3. Type of individual
Hypothetical Condition
Exposed Unexposed
1) No Effect (“doomed”) Case Case
2) Effect causative Case Noncase
3) Effect preventive Noncase Case
4) No effect (“immune”) Noncase Noncase
4. • The exposure has a biologic effect on the disease in
Types 2 and 3, but not in Types 1 and 4
• In practice, we cannot observe these types because we
cannot observe both exposure states simultaneously in
the same individuals. A given person is either exposed
or unexposed, I.e., one exposure condition is
counterfactual (counter to fact----not observed)
• Thus, if we observe the actual outcome of one
individual, e.g., an exposed person who becomes a case,
we cannot determine whether the exposure had an effect
on the disease. Is that exposed case a Type 1 or a Type 2?
5. • Since we cannot observe the outcome in exactly the same way
under both exposure conditions for the same individuals, in
epidemiology we must compare a group of individuals who were
exposed with a group of individuals who were unexposed.
• We observe whether the disease is more or less frequent in the
exposed group than in the unexposed group ---- i.e., we assess the
statistical association between exposure status and disease status
in the study pop.
• This general approach is the “epidemiologic method”.
• By assessing the statistical association in this way, we attempt to
estimate the net (average) effect of the exposure on disease
occurrence in the base population.
6. • The validity of this comparison between exposed and
unexposed populations, however, depends on the
comparability of exposure groups with respect to the
distribution of the 4 causal types.
• For example, it would not be valid to compare a group
of exposed persons who were all Type 1s with an
unexposed group who were all Type 4s; the exposed
would get the disease and the unexposed would not,
even though the exposure has no biologic effect in any
member of these groups
7. Necessary and Sufficient Causes and Preventives
• Consider the joint distribution of true exposure
and disease statuses in a given base pop.
•
• Case Noncase
• Exposed A B
• Unesposed C D
•
9. CAUSES: Are there any Type 2s in the population?
• The exposure is a necessary cause if no unexposed
individuals ever become cases. Cell C in the table is
always 0. Thus, there are no Type 1s or 3s in the pop.
•
• The exposure is a sufficient cause if all exposed
individuals inevitably become cases. Cell B is always
0. Thus, there are no Type 3s or 4s in the pop.
•
• If the exposure is both a necessary and sufficient cause
of the disease, both cells B and C are always 0. Thus,
every individual in the pop. is a Type 2.
11. PREVENTIVES: Are there any Type 3s in the population?
• The exposure is a necessary preventive if all unexposed
individuals inevitably become cases. Cell D is always 0.
Thus, there are no Type 2s or 4s in the pop.
•
• The exposure is a sufficient preventive if no exposed
individuals ever become cases. Cell A is always 0. Thus,
there are no Type 1s or 2s in the pop.
•
• If the exposure is both a necessary and sufficient
preventive of the disease, both cells A and D are always
0. Thus, every individual in the population is a Type 3.
14. • When focusing on causal parameters in the exposed base
population, there is no confounding if the total proportion of
Type 1 and Type 3 individuals is the same in exposed and
unexposed groups. This is the usual (often implied) meaning of
confounding in epidemiology
• If we were interested in what the risk would have been in the
unexposed group had they been exposed (I.e., when focusing on
causal parameters in the unexposed base population), no
confounding would mean that the total proportion of Type 1 and
Type 2 individuals is the same in exposed and unexposed
groups.
15. • If we were interested in estimating causal parameters
for the total base population, no confounding would
mean that both conditions described above would hold.
• This means the two exposure groups would be
completely exchangeable: the same exposure-risk
relation would exist if the two exposure states were
exchanged
• Complete exchangeability does not necessarily require
that the total distribution of causal types be the same in
exposed and unexposed populations
• In practice, we do not know the distributions of the 4
causal types. Thus, we can not observe confounding
16. • In practice, what we do instead is attempt to
identify and control for empirical manifestations
of confounding
• We search for differences between exposure
groups in the distribution of extraneous risk
factors for the disease
• Such differences could produce a violation of the
comparability assumption
• Those extraneous risk factors responsible for
confounding are called confounders or
confounding variables
18. Sufficient Cause and Component Causes
• A cause of a disease event is an event, condition, or
characteristics that preceded the disease event and
without which the disease event either would not have
occurred at all or would not have occurred until some
later time
• With this definition, it may be that no specific event,
condition, or characteristic is sufficient by itself to
produce disease
• This definition does not define a complete causal
mechanism but a component of it
19.
20. • Suppose that U is always present
(ubiquitous) and the above figure represents
all the sufficient causes.
23. Question 1-2
• Assuming that component cause A is
unmeasured, what are the incidence
proportions for combinations of component
causes B and E in hypothetical population 1?
• Which component cause has stronger causal
effect, B or E?
24.
25. Strength of Effects
• It is evident from Table 2-2 that for
population 1, E is a much stronger
determinant of incidence than B, because
the presence of E increases the incidence
proportion by 0.9, whereas the presence of
B increases it by only 0.1
26. Question 3-4
• Assuming that component cause A is
unmeasured, what are the incidence
proportions for combinations of component
causes B and E in hypothetical population 2?
• Which component cause has stronger causal
effect, B or E?
27.
28. Strength of Effects
• From Table 2-3, B is a much stronger
determinant of incidence than E.
• This is so despite the fact that in both
populations A, B, and E have no association
with one another and are each present in
exactly half the people
29. Question 5
• Why were the causal effects of B and E
different in population 1 and 2?
30. Strength of Effects
• Key difference between populations 1 and 2
is that the condition under which E acts as a
necessary and sufficient cause—the
presence of A or B, but not both—is
common in population 1 but rare in
population 2
• In population 1, 3600 have A or B but not
both; in population 2, only 400 have A or B
but not both
31. Strength of Effects
• We call the necessary and sufficient condition
for a factor to produce disease the causal
complement of the factor
• The condition of “A or B but not both” is the
causal complement of E
• The strength of a factor’s effect on a
population depends on the relative prevalence
of its causal complement
32. Strength of Effects
• This dependence of the effects of a specific
components cause on the prevalence of its
causal complement has nothing to do with the
biological mechanism of the component’s
action
• A factor will appear to have a strong effect if
its causal complement is common. A factor
with a rare causal complement will appear to
have a weak effect
33. Strength of Effects
• 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
• The strength of an effect may have tremendous
public-health significance, but it may have little
biologic significance
• Given a specific causal mechanism, any of the
component causes can have strong or weak effects
34. Strength of Effects
• The actual identities of the components of a sufficient cause are
part of the biology of causation, whereas the strength of a
factor’s effect depends on the time-specific distribution of its
causal complement in the population
• The strength of the effect of a given factor on the occurrence of
a given disease may change overtime because the prevalence of
its causal complement in various mechanisms may also change
• The causal mechanisms in which the factor and its cofactors act
could remain unchanged
35. Interaction Among Cases
• Two component causes acting in the same
sufficient cause may be thought of as
interacting biologically to produce disease
• Biologic interaction may be defined as the
participation of two component causes in
the same sufficient cause. Such interaction
is also known as causal co-action or joint
action
36. Limitations of the Sufficient-Component Cause Model
• It does not treat time in a fashion that allows for dynamic
analysis. In the sufficient cause model, time is invoked in the
definition of whether a factor is present or absent but dynamic
processes are not formulated
37. Limitations of the Sufficient-Component Cause Model
• Effects in the network plane are not incorporated in an
analyzable fashion: individual characteristics alone do not
determine the population risks
----particularly for infectious diseases, the outcome in one
individual depends on the outcomes in other individuals. This
makes it impossible for the sufficient cause model to define
individual infection risks in a transmission system before
infection spreads in the population
----In nonlinear population systems, such as infectious agent
transmission systems, population risks are not the sum of
individual risks as the sufficient cause model assumes
39. • Because standard epidemiological analyses and
the sufficient cause model ignore network
connections between individuals, they also
ignore the larger political, cultural and
economic forces that determine different
patterns of network connections
• Models that incorporate network structure
could help highlight these important
determinants of disease and bring them into the
realm of epidemiological investigation
40. Distinct Patterns of Connection between
Identical Individuals with 2 Connections
41. Network Connections, Individual Risk and
Population Risk
• Although all individuals in populations with either pattern A or
B would appear to be the same, the populations with pattern A
would have higher levels of infection
• This illustrates the fact that the 2 populations are not just the
sum of the individuals therein as would be assumed by analysis
restricted to the individual data plane (sufficient cause model)
• The 2 populations need to be defined by the pattern of
connections between individuals in the network plane as well
42. A Network in Which the Most Important Individual
Determining Population Levels of Infection Has the
Lowest Individual Risk of Infection
43. Different Effects of Network Roles and Individual Risk
on Population Risk
• Suppose that transmission across each link occurs with some
specified probability and there is random introduction of
infection into the network
• The individual with only 2 links has the lowest chance of
becoming infected after random introduction of infection to the
population
• Thus, from an individual risk view, this individual has the
lowest risk of infection
44. Different Effects of Network Roles and Individual Risk
on Population Risk
• However, the contribution of that individual to infection levels
in the population system can (at certain transmission
probabilities) be greater than that of any other individual
• Eliminating one connection to this individual can do more to
lower average infection levels in the population after
introduction of infection than eliminating a connection to any
other individual
• Any risk analysis assuming independence of outcomes in
individuals at risk would miss this fact
46. • The characteristic that most distinguishes
transmission models from the sufficient-
component cause model is that they model
nonlinear population effects
• Nonlinearity of effects at the population
system level has 2 important implications:
• ----1) individual effects will not sum to
population effects
• ----2) patterns of connection between
individuals will have effects at the
population level
47. Transmission Models
• Traditionally----Differential equation
models
• Recently----Discrete individual models:
allowing the combination of the theoretical
insights of transmission models and the
theoretical insights of sufficient cause
models
48. Graph Theoretic Models
• Causal diagram
• Is being elaborated to incorporate network
data
• To be introduced in much detail later on in
this course
