Epidemiology

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QUESTION 1

1. According to Hill’s criteria, a weak association rules out a causal connection between exposure and disease.

 

True

 False

QUESTION 2

1. A __________ component cause is an exposure that will not, on its own, cause a disease, but one that MUST be present for the disease to occur.

sufficient

necessary

vital

a or b

QUESTION 3

1. According to Hill’s criteria, lack of consistency rules out a causal connection between exposure and disease.

 True

 False

QUESTION 4

1. The AP for any necessary component cause = 100%

 True
 False

QUESTION 5

1. If a component cause is present in more than one sufficient cause, its AP is the sum of the APs of those sufficient causes.

 True
 False

QUESTION 6

1. If all sufficient causes are known, the sum of all sufficient cause APs=100%

 True
 False

QUESTION 7

1. Which statement is most true?

By examining events that precede a disease rate increase, we may identify causes and appropriate actions to control or prevent further occurrence of the disease.

By examining events that precede a disease decrease, we may identify causes and appropriate actions to control or prevent further occurrence of the disease.

Both statements are equally true.

Neither statement is true.

QUESTION 8

1. The triad of causation is most useful when looking at diseases that require multiple agents.

 True
 False

QUESTION 9

1. In 2014, 600 elderly KY residents living in an assisted-living facility were hospitalized for falls. Data from hospital admission records showed the following profiles: 

Profile 1 (180 patients) : Hearing loss, female, vision problem, living alone, lower body weakness, difficulty with balance.

Profile 2 (90 patients): Hearing loss, memory loss, vision problem, male, lower body weakness

Profile 3 (270 patients): Female, difficulties with balance, memory loss

Profile 4 (60 patients): Living alone, male, lower body weakness, difficulty with balance

 

1. Calculate the AP for each sufficient cause.

2. Calculate the AP for each component cause.

3. How could we best eliminate falls (based on the data).  Please be specific and use appropriate terminology.

American Journal of Public Health | Supplement 1, 2005, Vol 95, No. S1S144 | Public Health Matters | Peer Reviewed | Rothman and Greenland

⏐ PUBLIC HEALTH MATTERS ⏐

Concepts of cause and causal inference are largely self-taught from early learn-
ing experiences. A model of causation that describes causes in terms of suffi-
cient causes and their component causes illuminates important principles such
as multicausality, the dependence of the strength of component causes on the
prevalence of complementary component causes, and interaction between com-
ponent causes.

Philosophers agree that causal propositions cannot be proved, and find flaws or
practical limitations in all philosophies of causal inference. Hence, the role of logic,
belief, and observation in evaluating causal propositions is not settled. Causal
inference in epidemiology is better viewed as an exercise in measurement of an
effect rather than as a criterion-guided process for deciding whether an effect is pres-
ent or not. (Am J Public Health. 2005;95:S144–S150. doi:10.2105/AJPH.2004.059204)

Causation and Causal Inference in Epidemiology
| Kenneth J. Rothman, DrPH, Sander Greenland, MA, MS, DrPH, C Stat

What do we mean by causation? Even among
those who study causation as the object of their
work, the concept is largely self-taught, cob-
bled together from early experiences. As a
youngster, each person develops and tests an
inventory of causal explanations that brings
meaning to perceived events and that ulti-
mately leads to more control of those events.

Because our first appreciation of the con-
cept of causation is based on our own direct
observations, the resulting concept is limited
by the scope of those observations. We typi-
cally observe causes with effects that are im-
mediately apparent. For example, when one
turns a light switch to the “on” position, one
normally sees the instant effect of the light
going on. Nevertheless, the causal mechanism
for getting a light to shine involves more
than turning a light switch to “on.” Suppose
a storm has downed the electric lines to the
building, or the wiring is faulty, or the bulb
is burned out—in any of these cases, turning
the switch on will have no effect. One cause
of the light going on is having the switch in
the proper position, but along with it we
must have a supply of power to the circuit,
good wiring, and a working bulb. When all
other factors are in place, turning the switch
will cause the light to go on, but if one or
more of the other factors is lacking, the light
will not go on.

Despite the tendency to consider a switch
as the unique cause of turning on a light, the
complete causal mechanism is more intricate,
and the switch is only one component of sev-

eral. The tendency to identify the switch as
the unique cause stems from its usual role as
the final factor that acts in the causal mecha-
nism. The wiring can be considered part of
the causal mechanism, but once it is put in
place, it seldom warrants further attention.
The switch, however, is often the only part of
the mechanism that needs to be activated to
obtain the effect of turning on the light. The
effect usually occurs immediately after turn-
ing on the switch, and as a result we slip into
the frame of thinking in which we identify the
switch as a unique cause. The inadequacy of
this assumption is emphasized when the bulb
goes bad and needs to be replaced. These
concepts of causation that are established
empirically early in life are too rudimentary
to serve well as the basis for scientific theo-
ries. To enlarge upon them, we need a more
general conceptual model that can serve as a
common starting point in discussions of
causal theories.

SUFFICIENT AND COMPONENT
CAUSES

The concept and definition of causation
engender continuing debate among philoso-
phers. Nevertheless, researchers interested in
causal phenomena must adopt a working defi-
nition. We can define a cause of a specific dis-
ease event as an antecedent event, condition,
or characteristic that was necessary for the
occurrence of the disease at the moment it
occurred, given that other conditions are

fixed. In other words, a cause of a disease
event is an event, condition, or characteristic
that preceded the disease event and without
which the disease event either would not
have occurred at all or would not have oc-
curred until some later time. Under this defi-
nition it may be that no specific event, condi-
tion, or characteristic is sufficient by itself to
produce disease. This is not a definition, then,
of a complete causal mechanism, but only a
component of it. A “sufficient cause,” which
means a complete causal mechanism, can be
defined as a set of minimal conditions and
events that inevitably produce disease; “mini-
mal” implies that all of the conditions or
events are necessary to that occurrence. In
disease etiology, the completion of a sufficient
cause may be considered equivalent to the
onset of disease. (Onset here refers to the
onset of the earliest stage of the disease pro-
cess, rather than the onset of signs or symp-
toms.) For biological effects, most and some-
times all of the components of a sufficient
cause are unknown.1

For example, tobacco smoking is a cause of
lung cancer, but by itself it is not a sufficient
cause. First, the term smoking is too imprecise
to be used in a causal description. One must
specify the type of smoke (e.g., cigarette,
cigar, pipe), whether it is filtered or unfiltered,
the manner and frequency of inhalation, and
the onset and duration of smoking. More im-
portantly, smoking, even defined explicitly,
will not cause cancer in everyone. Appar-
ently, there are some people who, by virtue
of their genetic makeup or previous experi-
ence, are susceptible to the effects of smok-
ing, and others who are not. These suscepti-
bility factors are other components in the
various causal mechanisms through which
smoking causes lung cancer.

Figure 1 provides a schematic diagram of
sufficient causes in a hypothetical individual.
Each constellation of component causes rep-
resented in Figure 1 is minimally sufficient to
produce the disease; that is, there is no redun-
dant or extraneous component cause. Each
one is a necessary part of that specific causal

Supplement 1, 2005, Vol 95, No. S1 | American Journal of Public Health Rothman and Greenland | Peer Reviewed | Public Health Matters | S145

⏐ PUBLIC HEALTH MATTERS ⏐

FIGURE 1—Three sufficient causes of disease.

mechanism. A specific component cause may
play a role in one, two, or all three of the
causal mechanisms pictured.

MULTICAUSALITY

The model of causation implied by
Figure 1 illuminates several important princi-
ples regarding causes. Perhaps the most im-
portant of these principles is self-evident from
the model: 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. Consider
as an example the cause of a broken hip. Sup-
pose that someone experiences a traumatic
injury to the head that leads to a permanent
disturbance in equilibrium. Many years later,
the faulty equilibrium plays a causal role in a
fall that occurs while the person is walking
on an icy path. The fall results in a broken
hip. Other factors playing a causal role for the
broken hip could include the type of shoe the
person was wearing, the lack of a handrail
along the path, a strong wind, or the body
weight of the person, among others. The com-
plete causal mechanism involves a multitude
of factors. Some factors, such as the person’s
weight and the earlier injury that resulted in
the equilibrium disturbance, reflect earlier
events that have had a lingering effect. Some
causal components are genetic and would af-
fect the person’s weight, gait, behavior, recov-
ery from the earlier trauma, and so forth.
Other factors, such as the force of the wind,
are environmental. It is a reasonably safe as-

sertion that there are nearly always some
genetic and some environmental component
causes in every causal mechanism. Thus,
even an event such as a fall on an icy path
leading to a broken hip is part of a compli-
cated causal mechanism that involves many
component causes.

The importance of multicausality is that
most identified causes are neither necessary
nor sufficient to produce disease. Neverthe-
less, a cause need not be either necessary or
sufficient for its removal to result in disease
prevention. If a component cause that is nei-
ther necessary nor sufficient is blocked, a sub-
stantial amount of disease may be prevented.
That the cause is not necessary implies that
some disease may still occur after the cause
is blocked, but a component cause will never-
theless be a necessary cause for some of the
cases that occur. That the component cause is
not sufficient implies that other component
causes must interact with it to produce the
disease, and that blocking any of them would
result in prevention of some cases of disease.
Thus, one need not identify every component
cause to prevent some cases of disease. In the
law, a distinction is sometimes made among
component causes to identify those that may
be considered a “proximate” cause, implying
a more direct connection or responsibility for
the outcome.2

STRENGTH OF A CAUSE

In epidemiology, the strength of a factor’s
effect is usually measured by the change in

disease frequency produced by introducing
the factor into a population. This change may
be measured in absolute or relative terms. In
either case, the strength of an effect may
have tremendous public health significance,
but it may have little biological significance.
The reason is that given a specific causal
mechanism, any of the component causes can
have strong or weak effects. The actual iden-
tity of the constituent components of the
causal mechanism amounts to the biology of
causation. In contrast, the strength of a fac-
tor’s effect depends on the time-specific distri-
bution of its causal complements in the popu-
lation. Over a span of time, the strength of
the effect of a given factor on the occurrence
of a given disease may change, because the
prevalence of its causal complements in vari-
ous causal mechanisms may also change.
The causal mechanisms in which the factor
and its complements act could remain un-
changed, however.

INTERACTION AMONG CAUSES

The causal pie model posits that several
causal components act in concert to produce
an effect. “Acting in concert” does not neces-
sarily imply that factors must act at the same
time. Consider the example above of the per-
son who sustained trauma to the head that
resulted in an equilibrium disturbance,
which led, years later, to a fall on an icy
path. The earlier head trauma played a
causal role in the later hip fracture; so did
the weather conditions on the day of the
fracture. If both of these factors played a
causal role in the hip fracture, then they in-
teracted with one another to cause the frac-
ture, despite the fact that their time of action
is many years apart. We would say that any
and all of the factors in the same causal
mechanism for disease interact with one an-
other to cause disease. Thus, the head
trauma interacted with the weather condi-
tions, as well as with other component causes
such as the type of footwear, the absence of
a handhold, and any other conditions that
were necessary to the causal mechanism of
the fall and the broken hip that resulted.
One can view each causal pie as a set of in-
teracting causal components. This model
provides a biological basis for a concept of

American Journal of Public Health | Supplement 1, 2005, Vol 95, No. S1S146 | Public Health Matters | Peer Reviewed | Rothman and Greenland

⏐ PUBLIC HEALTH MATTERS ⏐

Table 1–Hypothetical Rates of Head
and Neck Cancer (Cases per 100 000
Person-Years) According to Smoking
Status and

Alcohol Drinking

Alcohol Drinking

Smoking Status No Yes

Nonsmoker 1 3

Smoker 4 12

interaction distinct from the usual statistical
view of interaction.3

SUM OF ATTRIBUTABLE FRACTIONS

Consider the data on rates of head and
neck cancer according to whether people
have been cigarette smokers, alcohol drink-
ers, or both (Table 1). Suppose that the differ-
ences in the rates all reflect causal effects.
Among those people who are smokers and
also alcohol drinkers, what proportion of the
cases is attributable to the effect of smoking?
We know that the rate for these people is 12
cases per 100 000 person-years. If these
same people were not smokers, we can infer
that their rate of head and neck cancer would
be 3 cases per 100 000 person-years. If this
difference reflects the causal role of smoking,
then we might infer that 9 of every 12 cases,
or 75%, are attributable to smoking among
those who both smoke and drink alcohol. If
we turn the question around and ask what
proportion of disease among these same
people is attributable to alcohol drinking,
we would be able to attribute 8 of every 12
cases, or 67%, to alcohol drinking.

How can we attribute 75% of the cases to
smoking and 67% to alcohol drinking among
those who are exposed to both? We can be-
cause some cases are counted more than
once. Smoking and alcohol interact in some
cases of head and neck cancer, and these
cases are attributable both to smoking and to
alcohol drinking. One consequence of interac-
tion is that we should not expect that the pro-
portions of disease attributable to various
component causes will sum to 100%.

A widely discussed (though unpublished)
paper from the 1970s, written by scientists at
the National Institutes of Health, proposed

that as much as 40% of cancer is attributable
to occupational exposures. Many scientists
thought that this fraction was an overestimate,
and argued against this claim.4,5 One of the
arguments used in rebuttal was as follows:
x percent of cancer is caused by smoking,
y percent by diet, z percent by alcohol, and
so on; when all these percentages are added
up, only a small percentage, much less than
40%, is left for occupational causes. But this
rebuttal is fallacious, because it is based on
the naive view that every case of disease has
a single cause, and that two causes cannot
both contribute to the same case of cancer.
In fact, since diet, smoking, asbestos, and vari-
ous occupational exposures, along with other
factors, interact with one another and with
genetic factors to cause cancer, each case of
cancer could be attributed repeatedly to
many separate component causes. The sum
of disease attributable to various component
causes thus has no upper limit.

A single cause or category of causes that is
present in every sufficient cause of disease
will have an attributable fraction of 100%.
Much publicity attended the pronouncement
in 1960 that as much as 90% of cancer is
caused by environmental factors.6 Since “envi-
ronment” can be thought of as an all-embracing
category that represents nongenetic causes,
which must be present to some extent in
every sufficient cause, it is clear on a priori
grounds that 100% of any disease is environ-
mentally caused. Thus, Higginson’s estimate
of 90% was an underestimate.

Similarly, one can show that 100% of any
disease is inherited. MacMahon 7 cited the ex-
ample of yellow shanks, 8 a trait occurring in
certain strains of fowl fed yellow corn. Both
the right set of genes and the yellow-corn diet
are necessary to produce yellow shanks. A
farmer with several strains of fowl, feeding
them all only yellow corn, would consider
yellow shanks to be a genetic condition, since
only one strain would get yellow shanks, de-
spite all strains getting the same diet. A differ-
ent farmer, who owned only the strain liable
to get yellow shanks, but who fed some of
the birds yellow corn and others white corn,
would consider yellow shanks to be an envi-
ronmentally determined condition because it
depends on diet. In reality, yellow shanks is
determined by both genes and environment;

there is no reasonable way to allocate a por-
tion of the causation to either genes or envi-
ronment. Similarly, every case of every dis-
ease has some environmental and some
genetic component causes, and therefore
every case can be attributed both to genes
and to environment. No paradox exists as
long as it is understood that the fractions of
disease attributable to genes and to environ-
ment overlap.

Many researchers have spent considerable
effort in developing heritability indices, which
are supposed to measure the fraction of dis-
ease that is inherited. Unfortunately, these
indices only assess the relative role of envi-
ronmental and genetic causes of disease in a
particular setting. For example, some genetic
causes may be necessary components of
every causal mechanism. If everyone in a
population has an identical set of the genes
that cause disease, however, their effect is
not included in heritability indices, despite
the fact that having these genes is a cause of
the disease. The two farmers in the example
above would offer very different values for
the heritability of yellow shanks, despite the
fact that the condition is always 100% depen-
dent on having certain genes.

If all genetic factors that determine disease
are taken into account, whether or not they
vary within populations, then 100% of dis-
ease can be said to be inherited. Analogously,
100% of any disease is environmentally
caused, even those diseases that we often
consider purely genetic. Phenylketonuria, for
example, is considered by many to be purely
genetic. Nonetheless, the mental retardation
that it may cause can be prevented by appro-
priate dietary intervention.

The treatment for phenylketonuria illus-
trates the interaction of genes and environ-
ment to cause a disease commonly thought to
be purely genetic. What about an apparently
purely environmental cause of death such as
death from an automobile accident? It is easy
to conceive of genetic traits that lead to psy-
chiatric problems such as alcoholism, which
in turn lead to drunk driving and consequent
fatality. Consider another more extreme envi-
ronmental example, being killed by lightning.
Partially heritable psychiatric conditions can
influence whether someone will take shelter
during a lightning storm; genetic traits such as

Supplement 1, 2005, Vol 95, No. S1 | American Journal of Public Health Rothman and Greenland | Peer Reviewed | Public Health Matters | S147

⏐ PUBLIC HEALTH MATTERS ⏐

athletic ability may influence the likelihood of
being outside when a lightning storm strikes;
and having an outdoor occupation or pastime
that is more frequent among men (or women),
and in that sense genetic, would also influ-
ence the probability of getting killed by light-
ning. The argument may seem stretched on
this example, but the point that every case of
disease has both genetic and environmental
causes is defensible and has important impli-
cations for research.

MAKING CAUSAL INFERENCES

Causal inference may be viewed as a spe-
cial case of the more general process of scien-
tific reasoning, about which there is substan-
tial scholarly debate among scientists and
philosophers.

Impossibility of Proof
Vigorous debate is a characteristic of mod-

ern scientific philosophy, no less in epidemiol-
ogy than in other areas. Perhaps the most im-
portant common thread that emerges from
the debated philosophies stems from 18th-
century empiricist David Hume’s observation
that proof is impossible in empirical science.
This simple fact is especially important to epi-
demiologists, who often face the criticism that
proof is impossible in epidemiology, with the
implication that it is possible in other scien-
tific disciplines. Such criticism may stem from
a view that experiments are the definitive
source of scientific knowledge. Such a view is
mistaken on at least two counts. First, the
nonexperimental nature of a science does not
preclude impressive scientific discoveries; the
myriad examples include plate tectonics, the
evolution of species, planets orbiting other
stars, and the effects of cigarette smoking on
human health. Even when they are possible,
experiments (including randomized trials) do
not provide anything approaching proof, and
in fact may be controversial, contradictory,
or irreproducible. The cold-fusion debacle
demonstrates well that neither physical nor
experimental science is immune to such
problems.

Some experimental scientists hold that
epidemiologic relations are only suggestive,
and believe that detailed laboratory study of
mechanisms within single individuals can

reveal cause–effect relations with certainty.
This view overlooks the fact that all relations
are suggestive in exactly the manner dis-
cussed by Hume: even the most careful and
detailed mechanistic dissection of individual
events cannot provide more than associations,
albeit at a finer level. Laboratory studies
often involve a degree of observer control
that cannot be approached in epidemiology;
it is only this control, not the level of observa-
tion, that can strengthen the inferences from
laboratory studies. Furthermore, such control
is no guarantee against error. All of the fruits
of scientific work, in epidemiology or other
disciplines, are at best only tentative formula-
tions of a description of nature, even when
the work itself is carried out without mistakes.

Testing Competing Epidemiologic
Theories

Biological knowledge about epidemiologic
hypotheses is often scant, making the hy-
potheses themselves at times little more than
vague statements of causal association be-
tween exposure and disease, such as “smok-
ing causes cardiovascular disease.” These
vague hypotheses have only vague conse-
quences that can be difficult to test. To cope
with this vagueness, epidemiologists usually
focus on testing the negation of the causal
hypothesis, that is, the null hypothesis that
the exposure does not have a causal relation
to disease. Then, any observed association
can potentially refute the hypothesis, subject
to the assumption (auxiliary hypothesis) that
biases are absent.

If the causal mechanism is stated specifi-
cally enough, epidemiologic observations
under some circumstances might provide
crucial tests of competing non-null causal
hypotheses. On the other hand, many epide-
miologic studies are not designed to test a
causal hypothesis. For example, epidemio-
logic data related to the finding that women
who took replacement estrogen therapy were
at a considerably higher risk for endometrial
cancer was examined by Horwitz and Fein-
stein, who conjectured a competing theory to
explain the association: they proposed that
women taking estrogen experienced symp-
toms such as bleeding that induced them to
consult a physician.9 The resulting diagnostic
workup led to the detection of endometrial

cancer at an earlier stage in these women, as
compared with women not taking estrogens.
Many epidemiologic observations could have
been and were used to evaluate these com-
peting hypotheses. The causal theory pre-
dicted that the risk of endometrial cancer
would tend to increase with increasing use
(dose, frequency, and duration) of estrogens,
as for other carcinogenic exposures. The
detection bias theory, on the other hand,
predicted that women who had used estro-
gens only for a short while would have the
greatest risk, since the symptoms related to
estrogen use that led to the medical consulta-
tion tend to appear soon after use begins.
Because the association of recent estrogen
use and endometrial cancer was the same
in both long-term and short-term estrogen
users, the detection bias theory was refuted
as an explanation for all but a small fraction
of endometrial cancer cases occurring after
estrogen use.

The endometrial cancer example illus-
trates a critical point in understanding the
process of causal inference in epidemiologic
studies: many of the hypotheses being evalu-
ated in the interpretation of epidemiologic
studies are noncausal hypotheses, in the
sense of involving no causal connection be-
tween the study exposure and the disease.
For example, hypotheses that amount to
explanations of how specific types of bias
could have led to an association between ex-
posure and disease are the usual alternatives
to the primary study hypothesis that the epi-
demiologist needs to consider in drawing in-
ferences. Much of the interpretation of epi-
demiologic studies amounts to the testing of
such noncausal explanations.

THE DUBIOUS VALUE OF CAUSAL
CRITERIA

In practice, how do epidemiologists sepa-
rate out the causal from the noncausal expla-
nations? Despite philosophic criticisms of in-
ductive inference, inductively oriented causal
criteria have commonly been used to make
such inferences. If a set of necessary and suf-
ficient causal criteria could be used to distin-
guish causal from noncausal relations in epi-
demiologic studies, the job of the scientist
would be eased considerably. With such

American Journal of Public Health | Supplement 1, 2005, Vol 95, No. S1S148 | Public Health Matters | Peer Reviewed | Rothman and Greenland

⏐ PUBLIC HEALTH MATTERS ⏐

criteria, all the concerns about the logic or
lack thereof in causal inference could be
forgotten: it would only be necessary to con-
sult the checklist of criteria to see if a relation
were causal. We know from philosophy that a
set of sufficient criteria does not exist. Never-
theless, lists of causal criteria have become
popular, possibly because they seem to
provide a road map through complicated
territory.

Hill’s Criteria
A commonly used set of criteria was pro-

posed by Hill,10 it was an expansion of a set
of criteria offered previously in the landmark
surgeon general’s report on smoking and
health,11 which in turn were anticipated by
the inductive canons of John Stuart Mill12

and the rules given by Hume. 13

Hill suggested that the following aspects of
an association be considered in attempting to
distinguish causal from noncausal associa-
tions: (1) strength, (2) consistency, (3) speci-
ficity, (4) temporality, (5) biological gradient,
(6) plausibility, (7) coherence, (8) experimen-
tal evidence, and (9) analogy. These criteria
suffer from their inductivist origin, but their
popularity demands a more specific discus-
sion of their utility.

1. Strength. Hill’s argument is essentially
that strong associations are more likely to be
causal than weak associations because, if they
could be explained by some other factor, the
effect of that factor would have to be even
stronger than the observed association and
therefore would have become evident. Weak
associations, on the other hand, are more
likely to be explained by undetected biases. To
some extent this is a reasonable argument but,
as Hill himself acknowledged, the fact that an
association is weak does not rule out a causal
connection. A commonly cited counterexam-
ple is the relation between cigarette smoking
and cardiovascular disease: one explanation
for this relation being weak is that cardiovas-
cular disease is common, making any ratio
measure of effect comparatively small com-
pared with ratio measures for diseases that are
less common.14 Nevertheless, cigarette smok-
ing is not seriously doubted as a cause of car-
diovascular disease. Another example would
be passive smoking and lung cancer, a weak
association that few consider to be noncausal.

Counterexamples of strong but noncausal
associations are also not hard to find; any
study with strong confounding illustrates the
phenomenon. For example, consider the
strong but noncausal relation between Down
syndrome and birth rank, which is con-
founded by the relation between Down syn-
drome and maternal age. Of course, once the
confounding factor is identified, the associa-
tion is diminished by adjustment for the fac-
tor. These examples remind us that a strong
association is neither necessary nor sufficient
for causality, nor is weakness necessary or
sufficient for absence of causality. Further-
more, neither relative risk nor any other mea-
sure of association is a biologically consistent
feature of an association; as described above,
such measures of association are characteris-
tics of a given population that depend on the
relative prevalence of other causes in that
population. A strong association serves only
to rule out hypotheses that the association is
entirely due to one weak unmeasured con-
founder or other source of modest bias.

2. Consistency. Consistency refers to the re-
peated observation of an association in differ-
ent populations under different circumstances.
Lack of consistency, however, does not rule
out a causal association, because some effects
are produced by their causes only under un-
usual circumstances. More precisely, the effect
of a causal agent cannot occur unless the com-
plementary component causes act, or have al-
ready acted, to complete a sufficient cause.
These conditions will not always be met. Thus,
transfusions can cause HIV infection but they
do not always do so: the virus must also be
present. Tampon use can cause toxic shock
syndrome, but only rarely when certain other,
perhaps unknown, conditions are met. Consis-
tency is apparent only after all the relevant de-
tails of a causal mechanism are understood,
which is to say very seldom. Furthermore,
even studies of exactly the same phenomena
can be expected to yield different results sim-
ply because they differ in their methods and
random errors. Consistency serves only to rule
out hypotheses that the association is attributa-
ble to some factor that varies across studies.

One mistake in implementing the consis-
tency criterion is so common that it deserves
special mention. It is sometimes claimed that
a literature or set of results is inconsistent

simply because some results are “statistically
significant” and some are not. This sort of
evaluation is completely fallacious even if one
accepts the use of significance testing meth-
ods: The results (effect estimates) from the
studies could all be identical even if many
were significant and many were not, the dif-
ference in significance arising solely because
of differences in the standard errors or sizes
of the studies. Furthermore, this fallacy is not
eliminated by “standardizing” estimates.

3. Specificity. The criterion of specificity
requires that a cause leads to a single effect,
not multiple effects. This argument has often
been advanced to refute causal interpreta-
tions of exposures that appear to relate to
myriad effects—for example, by those seeking
to exonerate smoking as a cause of lung can-
cer. Unfortunately, the criterion is invalid as a
general rule. Causes of a given effect cannot
be expected to lack all other effects. In fact,
everyday experience teaches us repeatedly
that single events or conditions may have
many effects. Smoking is an excellent exam-
ple; it leads to many effects in the smoker,
in part because smoking involves exposure
to a wide range of agents.15,16 The existence
of one effect of an exposure does not detract
from the possibility that another effect exists.

On the other hand, Weiss16 convincingly ar-
gued that specificity can be used to distinguish
some causal hypotheses from noncausal hy-
potheses, when the causal hypothesis predicts
a relation with one outcome but no relation
with another outcome. Thus, specificity can
come into play when it can be logically de-
duced from the causal hypothesis in question.

4. Temporality. Temporality refers to the
necessity for a cause to precede an effect in
time. This criterion is inarguable, insofar as
any claimed observation of causation must in-
volve the putative cause C preceding the pu-
tative effect D. It does not, however, follow
that a reverse time order is evidence against
the hypothesis that C can cause D. Rather,
observations in which C followed D merely
show that C could not have caused D in these
instances; they provide no evidence for or
against the hypothesis that C can cause D in
those instances in which it precedes D.

5. Biological gradient. Biological gradient
refers to the presence of a unidirectional
dose–response curve. We often expect such a

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monotonic relation to exist. For example,
more smoking means more carcinogen expo-
sure and more tissue damage, hence more op-
portunity for carcinogenesis. Some causal as-
sociations, however, show a single jump
(threshold) rather than a monotonic trend; an
example is the association between DES and
adenocarcinoma of the vagina. A possible ex-
planation is that the doses of DES that were
administered were all sufficiently great to pro-
duce the maximum effect from DES. Under
this hypothesis, for all those exposed to DES,
the development of disease would depend
entirely on other component causes.

Alcohol consumption and mortality is an-
other example. Death rates are higher among
nondrinkers than among moderate drinkers,
but ascend to the highest levels for heavy
drinkers. There is considerable debate about
which parts of the J-shaped dose-response
curve are causally related to alcohol con-
sumption and which parts are noncausal ar-
tifacts stemming from confounding or other
biases. Some studies appear to find only an
increasing relation between alcohol consump-
tion and mortality, possibly because the cate-
gories of alcohol consumption are too broad
to distinguish different rates among moderate
drinkers and nondrinkers.

Associations that do show a monotonic
trend in disease frequency with increasing lev-
els of exposure are not necessarily causal; con-
founding can result in a monotonic relation
between a noncausal risk factor and disease if
the confounding factor itself demonstrates a
biological gradient in its relation with disease.
The noncausal relation between birth rank
and Down syndrome mentioned in part 1
above shows a biological gradient that merely
reflects the progressive relation between ma-
ternal age and Down syndrome occurrence.

These examples imply that the existence of
a monotonic association is neither necessary
nor sufficient for a causal relation. A nonmo-
notonic relation only refutes those causal hy-
potheses specific enough to predict a monoto-
nic dose–response curve.

6. Plausibility. Plausibility refers to the bio-
logical plausibility of the hypothesis, an impor-
tant concern but one that is far from objective
or absolute. Sartwell, emphasizing this point,
cited the 1861 comments of Cheever on the
etiology of typhus before its mode of transmis-

sion (via body lice) was known: “It could be no
more ridiculous for the stranger who passed
the night in the steerage of an emigrant ship to
ascribe the typhus, which he there contracted,
to the vermin with which bodies of the sick
might be infested. An adequate cause, one rea-
sonable in itself, must correct the coincidences
of simple experience.”17 What was to Cheever
an implausible explanation turned out to be
the correct explanation, since it was indeed the
vermin that caused the typhus infection. Such
is the problem with plausibility: it is too often
not based on logic or data, but only on prior
beliefs. This is not to say that biological knowl-
edge should be discounted when evaluating a
new hypothesis, but only to point out the diffi-
culty in applying that knowledge.

The Bayesian approach to inference at-
tempts to deal with this problem by requiring
that one quantify, on a probability (0 to 1)
scale, the certainty that one has in prior be-
liefs, as well as in new hypotheses. This quan-
tification displays the dogmatism or open-
mindedness of the analyst in a public fashion,
with certainty values near 1 or 0 betraying a
strong commitment of the analyst for or
against a hypothesis. It can also provide a
means of testing those quantified beliefs
against new evidence.12 Nevertheless, the
Bayesian approach cannot transform plausi-
bility into an objective causal criterion.

7. Coherence. Taken from the surgeon gen-
eral’s report on smoking and health,11 the term
coherence implies that a cause-and-effect inter-
pretation for an association does not conflict
with what is known of the natural history and
biology of the disease. The examples Hill gave
for coherence, such as the histopathologic ef-
fect of smoking on bronchial epithelium (in ref-
erence to the association between smoking and
lung cancer) or the difference in lung cancer
incidence by gender, could reasonably be
considered examples of plausibility as well
as coherence; the distinction appears to be a
fine one. Hill emphasized that the absence of
coherent information, as distinguished, appar-
ently, from the presence of conflicting informa-
tion, should not be taken as evidence against
an association being considered causal. On the
other hand, presence of conflicting information
may indeed refute a hypothesis, but one must
always remember that the conflicting informa-
tion may be mistaken or misinterpreted.18

8. Experimental evidence. It is not clear what
Hill meant by experimental evidence. It might
have referred to evidence from laboratory ex-
periments on animals, or to evidence from
human experiments. Evidence from human ex-
periments, however, is seldom available for
most epidemiologic research questions, and an-
imal evidence relates to different species and
usually to levels of exposure very different
from those humans experience. From Hill’s ex-
amples, it seems that what he had in mind for
experimental evidence was the result of re-
moval of some harmful exposure in an inter-
vention or prevention program, rather than the
results of laboratory experiments. The lack of
availability of such evidence would at least be
a pragmatic difficulty in making this a criterion
for inference. Logically, however, experimental
evidence is not a criterion but a test of the
causal hypothesis, a test that is simply unavail-
able in most circumstances. Although experi-
mental tests can be much stronger than other
tests, they are often not as decisive as thought,
because of difficulties in interpretation. For ex-
ample, one can attempt to test the hypothesis
that malaria is caused by swamp gas by drain-
ing swamps in some areas and not in others to
see if the malaria rates among residents are af-
fected by the draining. As predicted by the hy-
pothesis, the rates will drop in the areas where
the swamps are drained. As Popper empha-
sized, however, there are always many alterna-
tive explanations for the outcome of every ex-
periment. In this example, one alternative,
which happens to be correct, is that mosqui-
toes are responsible for malaria transmission.

9. Analogy. Whatever insight might be de-
rived from analogy is handicapped by the in-
ventive imagination of scientists who can find
analogies everywhere. At best, analogy pro-
vides a source of more elaborate hypotheses
about the associations under study; absence of
such analogies only reflects lack of imagination
or experience, not falsity of the hypothesis.

Is There Any Use for Causal Criteria?
As is evident, the standards of epidemio-

logic evidence offered by Hill are saddled with
reservations and exceptions. Hill himself was
ambivalent about the utility of these “view-
points” (he did not use the word criteria in the
paper). On the one hand, he asked, “In what
circumstances can we pass from this observed

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⏐ PUBLIC HEALTH MATTERS ⏐

association to a verdict of causation?” Yet de-
spite speaking of verdicts on causation, he dis-
agreed that any “hard-and-fast rules of evi-
dence” existed by which to judge causation:
This conclusion accords with the views of
Hume, Popper, and others that causal infer-
ences cannot attain the certainty of logical de-
ductions. Although some scientists continue to
promulgate causal criteria as aids to inference,
others argue that it is actually detrimental to
cloud the inferential process by considering
checklist criteria.19 An intermediate, refutation-
ist approach seeks to transform the criteria
into deductive tests of causal hypotheses.20,21

Such an approach avoids the temptation to
use causal criteria simply to buttress pet theo-
ries at hand, and instead allows epidemiolo-
gists to focus on evaluating competing causal
theories using crucial observations.

CRITERIA TO JUDGE WHETHER
SCIENTIFIC EVIDENCE IS VALID

Just as causal criteria cannot be used to
establish the validity of an inference, there
are no criteria that can be used to establish
the validity of data or evidence. There are
methods by which validity can be assessed,
but this assessment would not resemble any-
thing like the application of rigid criteria.

Some of the difficulty can be understood by
taking the view that scientific evidence can
usually be viewed as a form of measurement.
If an epidemiologic study sets out to assess the
relation between exposure to tobacco smoke
and lung cancer risk, the results can and
should be framed as a measure of causal ef-
fect, such as the ratio of the risk of lung cancer
among smokers to the risk among nonsmok-
ers. Like any measurement, the measurement
of a causal effect is subject to measurement
error. For a scientific study, measurement error
encompasses more than the error that we
might have in mind when we attempt to mea-
sure the length of a piece of carpet. In addition
to statistical error, the measurement error sub-
sumes problems that relate to study design, in-
cluding subject selection and retention, infor-
mation acquisition, and uncontrolled
confounding and other sources of bias. There
are many individual sources of possible error.
It is not sufficient to characterize a study as
having or not having any of these sources of

error, since nearly every study will have nearly
every type of error. The real issue is to quan-
tify the errors. As there is no precise cutoff
with respect to how much error can be toler-
ated before a study must be considered in-
valid, there is no alternative to the quantifica-
tion of study errors to the extent possible.

Although there are no absolute criteria for
assessing the validity of scientific evidence, it
is still possible to assess the validity of a
study. What is required is much more than
the application of a list of criteria. Instead,
one must apply thorough criticism, with the
goal of obtaining a quantified evaluation of
the total error that afflicts the study. This type
of assessment is not one that can be done
easily by someone who lacks the skills and
training of a scientist familiar with the subject
matter and the scientific methods that were
employed. Neither can it be applied readily
by judges in court, nor by scientists who ei-
ther lack the requisite knowledge or who do
not take the time to penetrate the work.

About the Authors
Kenneth J. Rothman is with the Boston University Medical
Center, Boston, Mass. Sander Greenland is with the Uni-
versity of California, Los Angeles.

Requests for reprints should be sent to Kenneth J. Rothman,
DrPH, Boston University School of Public Health, Depart-
ment of Epidemiology, 715 Albany St., Boston, MA
02118 (e-mail: krothman@bu.edu).

This article was accepted November 18, 2004.

Contributors
Kenneth J. Rothman and Sander Greenland participated
equally in the planning and writing of this article.

Acknowledgments
This work is largely abridged from chapter 2 of Modern
Epidemiology, 2nd ed., by K. J. Rothman and S. Green-
land, Lippincott, Williams & Wilkins, 1998, and chap-
ter 2 of Epidemiology—An Introduction by K. J. Rothman,
Oxford University Press, 2002.

References
1. Rothman KJ. Causes. Am J Epidemiol. 1976;104:
587–592.

2. Honoreé A. Causation in the Law. In: Zalta EN,
ed. Stanford Encyclopedia of Philosophy. Winter 2001
ed. Stanford, Calif: Stanford University; 2001. Avail-
able at: http://plato.stanford.edu/archives/win2001/
entries/causation-law.

3. Rothman KJ, Greenland S. Modern Epidemiology.
Philadelphia, Pa: Lippincott; 1998: chap 18.

4. Higginson J. Proportion of cancer due to occupa-
tion. Prev Med. 1980;9:180–188.

5. Ephron E. Apocalyptics: Cancer and the Big Lie—
How Environmental Politics Controls What We Know
about Cancer. New York, NY: Simon and Schuster;
1984.

6. Higginson J. Population studies in cancer. Acta
Unio Internat Contra Cancrum 1960;16:1667–1670.

7. MacMahon B. Gene-environment interaction in
human disease. J Psychiatr Res. 1968;6:393–402.

8. Hogben L. Nature and Nurture. London, England:
Williams and Norgate; 1933.

9. Horwitz RI, Feinstein AR. Alternative analytic
methods for case-control studies of estrogens and
endometrial cancer. N Engl J Med. 1978;299:
1089–1094.

10. Hill AB. The environment and disease: association
or causation? Proc R Soc Med. 1965;58:295–300.

11. Smoking and Health: Report of the Advisory
Committee to the Surgeon General of the Public
Health Service. Washington, DC: US Department of
Health, Education, and Welfare; 1964. Public Health
Service Publication No. 1103.

12. Mill JS. A System of Logic, Ratiocinative and Induc-
tive. 5th ed. London, England: Parker, Son and Bowin,
1862. Cited in Clark DW, MacMahon B, eds. Preventive
and Community Medicine. 2nd ed. Boston, Mass: Little,
Brown; 1981:chap 2.

13. Hume D. A Treatise of Human Nature. (Originally
published in 1739.) Oxford University Press edition,
with an Analytical Index by L. A. Selby-Bigge, pub-
lished 1888. Second edition with text revised and
notes by P. H. Nidditch, 1978.

14. Rothman KJ, Poole C. A strengthening programme
for weak associations. Int J Epidemiol 1988;17(Suppl):
955–959.

15. Smith GD. Specificity as a criterion for causation:
a premature burial? Int J Epidemiol. 2002;31:710–713.

16. Weiss NS:. Can the specificity of an association be
rehabilitated as a basis for supporting a causal hypoth-
esis? Epidemiology. 2002;13:6-8.

17. Sartwell P. On the methodology of investigations
of etiologic factors in chronic diseases—further com-
ments. J Chron Dis. 1960;11:61–63.

18. Popper, KR. The Logic of Scientific Discovery. New
York, NY: Harper & Row; 1959 (first published in Ger-
man in 1934).

19. Lanes SF, Poole C. “Truth in packaging?” The
unwrapping of epidemiologic research. J Occup Med.
1984;26:571–574.

20. Maclure M. Popperian refutation in epidemiology.
Am J Epidemiol. 1985;121:343–350.

21. Weed D. On the logic of causal inference. Am J
Epidemiol. 1986;123:965–979.

Models of Causation
& Attributable Proportion

Lesson 2

The next few slides may be a review for those of you who’ve had undergraduate epi. These are basic terms for levels of disease in a population that you should know and be able to apply.
1

Recall…
The Philosophy of Causation:
If exposure to E and occurrence of D seem to go together, does E cause D?

2
Philosophy of Causation: If exposure to E and occurrence of D seem to go together, does E cause D? Example: If Jim has unprotected oral sex and then develops HIV, was it because of the unprotected oral sex?
 
We would like to answer this question because of the public health implications for preventing disease occurrence in other people.
 
Many scientists believe that causation cannot be proven by epi studies alone because of scientific reasoning problems and the observational nature of epidemiological studies. In order to characterize or explain a phenomenon such as causation, we must instead set up a model (or a system of a set of rules) to explain the biological phenomenon (people getting sick) that we observe.

Epidemiologic Triangle:
Triad of Causation

The epidemiologic triangle, or triad of causation, is the traditional model of infectious disease causation. It has three components: an external agent, a susceptible host, and an environment that brings the host and agent together. In this model, the environment influences the agent, the host, and the route of transmission of the agent from a source to the host.
The epidemiological triad (triad of causation) is one of the first theories of disease causation adopted by modern epidemiology. As depicted by the figure in the slide, there is an interdependence between three constructs: agent, host, and environment.

3

The Agent
The agent is the cause of the disease. When studying the epidemiology of most infectious diseases, the agent is a microbe—an organism too small to be seen with the naked eye. Disease-causing microbes are bacteria, virus, fungi, and protozoa (a type of parasite). They are what most people call “germs.” In non-infectious diseases, the agent can be behavioral risk factors…

The Host. Hosts are organisms, usually humans or animals, which are exposed to and harbor a disease. The host can be the organism that gets sick, as well as any animal carrier (including insects and worms) that may or may not get sick. Although the host may or may not know it has the disease or have any outward signs of illness, the disease does take lodging from the host. The “host” heading also includes symptoms of the disease. Different people may have different reactions to the same agent. For example, adults infected with the virus varacella (chickenpox) are more likely than children to develop serious complications
The Environment. The environment is the favorable surroundings and conditions external to the host that cause or allow the disease to be transmitted. Some diseases live best in dirty water. Others survive in human blood. Still others, like E. coli, thrive in warm temperatures but are killed by high heat. Other environment factors include the season of the year (in the U., the peak of the flu season is between November and March, for example). For any given pathogenic organism the range of tolerable environmental conditions may be wide or narrow. Any epidemic model of a specific disease must allow for these variations of the causative organism.
4

Triad of Causation
Interaction of Agent-Host-Environment is “cause” of disease
Efforts to prevent/control disease is constantly challenged by this interaction

The interaction of these three factors is the “cause” of disease, so when one changes, it affects the other. For example, an agent may mutate to negate previous immunity to influenza (person). This model would also apply to a situation where flood waters (environment) brought raw sewage (agent) into the water system thus increasing the chance of water-borne disease
 
Among these factors, there exists a dynamic situation in which the efforts to prevent and/or control disease are constantly challenged:
Populations are highly mobile and tend to live longer, thereby creating circumstances of increased risk of exposure and infection
Urbanization and suburbanization have exerted greater and greater pressures on the environment
Biological agents of disease have shown remarkable adaptability to modern control measures
Non-biological agents are often introduced into the milieu despite precautions of interested groups

5

Limitations
Many diseases do not have a single agent
Triad not particularly useful when looking at diseases that require multiple agents

This traditional model was most useful during the era when people died mainly from infectious diseases caused by a single agent. However, the leading causes of death today are non-infectious and not caused by one single factor. Think, for a moment, about heart disease which kills many folks each year. Can you identify a single agent that – on it’s own — causes heart disease? I’ll give you a few moments…
No?
Well, it’s because of this that the Triad of Causation has limited usefulness for diseases that are brought about by exposure to multiple agents… .
6

Contemporary Model
Diseases are caused not by exposure to one single agent, but rather by exposure to several different combinations of agents
Sometimes referred to as “Causal Web”

7
The contemporary model acknowledges the complexity of disease – that disease can be caused by several difference combinations of agents (aka risk factors). This is sometimes called a CAUSAL WEB and is difficult to identify because of the complexity of contributions of the component causes. This model is complex, but is needed in order to explain our observations of disease.
 
 

Terminology
Component Cause
Necessary Component Cause
Sufficient Cause

When looking at the contemporary model, there are some definitions that you need to burn into your memory so that you’ll be able to apply the concepts on your tests, read an epi article correctly, etc.
Component Cause: an agent (E+) that contributes to health outcome (D+), but that by itself will not cause D+
Necessary Component Cause – an exposure (E+) that will not, on its own, cause D+, but one that MUST be present for the health outcome (D+) to occur. Thus, a necessary component cause is present in EVERY case of D+
Sufficient Cause: a collection of component causes that interact to result in D+
Although these are fairly straightforward definitions, many students get tripped up when applying them… So let’s take a close look, shall we?
8

A pizza is composed of crust, sauce, cheese, and various toppings – or in the case of the pizza on the slide, pepperoni. Each of these items, individually, is a component cause, and on it’s own will not create a pizza. Collectively the component causes do compose a pizza. Got it?
9

Pizzas I like
Pepperoni with red sauce and mozzarella cheese
Salami, feta, onion, white sauce, and mushroom
Bacon, jalepeno, mushroom, and olives with red sauce and mozzarella cheese

Ok, so let’s say I only like the three kinds of pizzas listed on the slide. Each type of pizza is a way to make me happy. Thus, each pizza is a “sufficient cause” of my happiness.
So, in pizza 1, the component causes are crust, red sauce, mozzarella cheese, and pepperoni.
Pizza 2’s component causes are crust, white sauce, salami, onion, mushroom, and feta cheese.
Pizza 3’s component causes are crust, red sauce, bacon, jalepeno, mushroom, olives, and mozzarella cheese.
Would a pizza with crust, red sauce, pepperoni, feta, and mushrooms make me happy? No, because these component causes do not compose one of the three sufficient causes. Would a pizza with crust, white sauce, salami, onions, jalepenos, mushrooms, and feta make me happy? Yes, because all of the component causes for pizza 2 are present. The addition of the jalepenos does not change this.
Because each of the three sufficient causes (pizzas) have a crust as a component cause, crusts are necessary for there to be a sufficient cause. Thus, crusts are a necessary component cause.
Are there any other necessary component causes in this situation? Take a careful look.
10

No

No, there are not. While some of the component causes (red sauce, mushroom, and mozzarella cheese) were present in two of the three pizzas, in order to be necessary, they have to be present in all sufficient causes.
Ok, so back to the contemporary model….Most diseases have many sufficient causes. If, as in the case of my pizza happiness, all sufficient causes are known, then we can determine from epi data how much each component cause contributes to causing the disease, and therefore know how much of the disease we could eliminate if we got rid of that component cause.
Let’s look at a different example.
11

Crayolaitis

Crayolaitis (not a real disease) has three and only three sufficient causes as shown on the slide above Each circle represents one of the ways you can get crayolaitis. As such, each circle is a sufficient cause, which means that each circle as a whole – in and of itself – is sufficient for causing a disease. I’m repeating myself because this is a really important concept.
Within each circle (aka sufficient cause), each color represents a risk factor – or a component cause – for getting crayolaitis.
Ok, so let’s see if you got it… Pop quiz!
 
Can I get crayolaitis if I have light green, pink, and light blue?
No – because these three colors are not shown together in one of the sufficient cause circles. Recall, the ONLY way to get crayolaitis is to have one of the sufficient causes.
What about if I have yellow, dark green, pink, purple, and red?
Yes! I can because the yellow, dark green and pink are the colors that make up sufficient cause 3. Having the extra colors is of no consequence…
Now… is there a necessary component cause here?
No… there is no single color that is present in every circle (sufficient cause).
Which color (component cause) contributes the most to getting crayolaitis?
Ok, that’s a trick question… I haven’t taught you how to do that yet. =)
12

Attributable Proportion (AP)

Now, after that trick question, I know you are just on the edge of your seat wanting to know how to determine which component cause contributes the most to disease. =) So here’s how you do it… You calculate the attributable proportion (AP). AP is the proportion (percent) of cases of a disease associated with each sufficient cause.
Let’s say we know that 50% of the people with crayolaitis got it through Sufficient Cause 1, and that another 30% got it through Sufficient Cause 2. Given that there are three and only three sufficient causes for crayolaitis, this would mean that Sufficient Cause 3 is responsible for 20% of the cases…
In epi, we would state this as such: AP I = 50% ; APII = 30%; and APIII = 20%
Given that there are three and only three sufficient causes, AP I + APII + APIII = 100% of cases of crayolaitis. The sum of all sufficient causes will always = 100%
Still with me?
13

AP of Component Cause

The impact of various component causes in “manufacturing” cases of a disease can be estimated if we know enough about the disease to construct a model of how — or why — the disease occurs.  That is, if you know the AP of each sufficient cause, you can calculate the contribution of each component cause simply by giving each component cause the same AP as it’s sufficient cause.
Attributable Proportion (AP) is the proportion (percent) of cases of a disease associated with each sufficient cause
When a component cause appears in more than one sufficient cause, its AP is the sum of the sufficient cause APs that contains it.
For example, yellow is in sufficient cause 1 (AP = 50%) and sufficient cause 3 (AP = 20%). So, the AP for yellow is 70% (50% + 20%). So, APyellow= 70%, which you would interpret to say yellow is present in 70% of the cases of crayolaitis. Therefore, eliminating yellow would eliminate 70% of cases of crayolaitis.
Now, lets suppose that sufficient cause 2 also had yellow… That would make it a (insert correct answer here) and the AP would be (insert correct answer here). If the correct answers you inserted were “necessary component cause” and “100%,” you would be correct! And, you would interpret the , APyellow= 100%, as “Yellow was present in 100% of the cases of crayolaitis”. Now, to drive another point home about necessary causes, if we were to get rid of yellow, no one would ever get crayolaitis.
Got it?
NOTE: You’ve probably figured out that the sum of APs for component causes may exceed 100%. This is because the elimination of ANY component cause within a sufficient cause will render that sufficient cause inoperable…

 
14

In-Class Example
From 1999 to 2012 there were 150,000 cases of lung cancer in the US. According to the several studies all patients with lung cancer had one of these profiles:
Profile 1 (22,500 patients): Smoking, occupational exposure to PAH, obesity, presence of other cancers
Profile 2 (60,000 patients): Smoking, radon, particle pollution exposure, male
Profile 3 (37,500 patients); Particle pollution exposure, Smoking, geographical area of living, male
 Profile 4 (30,000 patients); Smoking, radon, presence the other cancers, particle pollution exposure, age > 50

From 1999 to 2012 there were 150,000 cases of lung cancer in the US. According to the several studies all patients with lung cancer had one of these profiles:
Profile 1 (22,500 patients): Smoking, occupational exposure to poly-aromatic hydrocarbons (PAH), obesity, presence of other cancers
Profile 2 (60,000 patients): Smoking, radon, particle pollution exposure, male
Profile 3 (37,500 patients): Particle pollution exposure, Smoking, geographical area of living, male
Profile 4 (30,000 patients): Smoking, radon, presence the other cancers, particle pollution exposure, age > 50
Questions you’ll be answering:
1. How many sufficient causes are there for lung cancer?
2. Determine the AP for each sufficient cause. 
3. How many component causes are there for lung cancer?
4. Calculate the AP for each component cause.
5. What is/are the necessary component cause(s), if any, for lung cancer?

15

1. How many sufficient causes are there for lung cancer?
From 1999 to 2012 there were 150,000 cases of lung cancer in the US. According to the several studies all patients with lung cancer had one of these profiles:
Profile 1 (22,500 patients): Smoking, occupational exposure to PAH, obesity, presence of other cancers
Profile 2 (60,000 patients): Smoking, radon, particle pollution exposure, male
Profile 3 (37,500 patients); Particle pollution exposure, Smoking, geographical area of living, male
 Profile 4 (30,000 patients); Smoking, radon, presence the other cancers, particle pollution exposure, age > 50

How many sufficient causes are there for lung cancer? Four. We know this because it states that “According to the several studies all patients with lung cancer had one of these profiles” and then four profiles were listed.
16

2. Determine AP for each sufficient cause.
Step 1: Calculate the total number of patients
Step 2: Divide number of patients in each profile by total number of patients

2. Determine the AP for each sufficient cause.
Step 1: The first thing we need to do is calculate our denominator, which we do by adding the number of patients in each of the profiles together:
Profile 1: 22,500 patients
Profile 2: 60,000 patients
Profile 3: 37,500 patients
Profile 4: 30,000 patients
Thus, 22,500 + 60,000 + 37,500 + 30,000 = 150,000 total patients
Step 2: Next, for each profile, we divide the number of patients in that profile by the total number of patients from all four profiles.
AP Profile 1 = 22,500 / 150,000 = 15%
AP Profile 2 = 60,000 / 150,000 = 40%
AP Profile 3 = 37,500 / 150,000 = 25%
AP Profile 4 = 30,000 / 150,000 = 20%
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3. How many component causes are there for lung cancer
Smoking
Occupational exposure to PAH
Obesity
Presence of other cancers
Radon
Particle pollution exposure
Male
Geographic area
Age > 50

3. How many component causes are there for lung cancer? Nine. To answer this, you simply count the number of unique risk factors from each of the profiles. Here’s the list of nine unique component causes listed in the four profiles:
Smoking
Occupational exposure to PAH
Obesity
Presence of other cancers
Radon
Particle pollution exposure
Male
Geographic area
Age > 50

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4. Calculate the AP for each component cause
 Component Cause SC 1
AP=15% SC 2
AP=40% SC 3
AP=25% SC 4
AP=20% AP Total
Smoking 15% 40% 25% 20% 100%
Occupational exp. to PAH 15%       15%
Obesity 15%       15%
Presence of other cancers 15%     20% 35%
Radon   40%   20% 60%
Particle pollution exposure   40% 25%  20% 85%
Male   40% 25%   65%
Geographic area     25%   25%
Age > 50     20% 20%

4. Calculate the AP for each component cause.
To answer this question, you’ll need to sum the AP% of each sufficient cause in which the component cause appears. To stay organized, I suggest creating a table such as the one shown on the slide, where each row is a component cause and the columns are sufficient causes (profiles) and their related APs. The total column adds the APs present in that row, and thus is the AP for that component cause.
Let’s take a look at the “male” component cause. Male is present in sufficient cause 2, which has an AP of 40%, and sufficient cause 3, which has an AP of 25%. Thus the AP for male is the 65% (40% + 20%).
IMPORTANT: The total column represents the amount of the disease that would be reduced if that component cause were eliminated.
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5. What is/are the necessary component cause(s), if any, for lung cancer?
 Component Cause SC 1
AP=15% SC 2
AP=40% SC 3
AP=25% SC 4
AP=20% AP Total
Smoking 15% 40% 25% 20% 100%
Occupational exp. to PAH 15%       15%
Obesity 15%       15%
Presence of other cancers 15%     20% 35%
Radon   40%   20% 60%
Particle pollution exposure   40% 25%  20% 85%
Male   40% 25%   65%
Geographic area     25%   25%
Age > 50     20% 20%

5. What is/are the necessary component cause(s), if any, for lung cancer?
Smoking, because it appears in all of the sufficient causes. Thus, is we could eliminate smoking, we would eliminate lung cancer.
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The End. =)

So, I could hear some of you on the last slide saying “But Dr. G, there are people who get lung cancer who don’t smoke, so eliminating smoking really won’t eliminate lung cancer entirely.” And that’s correct. Further, in real life, it is quite unlikely that we will know all of the sufficient causes of a disease, or all of the component causes of the known sufficient causes. Thus, there is always a presumption that while based on the known data, our answers are accurate, there are unknowns that could make them inaccurate. Epi (and research in general) is messy, like life, but it’s the best tool set we have. =)
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