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Epidemiological concepts
PhD-course in epidemiology
Lau Caspar Thygesen
Associate professor, PhD
18th February 2014
Agenda
• Measures of frequency and association
• Confounding vs. interaction vs. intermediate variable
• Choosing study design
• Causality
Epidemiological measures
• Measures of disease frequency
• Measures of association
• Measures of potential impact
Measures of disease frequency
• Incidence
• Cumulative incidence (CIP)
• Incidence proportion
• Risk
• Incidence rate (IR)
• Incidence density
• Person-time incidence
• CIP can be calculated from IR
• Prevalence
• Point prevalence (prevalence proportion)
• Period prevalence
Exposure-outcome table
Outcome
Yes No P-years
Exposure Yes a b RT1 a+b
No c d RT0 c+d
a+c b+d RT
Relationship between prevalence and incidence
• Prevalence depends on incidence and disease duration
• Inflow: Incidence
• Outflow: Cure and mortality
• Assumptions: – No change in incidence over time
– No change in duration over time
– No change in age structure
Example
• IR=0.001/p-years
• dur=5 years
• Prevalence = 0.001*5/(1+0.001*5) = 0.5%
• IR=0.001/p-years
• dur=10 years
• Prevalence = 0.001*10/(1+0.001*10) = 1.0%
Measures of association
• Relative measures
• Relative risk / risk ratio (RR)
• Relative incidence rate (incidence rate ratio - IRR)
• Odds ratio (OR)
• Prevalence ratio
• Absolute measures
• Risk difference (RD)
• Incidence rate difference (IRD)
• Number needed to treat (= 1 / RD)
Measures of potential impact
• Impact of exposure removal on exposed
• Attributable risk (AR)
• Attributable risk percent (AR%)
• (Excess risk / etiologic fraction among the exposed / relative risk reduction / attributable fraction (exposed))
• Impact of exposure removal on population
• Population attributable risk (PAR)
• Population attributable risk percent (PAR%)
• (Attributable fraction (population))
• Only for causal associations!
Attributable risk
• Risk among exposed = 5.1%
• Risk among non-exposed = 2.5%
• Risk difference = 5.1% - 2.5% = 2.6%
• Risk ratio = 5.1% / 2.5% = 2.04
• AR = risk difference (RD)
• AR% = RD / risk(exposed) = 2.6% / 5.1% = 51%
Population attributable risk
• PAR
= N(cases because of exposure) / N(all cases)
= CIP – CIP0
• PAR%
= (CIP – CIP0) / CIP * 100
= Pr(exp)*(RR-1) / (Pr(exp)*(RR-1) + 1) * 100
Population attributable risk
• Cum incidence exposed = 10.6 per 1000
• Cum incidence non-exposed = 3.4 per 1000
• Cum incidence in population = 5.8 per 1000
• Pr(exposure) = 32.5%
• AR = 10.6 – 3.4 = 7.2 per 1000
• RR = 10.6 / 3.4 = 3.1
• PAR = 5.8 – 3.4 = 2.4 per 1000
• PAR% = 2.4 / 5.8 = 41%
• PAR%(2) = .325*(3.1-1) / (.325*(3.1-1) + 1) = 41%
Cot death
• RR(sleep on stomach) = 5
• Pr(sleep on stomach) = 50%
• PAR% = 0.5*(5-1) / (0.5*(5-1)+1) = 2/3
• Today this exposure is less important because
fewer babies are exposed
Smoking and heart disease
Risk(exp) = 0.06
Risk(non-exp) = 0.03
Pr(exp) = 0.5
AR% = ?
PAR% = ?
RR
1
2
50 % 50 %
Non-smoker Smoker
Which situation is worst?
50 % 50 %
1,0
1,3
RR
95 % 5 %
1,0
4,0
RR
Many exposed
Low RR
PAR%=13%
Few exposed
High RR
PAR%=13%
Etiologic fractions of mortality in Denmark
Juel. Ugeskr Læger 2001;163:4190-95.
1993 - 1997
Males Females
Tobacco
Alcohol
Drugs
22.8 % 16.5 %
6.3 % 2.5 %
1.2 % 0.7 %
How do you add PAR%?
Example
Factor a: PAR% = 50%
Factor b: PAR% = 50%
Factor c: PAR% = 50%
The formula
• PAR%total= 1 - (1-PAR%a)*(1-PAR%b)*(1-PAR%c)
= 1 – 0.5 * 0.5 * 0.5
= 87.5%
• Even in this situation 12.5% will not be
preventable
More than 100%?
• The sum of PAR%s can be more than 100%
• PAR%(1) + PAR%(2)+…….+PAR%(n) à ∞
• PAR%(1+2+3…….n)= 100 %
Introduce a third variable
Mediator
Confounder
Effectmodifier
Exposure Outcome
?
21
Confounding
• When an observed association can be partly or
completely explained by different distributions
of other risk factors between exposed and non-
exposed
• The classic three conditions
• Confounder should be associated with exposure
• An independent risk factor for the outcome
• Not be a mediator between exposure and outcome 22
Confounding
Exposure Outcome
Confounder
Confounding: example
Drinker
Non-drinker
100
200
Lung cancer
No lung cancer
50
50
50
150
50 1503.0
50 50OR
´= =
´
Confounding: Is smoking a confounder?
Smoker
Non-
smoker
100
200
Drinker Non-
drinker
60
40
40
160
Smoker
Non-
smoker
100
200
Lung
cancer
No lung
cancer
75 25
25
175
OR=60x160/(40x40) = 6 OR=75x175/(25x25) = 21
Confounding: example
Drinker
Non-
drinker
75
25
Lung
cancer
No lung
cancer
45
15
30
10
45 101.0
15 30sOR
´= =
´
Drinker
Non-
drinker
25
175
Lung
cancer
No lung
cancer
5
35
20
140
5 1401.0
35 20n sOR
´= =
´
Smokers Non-smokers
Confounding: example
Drinking Lung cancer X
Smoking
• Drinking is not associated with lung caner
• Smoking is a confounder
Control of confounders
1. Confounder control in design phase
1. Randomization
2. Restriction
3. Matching
2. Confounder control in analysis phase
1. Standardization
2. Stratification
3. Multivariate analysis
Residual confounding
• Broad confounder categories
– Smoker/non-smoker
Introduce a third variable
Mediator
Confounder
Effectmodifier
Exposure Outcome
?
Effectmodification
• When the association between exposure and outcome varies with
respect to a third variable
• When effectmodification is observed it is incorrect to report only
one estimate – stratum specific estimates should be reported
• aka ’interaction’
Risk of oral cavity and pharynx cancer by alcohol
intake and smoking
0
20
40
60
80
100
120
140
160
0 1-13 14-28 >28
Genstande (per uge)
Kræ
ftti
lfæ
lde
(p
er
10
00
00
år) Ikke-ryger
Ryger
Effectmodification or interaction?
• The correct term is
”Effect-measure-modification”
• Effectmodification depends whether a absolute or relative association
measure is used (RD, IRD vs. RR, IRR)
Effectmodification
+ asbestos - asbestos
+ smoking 50 10
- smoking 5 1
Incidence rate of lung cancer (cases pr 100.000 person-years)
Interest in whether the effect of smoking on lung cancer depends
on asbestos exposure
Is there effectmodification?
Effectmodification
+ asbestos - asbestos
+ smoking 50 10
- smoking 5 1
Incidence rate of lung cancer (cases pr 100.000 person-years)
IRD+asbestos=50-5=45 IRR+asbestos=50/5=10
IRD-asbestos = 10-1= 9 IRR-asbestos=10/1=10
Effectmodification when calculating IRD but not when calculating IRR
Additive or multiplicative interaction
• Normally the ratio measure is used
• This means that interaction is measured on a multiplicative scale
• Additive scale interaction is often also of interst – public health
implications
Confounding
• Something we want to get rid off
• The association between exposure and
outcome is the same in all strata, when
stratifying on the confounder
• Mantel Haenzel can be used to adjust
• The weighted estimate will differ from
the crude estimate
Effectmodfication
• Interesting which can tell us something
about how causes co-work
• The association between exposure and
outcome varies between strata, when
stratifying on the confounder
• You cannot use Mantel Haenzel for
adjustment
• Stratified estimates should be presented
Interaction: example
Drinker
Non-drinker
100
200
Lung cancer
No lung cancer
50
50
50
150
50 1503.0
50 50OR
´= =
´
Interaction: example
Drinker
Non-
drinker
60
25
Lung
cancer
No lung
cancer
45
15
15
10
45 102.0
15 15sOR
´= =
´
Drinker
Non-
drinker
40
175
Lung
cancer
No lung
cancer
5
35
35
140
5 1400.57
35 35n sOR
´= =
´
Smokers Non-smokers
Introduce a third variable
Mediator
Confounder
Effectmodifier
Exposure Outcome
?
Mediator
• Mediation refers to intermediate variables on the causal pathway from exposure to outcome
• In observational epidemiology much energy spent on confounder control
• Intermediate variables are less considered
• Recently this area has come into focus in methodological research
Why interested in mediation?
• Strengthen evidence that the main effect is causal • Causal interpretation of observed association
• Less likely that main effect is caused by confounding
• Test of pathway-specific hypothesis • When primary interest is not exposure on outcome
• Focus on explaining an observed association that may be poorly understood
• Studying (inexpensive) surrogate outcomes • Precursor for chronic disease
• Prevention programs designed to change intermediate variables that prevent negative outcomes
Woodward (1999) – just one classic
• Definition of a confounder:
– Be related to the disease, but not be a consequence of the
disease.
– Be related to the risk factor, but not be a consequence of
the risk factor.
Woodward (1999): Not a confounder
”(…) smoking and fibrinogen are both risk
factors for CHD, but smoking promotes
increased fibrinogen. Controlling smoking
for fibrinogen would not be sensible
because this would mean controlling the
effect of smoking”
Epidemiologic textbooks
• Many textbooks do not deal with mediation
• Rothman et al (2002) give two examples:
Smoking
Heart disease
High blood pressure
Coffee Serum cholesterol
Rothman et al (2008)!
• Chapter on causal diagrams with intermediate variables
• Chapter on social epidemiology where effect decomposition
is presented
– Caution against comparing one model without the intermediate and one with the intermediate
Definitions
• Two pathways from exposure to outcome:
– Direct effect
– Indirect effect
• When we say direct effect we mean that the effect is direct relative
to measured variables.
Exposure
Intermediate
Outcome
Definitions
• Effects of exposure on outcome:
– Indirect effects: Exposure affects an intermediate variable which in
turn affects the outcome
– Direct effect: Effect of exposure are not through changes in the
intermediate
– Total effect: Effect of exposure on outcome
Total effect = direct effect + indirect effects
Example
• Petersen (2006): Air-pollution and children’s lung function
Use rescue
medication
Lung function Air pollution
Standard approach for estimating direct effects
• Multivariate regression models
– Estimate influence of exposure adjusted for intermediate
variable
– Termed the controlled direct effects (Petersen 2006)
Controlled direct effects
• Controlled direct effects
– The intermediate is fixed at one specific level
– The direct effects are defined as E(Yaz-Y0z), where Z = z
Controlled direct effects
• Could imagine separate direct effects for each level of
intermediate variable à Interaction
• (Therefore plural effects)
Natural direct effect
– E(YaZ0 -Y0Z0
)
– Defined as the effect of
an exposure on an
outcome, blocking only
the effect of the
exposure on the
intermediate
Natural direct effect
• Difference between outcome if exposed versus unexposed
where intermediate variable remained at level as under no
exposure
• Summary of direct effect in a population characterized by
intermediate at no exposure
When to use what?
• When exposure and intermediate interact, estimation of the controlled direct effects depends on the level at which the intermediate is fixed
• The natural direct effect provides a single summary of the direct effect
• NOTE: When exposure and mediator do not interact,
controlled and natural direct effects are equivalent
When to use what? (2)
• Natural direct effect may be of interest when the
intermediate should vary between individuals
• It may not be meaningful to fix the mediator at one level for
the general population
• à example
Example
• Petersen (2006): Example of air-pollution and children’s lung
function
Use rescue
medication
Lung function Air pollution
When to use what? (3)
• Controlled effects: If focus is to determine the exposure-
disease effect given an intervention that universally blocks
(assigns) the mediator
• May correspond to realistic and well-defined intervention
plans
Example
• Natural effect hard to implement experimental
Hypercholesterolemia
Cardiovascular disease Smoking
Main decision when estimating direct effects!
• What value is the intermediate variable allowed to have?
• the same value for all invididuals
or
• different values for each person conditioned on one specific
exposure level
Choosing study design
• Ecological study
• Cross-sectional study
• Case-control study
• Cohort study
• Randomized controlled trial
Causality
• If we observe an assocation, next question is
whether it reflects a causal relationship
• The ultimate goal of epidemiology
Epidemiological approaches
• Epidemiology is observational, unplanned and natural experiments
• Hierarchy of study designs – Clinical observations / case series
– Ecological study
– Cross-sectional study
– Case-control study
– Cohort study
– Randomised trial
Ecological study Epidemiological approaches
• Epidemiology is observational, unplanned and natural experiments
• Hierarchy of study designs – Clinical observations / case series
– Ecological study
– Cross-sectional study
– Case-control study
– Cohort study
– Randomised trial
Necessary / sufficient
• Necessary and sufficient
• Necessary, but not sufficient
• Sufficient but not necessary
• Neither sufficient nor necessary
Necessary / sufficient
• Necessary and sufficient
• Necessary, but not sufficient
• Sufficient but not necessary
• Neither sufficient nor necessary
Rothman’s pies
Three causal complexes
Each having 5 component causes
A is a necessary cause
Attributes of the causal pie
1. Completion of a sufficient cause is synonymous with occurrence (although not necessarily diagnosis) of disease
2. Component causes can act far apart in time
3. Presence of a causative exposure or the lack of a preventive exposure
4. Blocking the action of any component cause prevents the completion of the sufficient cause
Causal "guidelines" – Hill criteria (1965)
Strength of the association
Consistency
Specificity
Temporality
Biological gradient
Plausibility
Coherence
Experiment
Analogy
Causal "guidelines" – Hill criteria (1965)
Purpose: Guidelines to help determine if
associations are causal
Should not be used as rigid criteria to be
followed slavishly
Hill even stated that he did not intend for
these "viewpoints" to be used as “hard
and fast rules.”
Hill concludes…
“Here then are nine different viewpoints from all of which we should study association before we cry causation.... None of my nine viewpoints can bring indisputable evidence for or against the cause-and-effect hypothesis and none can be required as a sine qua non. What they can do, with greater or lesser strength, is to help us make up our minds on the fundamental question --is there any other way of explaining the set of facts before us, is there any other answer equally, or more, likely than cause and effect?”
• NOTE: Temporality is a sine qua non for causality
“without which it could not be”
Counterfactual model of causality
• When we are investigating causality, we are
interested in the individual counterfactual
outcome
• Observe the present outcome AND the
counterfactual outcome for the same
individual
• NOT POSSIBLE
Counterfactual model of causality
• Population counterfactual effect
• When we are interested to measure the effect of a particular cause, we measure the
– Observed amount of effect in a population who are exposed
– Imagine the amount of the effect which would have been observed, if the same population would not have been exposed to that cause, all other conditions remaining identical
– The difference of the two effect measures is the population effect due the cause we are interested in
Counterfactual model of causality
• The strength of randomized studies
– The two groups are identical
– Bias
• Perfect randomization
• Loss to follow-up (intention to treat)
• Also possible in observational studies
– Assumption of no unmeasured confounders!!
Three relationships
• If we observe an assocation, next question is whether it reflects a causal relationship
E O
B E C
O
E O