the practical uses of causal diagrams michael joffe imperial college london
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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
from Hernán, MA, Hernández-Díaz S, Robins, JM. A structural approach to selection bias. Epidemiology 2004; 15(5): 615-25
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”)
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
X
X
X
Y
Y
Y
Y
C
C
causation
reverse causation
common ancestor(confounding)
common descendant(Berkson bias)
The SIR model of infections
β ν
• 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?
Modelling the whole system I
Transport-related health problems
Respiratory morbidity
& mortality
Cardiovascular morbidity &
mortality
Impaired mental health
Fatal and non-fatal injuries
Osteo-porosis
etc
Air pollution
Physical activity Access
Community severance Noise
Collisions: number, severity
Traffic speed
Traffic volume
Distribution of vehicle emissions
Safe walking &
cycling
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
• 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 Y
diagram adapted from Best, Richardson & Jackson
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)
Conditional independence provides mathematical basis for splitting up large system into smaller components
D
EB
CA
F
CA
C
B
D
E
D
E
F
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
Respiratory morbidity
& mortality
Cardiovascular morbidity &
mortality
Impaired mental health
Fatal and non-fatal injuries
Osteo-porosis
etc
Air pollution
Physical activity Access
Community severance Noise
Collisions: number, severity
Traffic speed
Traffic volume
Distribution of vehicle emissions
Safe walking &
cycling
Altering the causes of the causes
Policy options alterable causes
Changes in alterable risk factors
Changes in health status
Health impact of transport policies
resp. morbidity &
mortality
cardiovascular morbidity &
mortality
impaired mental health
fatal and non-fatal injuries
osteo-porosis
etc
air pollution
physical activity
access
community severance
noise
collisions: number, severity
Speed control policies
Traffic reduction policies
Emissions control policies
Promotion of active transport
“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
resp. morbidity &
mortality
cardiovascular morbidity &
mortality
impaired mental health
fatal and non-fatal injuries
osteo-porosis
etc
air pollution
physical activity
access
community severance
noise
collisions: number, severity
Lower speed limits
Better enforcement
Traffic calming
Public education
Speed
Emissions control as a technical fix
resp. morbidity &
mortality
cardiovascular morbidity &
mortality
impaired mental health
fatal and non-fatal injuries
osteo-porosis
etc
air pollution
physical activity
access
community severance
noise
collisions: number, severity
Emissions control policies
Car dependence
reduction of active transport
traffic growth
community severance
unpleasantness & inconvenience of
non-car travel
increased car ownership
reduction of public transport
congestion
increased prosperity
vicious circle of decline
car dependence affecting e.g.
shopping
pro-bus policies
labor productivity
nutritional intake
healthstatus
labor productivity
nutritional intake
healthstatus
exposure to infectious agents contaminants e.g. aflatoxins chemicals e.g. pesticideswar, natural catastrophe, etc
micronutrient contentinfant feeding practices
land quantity & fertilityclimate & weatherpests, e.g. fungi, ratsinputs, e.g. irrigation,
chemicalstools & technology
The SIR model of infections
β ν
The SIR model of infections
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)
β ν
The SIR model of infections
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)
β ν
THANK YOU!
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