Measures of Association and Impact

Measures of Associationand Impact

Michael O’Reilly, MD, MPH

FETP Thailand

Introductory Course

Objectives

• Describe and calculate measures ofassociation such as risk ratio and oddsratio, and describe when use each

• Describe and calculate measures ofpublic health impact such asattributable risk percent and populationattributable risk percent

Example for calculations: NHANES follow-up study

Original enrollment 1971 – 1975

Follow-up 1982 – 1984

• Complete follow-up on:- 189 diabetic men- 3151 nondiabetic men- 218 diabetic women- 3823 nondiabetic women

Participants aged 40-77 years at enrollment

Ref: Kleinman J, et al. Mortality among diabetics in anational sample. AJE 1988; 128:389-401

Risk

# new cases during a specified periodsize of population at start of period

= "Attack rate"= Probability of getting disease= Risk of disease= Cumulative incidence= Incidence proportion

Example of Risk Calculation

1.Deaths in diabetic men

100 deaths189 men at start of follow-up period

2. Deaths in nondiabetic men



1.Deaths in diabetic men


Risk = 100/189 = 52.9%


2. Deaths in nondiabetic men


Risk = 811/3151 = 25.7%

Person-Time Rate# new cases during follow-up period

# person-years of follow-up

new cases during follow-up periodsum of the lengths of time each member of the population was at risk of disease

= instantaneous incidence rate= Incidence density= "Person-time rate"

Denominator of P-T Rate

In a cohort (follow-up) study, follow each person until:

• Onset of disease • Death • Loss to follow-up • End of studyAdd up the time each person was

followed

P-T Rate – Example

Deaths in diabetic menIf all enrolled in 1971, and if no deaths, and if all had

been followed through 1984, denominator is: 189 × 13 = 2457 Person Years

But some were enrolled 1972 - 1975, 100 died, & some were followed to 1982 or 1983. True denominator is:

1414.7 Person Years

Rate = 100 / 1414.7 PY= 70.7 deaths / 1,000 PY

(False rate 40.7 deaths/ 1,000 PY)

Odds

Odds in favor of an event =

probability that event will occur

probability that event will NOT occur

Odds of disease =

probability of disease

1 - probability of disease

or, more simply,

disease odds = # ill / # well

Example of an Odds Calculation

Deaths in diabetic men100 deaths189 men at start of follow-up periodProbability of death = 100/189 = 52.9%Odds = probability of dying / probability of not

dying= 0.529 / (1 - 0.529) = 0.529 / 0.471= 1.1:1Odds = # deaths / # survivors= 100 / 89= 1.1:1

Example of an Odds Calculation

Odds of diabetes among men who died100 deaths among diabetics811 deaths among non-diabeticsProb. of diabetes = 100 / 911 = 0.110 =

11.0%

ODDS = prob. of diabetes / prob. of non-diabetes

= 0.110 / (1 - 0.110) = 0.110 / 0.890= 1.23:1

"Every epidemiologic studycan be summarized in a 2-by-2 table."

- H. Ory

Two-by-Two Tables

Ill Well Total Risk

Exposed a b H1 a/H1

Not exp c d H2 c/H2

Total V1 V2 T or N

Mortality Among White Men, by Diabetic Status,

NHANES Follow-up Study, 1982-1984

Dead Alive Total Risk

Diabetic 100 89 189 52.9%

Not 811 2340 3151 25.7%

diabetic

Total 911 2429 3340 27.3%

Measures of Association

Quantify the relationship between an"exposure" and outcome of interest

Quantify the difference in occurrence of disease or death between two groups of people who differ on "exposure“

Types of measures:−Ratios: relative risk, rate ratio, odds ratio−Difference: attributable risk

Risk Ratio / Relative Risk

Risk in "exposed" groupRisk in "unexposed" group

EXAMPLE:Relative risk of death among diabetic men vs. nondiabetic men

RR: ?

Mortality Among White Men, by Diabetic Status,

NHANES Follow-up Study, 1982-1984

Dead Alive Total Risk

Diabetic 100 89 189 52.9%

Not 811 2340 3151 25.7%

diabetic

Total 911 2429 3340 27.3%



EXAMPLE:Relative risk of death among diabetic men vs. nondiabetic men

RR: 100/189 .257 811/3151 .529

= 2.1



EXAMPLE:Relative risk of illness for those who ate food A vs. those who did not eat food A

RR: ?


EXAMPLE:Relative risk of illness for those who ate food A vs. those who did not eat food A

RR:

.80

.14

= 5.7

Questions about Risk Ratio

Risk in "exposed" group

Risk in "unexposed" group

• What does RR > 1 mean?• What does RR = 1 mean?• What does RR < 1 mean?

Comments about Risk Ratio

• The further away from 1, the stronger the association between exposure and disease

• Can only calculate Risk Ratio from cohort study

Rate Ratio for P-T Rates

Person-time rate in "exposed" groupPT rate in "unexposed" group

Example:Death rate ratio among diabetic men vs. nondiabetic men

RR =100/1414.7 =70.7/1000 = 2.5 811/28,029.8 =28.9/1000

Comments about Rate Ratio

The further away from 1, the stronger the association between exposure and disease

Can only calculate Rate Ratio from follow-up cohort study

Odds Ratio: General

If you are not using cohort study data,

then relative risk is not obtainable

Under certain circumstances, odds ratios are good estimates of the relative risk

Odds Ratio

FORMULA 1 (“Disease Odds Ratio”):

Odds of disease/death in “exposed” groupOdds of dz/death in “unexposed” group

FORMULA 2 (“Exposure Odds Ratio”):

Odds of being "exposed" among casesOdds of "exposed" among non-cases

Disease Odds Ratio

Dead Alive Odds of disease

Diabetic 100 89 100/89

Not 811 2340 811/2340

Total 911 2429

Using formula 1:

OR 100/89 = 100 x 2340 = 3.2

811/2340 89 x 811

Exposure Odds Ratio

Dead Alive

Diabetic 100 89

Not 811 2340

Odds of 100/811 89/2340

Exposure

Using formula 2:

OR 100/811 = 100 x 2340 = 3.2

89/2340 89 x 811

When Can the Odds Ratio be used to approximate the Relative Risk?

Ill Well Total Risk

Exposed a b a + b a/a + b

Not exp c d c + d c/c + d

RR = a/a+b ≈ a/b ≈ ad

c/c+d c/d bc

For a rare disease, a <<< b, so a+b ≈ b c <<< d, so c+d ≈ d

Example of the “Rare Disease” Assumption?

Ill Well Total Risk

Exposed a b a + b a/a + b

Not exp c d c + d c/c + d

RR = a/a+b ≈ a/b ≈ ad

c/c+d c/d bc

For a rare disease, a <<< b, so a+b ≈ b c <<< d, so c+d ≈ d

Measures of Association and Impact

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