The Practical Uses of
Causal Diagrams
Michael Joffe
Imperial College London
The use of DAGs in epidemiology
• the theory of Directed Acyclic Graphs (DAGs) has
developed formal rules for controlling confounding,
equivalent to algebraic formulations in their rigour, but
simpler to use and less error-prone
• the resulting graphical theory is found to conform to
traditional “rules of thumb” – but is a better guide in
difficult conditions
A typical DAG in epidemiology
L is parental socioeconomic status
U is attraction towards physical activity (unmeasured)
C is “risk” of becoming a firefighter
E is being physically active (“exposure”)
D is heart disease (“outcome”)
from Hernán, MA, Hernández-Díaz S, Robins, JM. A structural
approach to selection bias. Epidemiology 2004; 15(5): 615-25
The use of DAGs in epidemiology
• the theory of Directed Acyclic Graphs (DAGs) has
developed formal rules for controlling confounding,
equivalent to algebraic formulations in their rigour, but
simpler to use and less error-prone
• the resulting graphical theory is found to conform to
traditional “rules of thumb” – but is a better guide in
difficult conditions
The use of DAGs in epidemiology
• the theory of Directed Acyclic Graphs (DAGs) has
developed formal rules for controlling confounding,
equivalent to algebraic formulations in their rigour, but
simpler to use and less error-prone
• the resulting graphical theory is found to conform to
traditional “rules of thumb” – but is a better guide in
difficult conditions
• the focus is on a single link: effect of E on D
• arrows mean causation: a variable alters the magnitude,
probability and/or severity of the next variable
• it can readily cope with multi-causation
– the representation of effect modification is still problematic
Pearl: causal & statistical languages
associational concept:
can be defined as a joint
distribution of observed
variables
• correlation
• regression
• risk ratio
• dependence
• likelihood
• conditionalization
• “controlling for”
causal concept:
• influence
• effect
• confounding
• explanation
• intervention
• randomization
• instrumental variables
• attribution
• “holding constant”
Four ways of explaining a
robust statistical association
X
Y
causation
X
Y
reverse causation
C
X
Y
C
X
Y
common ancestor
(confounding)
common descendant
(Berkson bias)
The SIR model of infections
β
ν
Modelling the whole system I
• this type of “compartmental model” is widely used in
infectious disease epidemiology
• it can only be used where the population can be divided
unambiguously into categories: a flow chart
• another example is Ross’ classic equation for malaria:
N = p.m.i.a.b.s.f
where N is new infections/month; p is population; m is proportion
infected; i is proportion infectious among the infected; a is av. no. of
mosquitoes/person; b is proportion of uninfected mosquitoes, s is
proportion of mosquitoes that survive; f is proportion of infected
mosqitoes that feed on humans
• this only applies to a uni-causal situation (mosquitoes)
• what is the equivalent in typical multi-causal situations?
Transport-related health problems
Safe
walking &
cycling
Distribution
of vehicle
emissions
Air
pollution
Respiratory
morbidity
& mortality
Physical
activity
Traffic
volume
Community
severance
Cardiovascular
morbidity &
mortality
Access
Osteoporosis
etc
Traffic
speed
Noise
Impaired
mental
health
Collisions:
number,
severity
Fatal and nonfatal injuries
Modelling the whole system II
• “web of causation”; “upstream” influences
• causal diagrams are constructed based on substantive
knowledge of the topic area plus evidence
• chains of causation, not just one link; and multiple chains
– assumption of independence
• multidisciplinary
• individual & group levels are combined
– as is routine in infectious disease epidemiology
• organised by economic/policy sector
• health determines the content of the diagram – “driven
by the bottom line”
Conditional independence
X and Y are conditionally independent given Z if, knowing Z,
discovering Y tells you nothing more about X
P(X | Y, Z) = P(X | Z)
• Z = genotype of parents
• X, Y = genotypes of 2 children
• If we know the genotype of the
parents, then the children’s genotypes
are conditionally independent
Z
X
diagram adapted from Best, Richardson & Jackson
Y
A
C
D
F
B
E
Conditional independence provides mathematical basis for
splitting up large system into smaller components
C
A
D
D
C
B
F
E
E
diagram adapted from Best, Richardson & Jackson
Functions of diagrams: scientific
• the aim is a diagram that describes causal relations
“out there” in the world, not a mental map
• a framework for analysis, e.g. statistical modelling
• to make assumptions and hypotheses explicit for
discussion, and for planning data collection and
analysis
• to place hypotheses in the public domain prior to
testing – a conjecture that is open to refutation
• to identify evidence gaps
• to generate a research agenda
Empirical aspects
• default: “all arrows” (saturated model) is conservative –
omission is a stronger statement than inclusion
• corollary: deletion following statistical analysis is the
strong step – uses model selection methods, e.g. AIC
• quantification of the links that remain
• transmissibility: X → Y and Y → Z does not necessarily
imply that X → Y → Z, e.g. in the case of a threshold
• a diagram is not like a single study, it’s more like a
synthesis, => the issue of generalisability
• a single diagram can be used to integrate multiple
datasets
• suitable both for qualitative and quantitative analysis
Diagrams and evidence
• a conjectural diagram can be formed from substantive
knowledge of a subject, as a basis for analysis
• diagrams evolve from conjectural to well-supported,
as evidence is accumulated
• it is crucial to specify the status of any particular
diagram – an analysis of the assumptions and
judgements that have been made, the degree of
uncertainty and the strength of evidence for the
structure of the diagram and for each of the links
(including those thought to be absent)
Causes of the causes of health
Underlying causes e.g. socioeconomic factors
Determinants (risk factors)
Health status (diseases etc)
Transport-related health problems
Safe
walking &
cycling
Distribution
of vehicle
emissions
Air
pollution
Respiratory
morbidity
& mortality
Physical
activity
Traffic
volume
Community
severance
Cardiovascular
morbidity &
mortality
Access
Osteoporosis
etc
Traffic
speed
Noise
Impaired
mental
health
Collisions:
number,
severity
Fatal and nonfatal injuries
Altering the causes of the causes
Policy options
alterable causes
Changes in alterable risk factors
Changes in health status
Health impact of transport policies
Emissions
control
policies
Promotion
of active
transport
Traffic
reduction
policies
Speed
control
policies
 collisions:
 physical  community
 air
number,


severity
severance access noise
activity
pollution
 resp.
morbidity &
mortality
 cardiovascular  osteo-  impaired  fatal and
non-fatal
mental
porosis
morbidity &
injuries
health
etc
mortality
“Change” models: advantages
• Parsimony: the immense complexity of the
pathways can be greatly reduced by focusing on
changes, especially in the absence of effect
modification;
• Philosophy: causality is more readily grasped
when something is altered, e.g. a particular road
layout rather than “roads” as a necessary
condition of “road deaths”;
• Pragmatism: changes in the determinants of
health determinants link naturally to policy
options (cf Wanless: “natural experiments”).
Effect of the coal ban, Dublin, 1990
• before-after comparison of pollution
concentration, adjusted for weather etc
• 72 months before and after the ban
• also controls for influenza and age structure
• all-Ireland controls for secular changes
Speed control and health gain
Lower
speed limits
Better
enforcement
Traffic
calming
Public
education


access noise
 collisions:
number,
severity
Speed

 air
physical
pollution
activity
 community
severance
 resp.
 cardiovascular  osteo-  impaired  fatal and
morbidity &
morbidity &
porosis
mental
non-fatal
mortality
mortality
etc
health
injuries
Emissions control as a technical fix
Emissions
control
policies
 collisions:
 air
 physical  community
number,


pollution activity
severance access noise
severity
 resp.
 cardiovascular  osteo-  impaired  fatal and
morbidity &
morbidity &
porosis
mental
non-fatal
mortality
mortality
etc
health
injuries
Car dependence
community
severance
congestion
traffic growth
pro-bus policies
unpleasantness &
inconvenience of
non-car travel
reduction of
active transport
increased car ownership
vicious circle
of decline
reduction of
public transport
car dependence
affecting e.g.
shopping
increased prosperity
labor
productivity
health
status
nutritional
intake
land quantity & fertility
climate & weather
pests, e.g. fungi, rats
inputs, e.g. irrigation,
chemicals
tools & technology
health
status
micronutrient content
infant feeding practices
labor
productivity
nutritional
intake
exposure to infectious agents
contaminants e.g. aflatoxins
chemicals e.g. pesticides
war, natural catastrophe, etc
The SIR model of infections
β
ν
The SIR model of infections
β
ν
The basic reproductive number R0 is given by:
where β is the contact
rate (infectivity), and
ν is the recovery rate
(= 1/D where D is
duration)
The SIR model of infections
β
ν
The basic reproductive number R0 is given by:
where β is the contact
rate (infectivity), and
ν is the recovery rate
(= 1/D where D is
duration)
THANK YOU!