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

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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

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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

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The world

persons “exposed” persons “unexposed”

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The epidemiologic study


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persons “exposed” with disease persons “unexposed” with disease

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Prevalence = Number of cases

Number of persons in population

at a specified time

Reminder...prevalence (proportion)

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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 class 3 9

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

exp

exp

osed

un osed

RRR

R=

Ranges from 0 to +∞ , has no units

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Risk difference

exp exposed un osedRD R R= −

Ranges from -1 to +1, has no units

The additional risk among those exposed when compared to those unexposed

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Reminder...incidence rate

Incidence Rate = Number of new cases

Total time at risk of persons followed

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Relative rate (incidence rate ratio)

The ratio of rates for two populations

exp

exp

osed

un osed

IRIRR

IR=

Ranges from 0 to +∞ , has no units

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Rate difference

The additional incidence rate comparing those exposed vs. those unexposed

exp exposed un osedIRD IR IR= −

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

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

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


GI infection and SES

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

Danish Civil Registration

System

Integrated Database for Longitudinal Labor Market

Research

National Registry of Enteric

Pathogens

Identify a cohort of interest

Find information on

each individual’s

SES

Obtain information on their disease

patterns

Create extended 2x2 tables and do an analysis

DATA SOURCE

RESEARCH PROCESS

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Income

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

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

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


Reminder...odds

1poddsp

=−

probability, or risk

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Relative odds (odds ratio)

exp

exp exp

expexp

exp

1

1

osed

osed osed

un osedun osed

un osed

podds p

OR poddsp

−= =

−

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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 is y x

x−

Relative effect = Risk difference

Risk in unexposed

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Therefore...

exp exp exp xp

exp exp exp

1osed un osed osed un osed

un osed un osed un osed

R R R RRR

R R R−

= = − = −Relative effect

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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...

exp exp exp

exp exp exp

**

osed osed osed


Risk Incidence time IncidenceRR IRR

Risk Incidence time Incidence= = = =

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Reminder...risk and incidence rate

Risk = Incidence rate x time....therefore...

exp exp exp

exp exp exp

**

osed osed osed


Risk Incidence time IncidenceRR IRR

Risk Incidence time Incidence= = = =

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


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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

exp

exp

osed

un osed

aRa bcRc d

aa bRR cc d

=+

=+

+=

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Relative odds, i.e., odds ratio

expexp

exp

xpxp

xp

exp

exp

1 1

1 1

**

osedosed

osed

une osedun osed

un osed

osed

un osed

a a aP aa b a b a bOdds a a b a bP b

a b a b a bc c c

P cc d c d c dOdds c c d c dP dc d c d c d

aOdds a dbOR cOdds 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


Exposed a b a+b

Not exposed c d c+d


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Example



Exposed a b 100

Not exposed c d 200

Total a+c b+d 300

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Example



Exposed 20 b 100

Not exposed 25 d 200

Total 45 b+d 300

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Example



Exposed 20 80 100

Not exposed 25 175 200

Total 45 255 300

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Example

20100 1.6025200

RR = =


Exposed 20 80 100

Not exposed 25 175 200

Total 45 255 300

20*175 1.7525*80

OR = =

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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


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


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

exp

exp

exp

exp

exp

exp

exp

exp

2 2(14 20 10 2) 46 4.01 1

(20 11 11 20 20 10) 9224 3.016

0.51 2*51 0.5 5.0 5.00.167 1*2

1 0.1671

osed

un osed

osed

un osed

un

un

IRIRR

IR

RRR

R

pp

OR also can be calculated as pp

+ + += = = =

+ + + + +

= = =

− −= = = =

−−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)


Exposed a b a+b

Not exposed c d c+d


1, , ,

aa b RR cc d

a a is always a b bc c is always <

c+d da a a

a ca+b b a+band if then and >c c ca b c dc+d d c+d

+=

+

<+

> >+ +

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Why? (second premise)


Exposed a b a+b

Not exposed c d c+d


aa b RR cc d

+=

+

,

*,*

if disease is rare then a b b and c d da

a dbtherefore RR ORc b cd

+ ≅ + ≅

≅ ≅ ≅

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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

exp1

exp0

1

0

osed

un osed

aIRTcIRT

aTIRR cT

=

=

=

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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 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

2010,000 1.62520,000

IRR = =

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Attributable fraction among exposed

AFexposed =

Rexposed -Runexposed

Rexposed

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

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And...

AFexposed =

Rexposed -Runexposed

Rexposed

=Rexposed

R exposed

-Runexposed

Rexposed

=1-1

RR=

RR-1RR

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

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Attributable fraction in population

AFpopulation =

Rpopulation -Runexposed

Rpopulation

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

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...

AFpopulation =

p*(RR-1)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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Epid 600 Class 4 Measures of Association

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