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