Chapter 3 discusses various epidemiologic measures, including disease frequency (incidence proportions, incidence rates, and prevalence), measures of association, and measures of potential impact. It outlines how these measures are calculated, their interpretations, and the distinction between absolute and relative comparisons in assessing health outcomes. Additionally, it includes examples and formulas to illustrate the assessment of risk associated with exposures in both cohort and open population settings.

1. (c) B. Gerstman 1
Epi Kept Simple
Chapter 3
Epidemiologic Measures

2. Outline
3.1 Measures of disease frequency
3.2 Measures of association
3.3 Measures of potential impact
3.4 Rate adjustment
mea·sure noun ˈme-zhər, ˈmā-
Definition of MEASURE
1b : the dimensions, capacity, or amount of something ascertained by
measuring

3. 3.1 Disease Frequency
• Incidence proportion
(risk)
• Incidence rate
(incidence density)
• Prevalence
(c) B. Gerstman Chapter 3 3
All are loosely called
“rates,” but only the
second is a true
mathematical rate

4. Types of Populations
We measure disease frequency in:
• Closed populations  “cohorts”
• Open populations
(c) B. Gerstman Chapter 3 4

5. Closed Population ≡ Cohort
(c) B. Gerstman Chapter 3
5
Cohort (Latin cohors,
meaning “enclosure”; also
the basic tactical unit of a
Roman legion
Epidemiologic cohort
≡ a group of
individuals followed
over time

6. Open Populations
• Inflow (immigration,
births)
• Outflow (emigration,
death)
• An open population
in “steady state”
(constant size and
age) is said to be
stationary
(c) B. Gerstman Chapter 3 6

7. Numerators & Denominators
• Most measures of disease
occurrence are ratios
• Ratios are composed of a
numerator and
denominator
• Numerator  case count
Incidence count  onsets only
Prevalence count  all cases
(c) B. Gerstman Chapter 3 7

8. Denominators
(c) B. Gerstman Chapter 3 8
Denominators  a
measure of
population size or
person-time*
* Person-time ≈ (no. of
people) × (time of
observation)

9. Incidence Proportion (IP)
• Synonyms: risk, cumulative incidence, attack
rate
• Interpretation: average risk
(c) B. Gerstman Chapter 3 9
IP =
no. of onsets during study interval
no. @ risk at beginning of study interval
Can be calculated in cohorts only
Requires follow-up of individuals

10. Example: Incidence
Proportion (Average Risk)
• Objective: estimate the average risk of uterine
cancer in a group
• Recruit 1000 women (cohort study)
• 100 had hysterectomies, leaving 900 at risk
• Follow the cohort for 10 years
• Observe 10 new uterine cancer cases
(c) B. Gerstman Chapter 3 10
women
900
women
10
risk
@
no.
onsets
of
no.
IP 

10-year average risk is .011 or 1.1%.
0111
.
0


11. Incidence Rate (IR)
• Synonyms: incidence density, person-time
rate
• Interpretation A: “Speed” at which events
occur in a population
• Interpretation B: When disease is rare:
rate per person-year ≈ one-year average risk
• Calculated differently in closed and open
populations
(c) B. Gerstman Chapter 3 11
risk
@
time
-
person
of
Sum
onsets
no.
IR 

12. (c) B. Gerstman 12
(c) B. Gerstman 12
Example
• Objective: estimate rate of uterine cancer
• Recruit cohort of 1000 women
• 100 had hysterectomies, leaving 900 at risk
• Follow at risk individuals for 10 years
• Observe 10 onsets of uterine cancer
time
-
person
onsets
of
no.
IR 
Rate is .00111 per year or 11.1 per 10,000 years
years
9000
10

years
10
women
900
women
10


year
.00111


13. (c) B. Gerstman 13
(c) B. Gerstman 13
Individual follow-up in a Cohort
years
50
years
25
onsets
2


IR =
onsets
person-time
å
= 0.0267 per PY = 2.67 per 100 PYs
years
75
onsets
2

PY = “person-year”
25 PYs
50 PYs

14. Incidence Rate, Open Population
(c) B. Gerstman Chapter 3 14
years
-
person
100,000
per
877

n
observatio
of
duration
size
population
Avg
onsets
IR


-1
year
deaths
008770
.
0

Example: 2,391,630 deaths in 1999 (one year)
Population size = 272,705,815
year
1
persons
5
272,705,81
deaths
2,391,630
IR



15. Prevalence
• Interpretation A: proportion with condition
• Interpretation B: probability a person
selected at random will have the condition
(c) B. Gerstman Chapter 3 15
people
of
no.
cases
new
and
old
no.
Prevalence 

16. Example: Prevalence of
hysterectomy
• Recruit 1000 women
• Ascertain: 100 had hysterectomies
(c) B. Gerstman Chapter 3 16
people
of
no.
cases
no.
Prevalence 
Prevalence is 10%
10
.
0

people
1000
people
100


17. Dynamics of Prevalence
Cistern Analogy
(c) B. Gerstman Chapter 3 17
Increase incidence  increase
inflow
Increase average duration of
disease  decreased outflow
Ways to increase prevalence

18. Relation Between Incidence and
Prevalence
duration)
(average
rate)
(incidence
prevalence 

(c) B. Gerstman Chapter 3 18
Example:
• Incidence rate = 0.01 / year
• Average duration of the illness = 2 years.
• Prevalence ≈ 0.01 / year × 2 years = 0.02
When disease rare & population stationary

19. Gerstman 19
3.2 Measures of
Assocation
• Exposure (E)  an explanatory factor
or potential health determinant; the
independent variable
• Disease (D)  the response or
health-related outcome; the dependent
variable
• Measure of association (syn.
measure of effect)  any statistic
that measures the effect on an
exposure on the occurrence of an
outcome

20. Gerstman Chapter 8 20
Arithmetic (αριθμός)
Comparisons
• Measures of association are
mathematical comparisons
• Mathematic comparisons can
be done in absolute terms or
relative terms
• Let us start with this ridiculously
simple example:
• I have $2
• You have $1
"For the things of this world
cannot be made known
without a knowledge of
mathematics."- Roger Bacon

21. Gerstman Chapter 8 21
Absolute Comparison
• In absolute terms, I
have $2 MINUS $1
= $1 more than you
• Note: the absolute
comparison was
made with
subtraction
It is as simple as that…

22. Gerstman Chapter 8 22
Relative Comparison
• Recall that I have $2
and you have $1.
• In relative terms,
I have $2 ÷ $1 = 2 times
as much as you
• Note: relative
comparison was made
by division

23. Gerstman Chapter 8 23
• Suppose, I am exposed to a risk
factor and have a 2% risk of
disease.
• You are not exposed and you
have a 1% risk of the disease.
Absolutes Comparisons
Applied to Risks
• In absolute terms, I have 2%
MINUS 1% = 1% greater risk of
the disease
• This is the risk difference

24. Gerstman Chapter 8 24
• In relative terms I have
2% ÷ 1% = 2 
twice your risk
• This is the relative risk
associated with the
exposure
Relative Comparisons
Applied to Risks

25. Gerstman Chapter 8 25
Terminology
For simplicity sake, the terms
“risk” and “rate” will be applied
to all incidence and prevalence
measures.

26. Gerstman Chapter 8 26
Rate or Risk Difference
Let RD represent the rate or risk difference
0
1 R
R
RD 

where
R1 ≡ the risk or rate in the exposed group
R0 ≡ the risk or rate in the non-exposed group
Interpretation: Excess risk associated with
the exposure in absolute terms

27. Gerstman Chapter 8 27
Rate or Risk Ratio
Let RR represent the rate or risk ratio
0
1
R
R
RR 
where
R1 ≡ the risk or rate in the exposed group
R0 ≡ the risk or rate in the non-exposed group
Interpretation: excess risk associated with
the exposure in relative terms.

28. Gerstman 28
Example
Fitness & Mortality (Blair et al., 1995)
• Is improved fitness associated
with decreased mortality?
• Exposure ≡ improved fitness
(1 = yes, 0 = no)
• Disease ≡ death
(1 = yes, 0 = no)
• Mortality rate, group 1:
R1 = 67.7 per 100,000 PYs
• Mortality rate, group 0:
R0 = 122.0 per 100,000 PYs

29. Gerstman 29
Fitness and Mortality: RD
0
1 R
R
RD 

The effect of improved fitness was to decrease
mortality by 54.4 per 100,000 person-years
What is the effect of improved fitness on mortality in
?
=
67.7
100,000 PYs
-
122.0
100,000 PYs
=
-54.4
100,000 PYs

30. Gerstman 30
Example
Relative Risk
0
1
R
R
RR 
What is the effect of improved fitness on mortality in
?
55
.
0

yrs
-
p
100,000
per
0
.
122
yrs
-
p
100,000
per
7
.
67

The effect of the improved fitness was to almost cut the rate
of death in half.

31. Gerstman Chapter 8 31
Designation of Exposure
• Switching the designation of
“exposure” does not materially
affect interpretations
• For example, if we had let
“exposure” refer to failure to
improve fitness
• RR = R1 / R0
= 122.0 / 67.7
= 1.80
(1.8 times or “almost twice
the rate”)

32. Gerstman Chapter 8 32
2-by-2 Table Format
Disease + Disease − Total
Exposure + A1 B1 N1
Exposure – A0 B0 N0
Total M1 M0 N
For person-time data: let N1 ≡ person-time in group 1 and N0 ≡
person-time in group 0, and ignore cells B1 and B0
1
1
1
N
A
R 
0
0
0
N
A
R 

33. Gerstman Chapter 8 33
Fitness Data, table format
Fitness
Improved?
Died Person-years
Yes 25 -- 4054
No 32 -- 2937
67
.
61
000
,
10
4054
25
1
1
1 



N
A
R
95
.
108
000
,
10
2937
32
0
0
0 



N
A
R
Rates per 10,000 person-years

34. Gerstman Chapter 8 34
Food borne Outbreak Example
Disease + Disease − Total
Exposure + 63 25 88
Exposure – 1 6 7
Total 64 31 95
7159
.
0
88
63
1
1
1 


N
A
R 1429
.
0
7
1
0
0
0 


N
A
R
Exposure ≡ eating a particular dish
Disease ≡ gastroenteritis

35. Gerstman Chapter 8 35
Food borne Outbreak Data
7
1
88
63
0
1


R
R
RR
1429
.
0
7159
.
0
 01
.
5

Exposed group had 5 times the risk
Disease + Disease − Total
Exposure + 63 25 88
Exposure – 1 6 7
Total 64 31 95

36. Gerstman Chapter 8 37
What do you do when you have
multiple levels of exposure?
Compare rates to least exposed “reference” group
LungCA Rate
(per 100,000 person-years)
RR
Non-smoker (0) 10 1.0 (ref.)
Light smoker (1) 52 5.2
Mod. smoker (2) 106 10.6
Heavy sm. (3) 224 22.4
2
.
5
0
1
2
5
0
1
1 


R
R
RR 6
.
10
0
1
106
0
2
2 


R
R
RR

37. Gerstman Chapter 8 38
The Odds Ratio
• When the disease is
rare, interpret the
same way you
interpret a RR
• e.g. an OR of 1
means the risks are
the same in the
exposed and
nonexposed groups
D+ D− Total
E+ A1 B1 N1
E− A0 B0 N0
Total M1 M0 N
0
1
0
1
0
0
1
1
A
B
B
A
B
A
B
A
OR 

“Cross-product ratio”
Similar to a RR, but based on odds rather than risks

38. Gerstman Chapter 8 39
Odds Ratio, Example
Milunsky et al, 1989, Table 4
NTD = Neural Tube Defect
NTD+ NTD−
Folic Acid+ 10 10,703
Folic Acid− 39 11,905
0
1
0
1
A
B
B
A
OR 
Exposed group had 0.29 times (about a quarter)
the risk of the nonexposed group
39
703
,
10
905
,
11
10


 29
.
0


39. Gerstman Chapter 8 40
Measures of Potential Impact
• These measures
predicted impact of
removing a hazardous
exposure from the
population
• Two types
– Attributable fraction in
exposed cases
– Attributable fraction in
the population as a
whole

40. Gerstman Chapter 8 41
Attributable Fraction
Exposed Cases (AFe)
RR
RR
AFe
1
:
formula
Equivalent


1
0
1
:
formula
al
Definition
R
R
R
AFe


Proportion of exposed cases averted with
elimination of the exposure

41. Gerstman Chapter 8 42
Example: AFe
RR of lung CA associated with moderate smoking
is approx. 10.4. Therefore:
RR
RR
AFe
1


Interpretation: 90.4% of lung cancer in moderate
smokers would be averted if they had not smoked.
904
.
4
.
10
1
4
.
10




42. Gerstman Chapter 8 43
Attributable Fraction,
Population (AFp)
population
nonexposed
in
rate
rate
overall
where
:
formula
al
Definition
0
0




R
R
R
R
R
AFp
Proportion of all cases averted with
elimination of exposure from the population

43. Gerstman Chapter 8 44
AFp equivalent formulas
population
in
exposure
of
prevalence
where
)
1
(
1
)
1
(





e
e
e
p
p
RR
p
RR
p
AF
exposed
are
that
cases
of
proportion
where 


c
c
e
p
p
p
AF
AF

44. Gerstman Chapter 8 45
AFp for Cancer Mortality,
Selected Exposures
Exposure Doll & Peto, 1981 Miller, 1992
Tobacco 30% 29%
Dietary 35% 20%
Occupational 4% 9%
Repro/Sexual 7% 7%
Sun/Radiation 3% 1%
Alcohol 3% 6%
Pollution 2% -
Medication 1% 2%
Infection 10% -