
that are clinically important. Therefore, we presented a series of
five questions that should be asked when one attempts to
interpret an epidemiologic observation. The chapter closed with
a discourse on causal models, which may be particularly
instructive when trying to interpret epidemiologic data.
DATAProductAgeGenderEducationMarital
StatusUsageFitnessIncomeMilesTM19518Male14Single3429562
112TM19519Male15Single233183675TM19519Female14Partner
ed433069966TM19519Male12Single333297385TM19520Male13
Partnered423524747TM19520Female14Partnered333297366TM
19521Female14Partnered333524775TM19521Male13Single3332
97385TM19521Male15Single5435247141TM19521Female15Par
tnered233752185TM19522Male14Single333638485TM19522Fe
male14Partnered323524766TM19522Female16Single433638475
TM19522Female14Single333524775TM19523Male16Partnered3
13865847TM19523Male16Partnered334093275TM19523Female
14Single2334110103TM19523Male16Partnered433979594TM19
523Female16Single4338658113TM19523Female15Partnered223
411038TM19523Male14Single4338658113TM19523Male16Sing
le434093294TM19524Female16Single434206994TM19524Fema
le16Partnered5544343188TM19524Male14Single2345480113T
M19524Male13Partnered324206947TM19524Female16Single43
4661775TM19525Female14Partnered334889175TM19525Male1
4Partnered234548056TM19525Female14Partnered225343947T
M19525Female14Partnered333979585TM19525Male16Single34
40932113TM19525Female16Partnered224093247TM19525Male
16Single334320685TM19526Female14Partnered3444343113TM
19526Female16Partnered4352302113TM19526Male16Partnered
225343947TM19526Male16Partnered335116585TM19526Femal
e16Single333638466TM19526Male16Partnered4444343132TM1
9526Male16Single335002885TM19527Female14Partnered32454
8066TM19527Male16Single435457685TM19527Female14Partn
ered234548056TM19528Female14Partnered234661756TM19528
Female16Partnered235230266TM19528Male14Single335230210
3TM19528Female14Partnered335457694TM19528Male14Single
4354576113TM19528Female16Partnered335116556TM19529Ma
le18Partnered336822085TM19529Female14Partnered224661738
TM19529Female16Partnered435002894TM19530Male14Partner
ed4446617141TM19530Male14Single335457685TM19531Male1
4Partnered225457647TM19531Female14Single224548047TM19
532Female14Single3446617113TM19532Male14Partnered43523
0285TM19533Female16Single225571338TM19533Female16Part
nered334661785TM19534Male16Single4551165169TM19534Fe
male16Single225230266TM19535Male16Partnered434889185T
M19535Female16Partnered336026194TM19535Female18Single
336708385TM19536Male12Single434434394TM19537Female16
Partnered333752185TM19538Male16Partnered334661775TM19
538Female14Partnered235457656TM19538Male14Single235230
256TM19538Male16Partnered335685075TM19539Male16Partne
red4459124132TM19540Male16Partnered336139866TM19541M
ale16Partnered4354576103TM19543Male16Partnered335343966
TM19544Female16Single345798775TM19546Female16Partnere
d326026147TM19547Male16Partnered435685094TM19550Fema
le16Partnered336480966TM49819Male14Single333183664TM4
9820Male14Single233297353TM49820Female14Partnered33341
10106TM49820Male14Single333865895TM49821Female14Part
nered5434110212TM49821Male16Partnered223411042TM4982
1Male12Partnered223297353TM49823Male14Partnered3336384
95TM49823Male14Partnered333865885TM49823Female16Singl
e334548095TM49823Male16Partnered4345480127TM49823Fem
ale16Partnered324320674TM49823Female14Single324093253T
M49823Male16Partnered334548064TM49824Female14Single32
4093285TM49824Male14Single3448891106TM49824Female16S
ingle3350028106TM49825Female14Partnered234548085TM498
25Female14Single3443206127TM49825Male16Partnered225230
242TM49825Female14Partnered5347754106TM49825Male14Si
ngle334548095TM49825Female14Single234320664TM49825Ma
le14Partnered4345480170TM49825Male14Partnered344320610
6TM49825Male16Partnered235002853TM49825Female14Single
224548042TM49825Male14Single4348891127TM49826Female1
6Partnered434548085TM49826Female16Single4450028127TM4
9826Male16Single4351165106TM49827Male14Single42454805
3TM49829Female14Partnered335116595TM49830Female14Sing
le335798774TM49830Female13Single4346617106TM49831Mal
e16Partnered335230295TM49831Female16Partnered235116564
TM49831Female18Single216522021TM49832Male16Single436
0261127TM49832Male16Partnered335343995TM49833Male13P
artnered4453439170TM49833Female16Partnered235002885TM
49833Male16Partnered335116595TM49833Female16Partnered5
35343995TM49833Female18Single344775474TM49834Female1
6Partnered436480995TM49834Male16Partnered345912485TM4
9834Male15Single336708385TM49835Female14Partnered32523
0253TM49835Male16Partnered325343953TM49835Female16Si
ngle325002864TM49835Male16Partnered335343995TM49837F
emale16Partnered234889185TM49838Female16Partnered43625
3585TM49838Male16Partnered3359124106TM49840Female16P
artnered336139885TM49840Female16Single335798785TM4984
0Male16Partnered336480995TM49845Male16Partnered2254576
42TM49848Male16Partnered235798764TM79822Male14Single4
348658106TM79822Male16Single3554781120TM79822Male18
Single4548556200TM79823Male16Single4558516140TM79823
Female18Single5453536100TM79823Male16Single4548556100
TM79824Male16Single4561006100TM79824Male18Partnered45
5727180TM79824Female16Single5552291200TM79824Male16S
ingle5549801160TM79825Male16Partnered4549801120TM7982
5Male16Partnered4462251160TM79825Female18Partnered5561
006200TM79825Male18Partnered4364741100TM79825Male18P
artnered6470966180TM79825Male18Partnered6575946240TM7
9825Male20Partnered4574701170TM79826Female21Single4369
721100TM79826Male16Partnered5464741180TM79827Male16P
artnered4583416160TM79827Male18Single4388396100TM7982
7Male21Partnered4490886100TM79828Female18Partnered6592
131180TM79828Male18Partnered7577191180TM79828Male18S
ingle6588396150TM79829Male18Single5552290180TM79829M
ale14Partnered7585906300TM79830Female16Partnered6590886
280TM79830Male18Partnered54103336160TM79830Male18Part
nered5599601150TM79831Male16Partnered6589641260TM798
33Female18Partnered4595866200TM79834Male16Single559213
1150TM79835Male16Partnered4592131360TM79838Male18Part
nered55104581150TM79840Male21Single6583416200TM79842
Male18Single5489641200TM79845Male16Single5590886160T
M79847Male18Partnered45104581120TM79848Male18Partnere
d4595508180
ADMN 210 – Dr. Barbara Sirotnik
Case #2 of 3, Summer 2019
In the last case you reviewed chapters 1 – 3 material and also
applied your knowledge of chapter 8 material (estimation). I’d
like for you to use the same dataset, but this time apply chapter
9 material (hypothesis testing).
As a reminder: On page 28 – 29 of your text you will find the
description of a data set for a company that sells three different
levels of treadmills (as well as other exercise equipment).
1) Download a clean copy of the file CardioGoodFitness.xlsx to
your computer.Remember, don’t try to work on it by just
clicking on the file name from Blackboard. You need to save it
first.
2) Years ago the company did an analysis of their entire
customer base and found that the average income for their
customers was $50,000. They believe that incomes of their
current customers are significantly higher than that. Test at the
10% significance level, showing all steps of the hypothesis
testing procedure (see the text, page 307). Be sure to include a
practical statement indicating how the company could use the
results you’ve found. HINT: here are the steps to follow…
· Write your Ho and H1
· Make note of your alpha (level of significance)
· Determine your test statistic (that is, find the proper formula
to use)
· Find the critical value of the test statistic from the table, and
define your rejection region
· Find your sample mean and standard deviation using the
proper Excel formulas. Compute the value of the test statistic
(that is, do the number crunching in the formula you identified
in the third step)
· Make the statistical decision and interpret in practical form
3) Years ago about 30% of purchases were for the TM 798 (the
“high end” expensive treadmill), however since those data were
collected we’ve gone through a recession, and a lot of people’s
finances haven’t really recovered. Has the proportion of people
purchasing the TM 798 dropped significantly? Test at the 5%
level of significance. Be sure to include a practical statement
indicating how the company could use the results you’ve found.
That’s it! The final case (for chapter 13) will use the same data
set but will focus on relationships between variables.
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