Measures of Association

Dambi Dollo University

Learning Objectives
 List common measures of association and
measures of public health impact
 Define, calculate and interpret relative risk and
odds ratio and describe their use
 Calculate and interpret attributable risk
percent and population attributable risk
 Outline the advantages and disadvantages of
each of the different measures.

2 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

 Exposure
 Exposure in usual sense,
 E.g. Ingestion of contaminated food
 E.g. Droplets from someone with active
pulmonary tuberculosis
 Behaviors
 E.g. Sharing needles, drinking alcohol, etc
 Treatment
 E.g. Intervention , education program
 Trait
 E.g. Genotype
3 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024
 Outcome
 Disease
 E.g. Malaria, TB
 E.g. Diabetes
 Event
 E.g. Injury from land mine, car accident
 Condition
 E.g. Blindness
 Death
 Other
4 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024
 Why? (Cont…)

Exposure Outcome

 Is there a relationship between the

exposure and outcome of interest?

5 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

 Description of Relationships

 Variables can be related or unrelated to

one another.

 If related, variables can be

 positively or negatively related
 strongly or weakly related (one variable can
have large or small effect on the other)
 significantly or not significantly related

6 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

 Relationships between variables: Related or unrelated?

10

2.00
8

Dependent variable
1.50 6
Dependent variable

4
1.00

2
0.50
0

0.00
0.00 20.00 40.00 60.00
0.00 0.20 0.40 0.60 0.80 1.00 1.20
Independent Variable
Independent variable

Related unrelated

7 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Relationships between variables — Positive
and negative association?
.

10 10

Y Y

0 0

0 X 1 0 X 1

Positive Negative

8 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Relationships between variables —Large or
small effect?
.

10 10

Y Y

0 0

0 X 1 0 X 1

Small
Large

9 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

 Association

 Statistical relationship between two or

more variables.

 Probability of occurrence of an outcome

depends on,
 Presence of one or more characteristics
 Occurrence of one or more events
 Quantity of one or more other variables

10 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

 Measures of Association

 Epidemiologic Measure of Association

 Quantifies or expresses the strength of the
relationship between an "exposure" and
“outcome” of interest
 Quantifies the difference in occurrence of
disease or death between two groups of people
who differ on "exposure“

11 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Cont…

 Types of measures of association:

 Relative Risk (RR) or Risk Ratio,
 Odds Ratio (OR) or Cross Product Ratio,
 Attributable Risk (AR),
 Attributable Risk Percent (AR%)
 Population Attributable Risk (PAR)
 Population Attributable Risk Percent (PAR%)

12 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Standard Two-by-Two Table/Contingency
Table
Disease
Yes No Total
Exposure a b
Yes a+b

No c d c+d
Total a+c b+d a+b+c+d
2X2 (Cont…)
 The Two-by-Two Table is useful in calculating
the basic measures:
 Risk in Exposed
 Risk in Unexposed
 Relative Risk (RR)
 Odds of Exposure
 Odds Ratio (OR)
 Attributable Risk (AR)

14 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Risk
 It is a measure of probability of getting a
disease.

• It is also anonymously called:

– “Attack Rate”
– Risk of Disease
– Cumulative Incidence
– Incidence Proportion

15 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

1. Relative risk (Risk ratio)
 Indicate the likelihood of developing the
disease in the exposed group relative to
those who are not exposed
 For a cohort study with count data

RR== = Re / Ro

 It is a direct measurement of a risk

 It is usually used in Cohort and Experimental
study design
Relative Risk: Example (Cohort Study)
 Example: Birth Cohort….

Number
Maternal Number IMR per Risk
of
Education of Deaths 1,000 Ratio
Infants

Illiterate 5,021 579

Literate
1,368 99
(Formal)

17 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Example: Cohort Study (Cont…)
 Example: Birth Cohort.

Number
Maternal Number IMR per Risk
of
Education of Deaths 1,000 Ratio
Infants

Illiterate 5,021 579 115.3

Literate
1,368 99 72.4
(Formal)

18 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Example: Cohort Study (Cont…)
 Example: Birth Cohort.

Number
Maternal Number IMR per Risk
of
Education of Deaths 1,000 Ratio
Infants

Illiterate 5,021 579 115.3 1.59

Literate
1,368 99 72.4 1.00
(Formal)

19 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Example: Cohort Study 2X2 Table
.
Outcome (Death)
Total
Infant Infant
s s
Died Alive
Illiterate 579 4,442 5,021
Mother’
s Literate 99 1,269 1,368
Educatio
n
Illiterate mothers would be
Total 678 5,711
1.59 times as 6,389likely as
literate mothers to have
their infants died.

20 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Relative Risk: Example (Cohort Study)
Example: Birth Cohort

ANC Numbe Number IMR per Risk

r of of 1000 Ratio
Attendanc Infants
e deaths

Yes 4262 354

No 4011 493

21 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Example: Cohort Study (Cont…)
 Example: Birth Cohort

ANC Numbe Number IMR per Risk

r of of 1000 Ratio
Attendanc Infants
e deaths

Yes 4262 354 83.1

No 4011 493 122.9

22 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Example: Cohort Study (Cont…)
 Example: Birth Cohort

Number
ANC Number IMR per Risk Ratio
of
Attendance of Deaths 1000
Infants

Yes 4262 354 83.1 1.00

No 4011 493 122.9 1.48

23 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

2) Odds ratio
 In case control and cross sectional studies RR can be
estimated by calculating the ratio of the odds of
exposure among the cases to that among the controls
 odds – the ratio of the probability of occurrence of an
event to that of nonoccurrence
 OR indicates the likelihood of having been exposed
among cases relative to controls
Odds ratio=
or
Odds ratio=
Odds ratio…
 In 2X2 table:
 Odds of disease among exposed group=

 Odds of disease among non exposed =

 Odds of exposure among disease group =

 Odds of exposure among non diseased group =

Exposure Odds Ratio= Odds Ratio=

Disease Odds Ratio=
Odds Ratio: Example
 Example: Women’s Health & Life Events

Physical Poor Good Odds

Violence Health Health Ratio

Yes 677 424

No 566 594

26 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Example:….
 Example: Women’s Health & Life Events

Physica Poor Good Odds

l Healt Healt
Violenc h h Rati
e o
Yes 677 424 1.68

No 566 that Poor

594The odds 1.00 Health
because of physical
violence was
1.68 as compared to Good
Health. 30

27 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Example 2
• A case control study was conducted on 200 cases
of heart disease and 400 controls to determine
whether heart disease is associated with smoking
status. The results are shown in the table below

CHD
Total
Yes No
Smoking
Yes a=112 b=176 288
No c=88 d=224 312

Total ad 112 x 224 Interpretation:

200 400the odds of having CHD is
600
OR   1.62 1.6 times high among smokers compared to
bc 176 x88
that of the non smoker
Example 3
Table 3: Data from a case-control study of current oral
contraceptive (OC) use and MI in pre-menopausal female nurses

Myocardial infarction
Yes No Total
Current OC use
Yes 23 304 327
No 133 2816 2949
Total 156 3120 3276

 OR = = = 1.6
 women who were current OC users had a risk of
MI 1.6 times that of nonusers
Attributable Risk (AR)
• AR indicates the number of cases of the
disease among the exposed that can be
attributed to the exposure itself.
 It is the incidence of a disease in the
exposed that would be eliminated if
exposure were eliminated.
• AR measures public health impact.

 AR = Risk in Exposed – Risk in Unexposed

30 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

AR: Example
. There is 14-fold
Annual Death Rates Per 100,000 increase death
rate from lung
Coronar cancer among
Smoking Lung
y Heart heavy smokers
Cancer
Disease compared to non-
smokers.
The RR of CHD
Heavy 140 669 mortality among
Smokers heavy smokers
compared to non-
Non-smokers 10 413 smokers was 1.6.

Relative Risk 14 1.6

31 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

AR: Example …
.
Annual Death Rates Per 100,000 The AR of Lung
Cancer and CHD
Smoking Lung CHD are 130/105/Year &
Cance 256/105/Year
r respectively
Heavy 140 669 Therefore, if
smoking is causally
Smoke related to both
rs diseases, the
elimination of
Non-smokers 10 413 smoking would
Relative prevent far more
14 1.6 deaths among
Risk smokers from CHD
(RR) than from lung
Attributab
32 BY Wakgari M (BSc, MPH in Epid) cancer.
Oct 9, 2024
130/105/Year 256/105/
Attributable Risk Percent (AR%)
 AR% estimates the proportion of diseases
among the exposed that is attributable to
the exposure, or the proportion of the
disease that could be
prevented by
eliminating the exposure among the
exposed.
 AR% measures public health impact of an
exposure.

33 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

AR%: Example
. 10 Year
Enrolled Died
Follow-up
About half
Diabetics 189 100 (51.4%) of the
Non- deaths among
3,151 811
Diabetics diabetic
Total 3,340 2,429 patients may
be attributed
to their
diabetes.

34 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Population Attributable Risk (PAR)
 PAR estimates the excess rate of disease in
the total population that is attributable to
the exposure.
 PAR = Risk in Population – Risk in Unexposed
PAR=AR*Proportion of Exposed in Population

 PAR helps in determining exposure relevant

to public health in a community.

35 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Population Attributable Risk Percent (PAR
%)
 PAR% estimates the proportion of disease in
the study population that is attributable to
the exposure among the general population
and thus could be eliminated if the exposure
were eliminated.
 PAR% measures public health impact of an
exposure.

36 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Interpretation of Measures of
Association
 RR/OR=1 No Association

 RR/OR>1 Exposure is Risk (Positive Association)

 RR/OR<1(Fraction) Exposure is Preventive (Negative

Association)

 AR/PAR=0 No Attribution

 AR/PAR>0 Exposure is Attributing

 AR/PAR<0 (Negative) Exposure is Not

Attributing
37 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024
Summary of Measures
. Gastroenteritis
Total Risk
Ill Not ill

Yes 53 28 81
Ate
Beef No 4 31 35

Total 57 59 116

38

38 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024

Thank you

39 BY Wakgari M (BSc, MPH in Epid) Oct 9, 2024