Epid 600 Class 4 Measures Of Association

EPID 600; Class 4 Measures of association University of Michigan School of Public Health

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Three key dimensions to epidemiologic studies Measures of association Relative measures (relative risks, rates, and odds) Absolute measures (risk and rate differences) Study design Observational Cohort Case-control Cross-sectional Experimental Randomized trial Field trials Group randomized trials Units of analysis Individual Group 2

Three key dimensions to epidemiologic studies Measures of association Relative measures (relative risks, rates, and odds) Absolute measures (risk and rate differences) Study design Observational Cohort Case-control Cross-sectional Experimental Randomized trial Field trials Group randomized trials Units of analysis Individual Group 3

Measurement of association Epidemiologic studies strive to determine the difference in measures of disease occurrence between populations Populations typically considered as “exposed” vs “unexposed” and measures of association then seek to define an association between “exposure” and disease “outcome” of interest Measures of association reflect statistical relations between variables, they are not measures of “effect” which are unobserveable counterfactual contrasts, but they are the best we can do 4

The world

persons “exposed”

persons “unexposed”

5

The epidemiologic study

persons “exposed”

persons “unexposed”

6

The epidemiologic study

persons “exposed” with disease

persons “unexposed” with disease

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Reminder...prevalence (proportion)

Number of cases Prevalence

= Number of persons in population

at a specified time

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Prevalence ratio

prevalence ratio =

prevalenceexp osed prevalenceun exp osed

Prevalence ratio is uncommonly used in epidemiology due to limitations of prevalence (including both incidence and duration of disease) discussed in 9 class 3

Reminder...risk (incidence proportion) The probability that a person will develop a given disease

Risk =

Number of new cases of disease Number of persons followed

over a time period

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Relative risk (risk ratio) The ratio of risks for two populations

RR =

Rexp osed Run exp osed

Ranges from 0 to +∞ , has no units

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Risk difference The additional risk among those exposed when compared to those unexposed

RD = Rexp osed − Run exp osed Ranges from -1 to +1, has no units

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Reminder...incidence rate

Number of new cases Incidence Rate = Total time at risk of persons followed

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Relative rate (incidence rate ratio) The ratio of rates for two populations

IRR =

IRexp osed IRun exp osed

Ranges from 0 to +∞ , has no units

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Rate difference The additional incidence rate comparing those exposed vs. those unexposed

IRD = IRexp osed − IRun exp osed Ranges from -∞ to +∞ , has unit of time-1

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GI infection: what are the causes? Bacterial gastrointestinal infections cause considerable morbidity even in industrialized countries We’ve figured out that certain microbes produce illness in certain people – but what beyond that? Who gets those microbes? What determines who gets symptomatic GI infection? We start by looking for associations between the illness and factors of interest

16 Simonsen, Frisch, and Ethelberg. Socioeconomic Risk Factors for Bacterial Grastrointestinal infections. Epidemiology. 2008; 19(2):282-290

GI infection and SES: an association? Little is known about socioeconomic factors affecting the risk of infection in industrialized settings A group in Denmark got curious… What did they do? Link 3 national registries and follow the entire population of Denmark (5.3 million people) from 1993 to 2004 to track GI infection 17 Simonsen, Frisch, and Ethelberg. Socioeconomic Risk Factors for Bacterial Grastrointestinal infections. Epidemiology. 2008; 19(2):282-290

GI infection and SES RESEARCH PROCESS Identify a cohort of interest Find information on each individual’s SES Obtain information on their disease patterns

DATA SOURCE Danish Civil Registration System Integrated Database for Longitudinal Labor Market Research

Create extended 2x2 tables and do an analysis

National Registry of Enteric Pathogens 18

Simonsen, Frisch, and Ethelberg. Socioeconomic Risk Factors for Bacterial Grastrointestinal infections. Epidemiology. 2008; 19(2):282-290

GI infection and SES

19 Simonsen, Frisch, and Ethelberg. Socioeconomic Risk Factors for Bacterial Grastrointestinal infections. Epidemiology. 2008; 19(2):282-290

GI infection and SES These data provide evidence that higher SES is associated with Campylobacter infection

Cases

Person years (1000s)

Adjusted risk ratio

<100,000

6487

13,490

0.93

100,000-199,000

9718

21,604

1.00

200,000-299,999

5507

11,051

1.10

300,000-399,999

1190

2165

1.28

>400,000

639

1068

1.51

Income

We compare the risk of each income bracket to the median bracket (the reference category)

Simonsen, Frisch, and Ethelberg. Socioeconomic Risk Factors for Bacterial Grastrointestinal infections. Epidemiology. 2008; 19(2):282-290

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Reminder...odds probability, or risk

p odds = 1− p

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Relative odds (odds ratio)

pexp osed OR =

oddsexp osed oddsun exp osed

1 − pexp osed = pun exp osed 1 − pun exp osed 22

Absolute vs. relative scales The two types of effect measures we have articulated here are on an absolute scale (i.e., subtraction) and on a relative scale (i.e., division) In epidemiology we may be interested in both Absolute differences tell us the increase (or decrease) in effect Relative differences tell us the relative increase or decrease in effect comparing one quantity to another

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Absence of an effect in the absolute scale If there is no effect on an absolute scale, the Risk Difference (RD), or the Rate Difference (IRD) are equal to 0 That is, there is no increased risk or increased rate of disease among exposed compared to unexposed Therefore, on an absolute scale, the “null” is 0

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The relative effect on a relative scale The relative effect is equivalent to the proportion change in absolute effect among exposed compared to unexposed (e.g., if original amount is x, and new amount is y, the proportion increase y−x is x

Risk difference Relative effect

= Risk in unexposed

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Therefore...

Relative = effect

Rexp osed − Run exp osed Run exp osed

=

Rexp osed Run exp osed

−

Run xp osed Run exp osed

= RR − 1

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Implications When we talk about greater population risk of a particular outcome among exposed compared to unexposed, we should be using RR-1, not RR Typically, we present RR So, if RR=3, relative effect=3-1=2 So, if RR=3 we say, there is a 200% increase in risk of disease among exposed compared to unexposed So, NO EFFECT is 0, i.e., RR-1=0, i.e., RR=1 RR=1 is then the “null”

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Key way to see through this All these formulas are related to one another in relatively simple ways that rest on understanding (not memorizing) what they mean and where they come from

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Reminder...risk and incidence rate Risk = Incidence rate x time....therefore...

RR =

Riskexp osed Riskun exp osed

=

Incidenceexp osed * time Incidenceun exp osed * time

=

Incidenceexp osed Incidenceun exp osed

= IRR

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Reminder...risk and incidence rate Risk = Incidence rate x time....therefore...

RR =

Riskexp osed Riskun exp osed

=

Incidenceexp osed * time Incidenceun exp osed * time

=

Incidenceexp osed Incidenceun exp osed

= IRR

if....time period is sufficiently comparable among exposed group and unexposed group; typically this is if the time period is short remember...we had said that R=IR*t when R is low therefore...RR is a reasonable approximation for IRR when both risk is low and when time period of observation is short

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Epidemiologic confusion Sometimes epidemiologists use the term “relative risk” to refer to either risk ratio or to incidence rate ratio assuming the two are equivalent This is obviously wrong; please do not do that

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The world

persons “exposed”

persons “unexposed”

32

The epidemiologic study

persons “exposed”

persons “unexposed”

33

The epidemiologic study

persons “exposed” with disease

persons “unexposed” with disease

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The “2x2” table

Disease

No disease

Total

Exposed

a

b

a+b

Not exposed

c

d

c+d

Total

a+c

b+d

a+b+c+d

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Relative risk, i.e., risk ratio

a Rexp osed = a+b c Run exp osed = c+d a RR = a + b c c+d 36

Relative odds, i.e., odds ratio a a a Pexp osed a a + b a + b a + b Oddsexp osed = = = = = a+b−a b 1 − Pexp osed 1 − a b a+b a+b a+b c c c Pune xp osed c c + d c + d c + d Oddsun xp osed = = = = = c+d −c d 1 − Pun xp osed 1 − c d c+d c+d c+d a Oddsexp osed a*d b OR = = = Oddsun exp osed c b * c d 37

Example In a particular study out of 100 exposed persons, 20 develop disease; out of 200 unexposed, 25 develop disease

Disease

No disease

Total

Exposed

a

b

a+b

Not exposed

c

d

c+d

Total

a+c

b+d

a+b+c+d

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Example In a particular study out of 100 exposed persons, 20 develop disease; out of 200 unexposed, 25 develop disease

Disease

No disease

Total

Exposed

a

b

100

Not exposed

c

d

200

Total

a+c

b+d

300

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Example In a particular study out of 100 exposed persons, 20 develop disease; out of 200 unexposed, 25 develop disease

Disease

No disease

Total

Exposed

20

b

100

Not exposed

25

d

200

Total

45

b+d

300

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Example In a particular study out of 100 exposed persons, 20 develop disease; out of 200 unexposed, 25 develop disease

Disease

No disease

Total

Exposed

20

80

100

Not exposed

25

175

200

Total

45

255

300

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Example Disease

No disease

Total

Exposed

20

80

100

Not exposed

25

175

200

Total

45

255

300

20 RR = 100 = 1.60 25 200

20*175 OR = = 1.75 25*80 42

Going back to an example T1

T2

T3

T4

T5

T6

T7

T8

T9

T10

T11

T12

T13

T14

T15

T16

T17

T18

T19

T20

TT

P1

14

P2

20

P3

11

P4

11

P5

20

P6

20

P7

10

P8

20

P9

2

P10

9

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An example T1

T2

T3

T4

T5

T6

T7

T8

T9

T10

T11

T12

T13

T14

T15

T16

T17

T18

T19

T20

TT

P1

14

P2

20

P3

11

P4

11

P5

20

P6

20

P7

10

P8

20

P9

2

P10

9

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An example T1

T2

T3

T4

T5

T6

T7

T8

T9

T10

T11

T12

T13

T14

T15

T16

T17

T18

T19

T20

TT

P1

14

P2

20

P3

11

P4

11

P5

20

P6

20

P7

10

P8

20

P9

2

P10

10

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Cohort approach 2 2 IRexp osed (14 + 20 + 10 + 2) IRR = = = 46 = 4.0 1 1 IRun exp osed (20 + 11 + 11 + 20 + 20 + 10) 92 2 Rexp osed RR = = 4 = 3.0 Run exp osed 1 6 pexp 0.5

1 − pexp 2*5 1 − 0.5 OR = = = 5.0 also can be calculated as = 5.0 pun exp 0.167 1* 2 1 − pun exp 1 − 0.167 46

Notes As in this example, OR is greater than RR when OR and RR are > 1 OR approximates RR when disease is rare (<1% typically)

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Why? (first premise) a RR = a + b c c+d a a is always < a+b b c c is always < c+d d a a c a +b and if > 1, then, > , and c a+b c+d c+d

Disease

No disease

Total

Exposed

a

b

a+b

Not exposed

c

d

c+d

Total

a+c

b+d

a+b+c+d

a a b > a +b c c d c+d 48

Why? (second premise)

a a + b RR = c c+d

Disease

No disease

Total

Exposed

a

b

a+b

Not exposed

c

d

c+d

Total

a+c

b+d

a+b+c+d

if disease is rare, then a + b ≅ b and c + d ≅ d a a*d b therefore, RR ≅ ≅ ≅ OR c b*c d

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Some notes about terminology... For OR, RR, and IRR, if value is >1 typically we say that there is a “positive association”, 1 is no association, and < 1 is a “negative association” Of course, interpretation fully depends on what is “exposed” and what is “non-exposed” Remember...the “null” is 1 for relative measures of association and 0 for absolute measures; hence “away from” or “towards” the null

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The “2x2” table involving time

Disease

Time

Exposed

a

T1

Not exposed

c

To

Total

a+c

T1+To

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Incidence rate ratio

IRexp osed

a = T1

IRun exp osed

c = T0

a T1 IRR = c T0 52

Example In a particular study 20 smokers out of 10,000 PY of exposure developed heart disease and 25 nonsmokers out of 20,000 PY of follow-up develop heart disease

Disease

Time

Exposed

a

T1

Not Exposed

c

To

Total

a+c

T1+To

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Example In a particular study 20 smokers out of 10,000 PY of exposure developed heart disease and 25 nonsmokers out of 20,000 PY of follow-up develop heart disease

Disease

Time

Exposed

20

10,000

Not Exposed

25

20,000

Total

45

30,000

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Example Disease

Time

Exposed

20

10,000

Not Exposed

25

20,000

Total

45

30,000

20 10, 000 IRR = = 1.6 25 20, 000

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Attributable fraction among exposed

Proportion of the disease burden among exposed people that is due to the exposure

AFexposed =

R exposed -R unexposed R exposed

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And...

AFexposed =

R exposed -R unexposed R exposed

R exposed R unexposed 1 RR-1 = =1= R exposed R exposed RR RR

so....if RD is the R among exposed when subtracting R among unexposed, then dividing RD by R among exposed gives the proportion of effect among exposed that is due to exposure this is often interpreted as the proportion of disease cases among exposed that would be removed if there were no longer any exposure note, that among exposed, we do NOT remove ALL of effect, even if exposure is not longer there WHY?....clearly “exposure” is not the only cause 57

Attributable fraction in population Proportion of the disease burden among the whole population that is due to the exposure

AFpopulation =

R population -R unexposed R population

so....if subtracting the R among unexposed from overall population R gives us the effect, then dividing this by R among population gives the proportion of effect among population that is due to exposure this is often interpreted as the proportion of disease cases in the population that would be removed if there were no longer any exposure

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And...

p*(RR-1) AFpopulation = p*(RR-1)+1 where p is the prevalence of exposure in the whole population so...if the population attributable fraction is 20%, then if exposure is removed, we would expect that disease would be reduced by 20% in the population

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