Epi Kept Simple

(c) B. Gerstman 1

Epi Kept Simple

Chapter 3

Epidemiologic Measures

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 MEASURE1b : the dimensions, capacity, or amount of something ascertained by measuring

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

Types of Populations

We measure disease frequency in:

• Closed populations “cohorts”

• Open populations

(c) B. Gerstman Chapter 3 4

Closed Population ≡ Cohort

(c) B. Gerstman Chapter 35

Cohort (Latin cohors, meaning “enclosure”; also the basic tactical unit of a Roman legion

Epidemiologic cohort ≡ a group of individuals followed over time

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

Numerators & Denominators

• Most measures of disease occurrence are ratios

• Ratios are composed of a numerator and denominator

• Numerator case countIncidence count onsets only

Prevalence count all cases

(c) B. Gerstman Chapter 3 7

Denominators

(c) B. Gerstman Chapter 3 8

Denominators a measure of population size or person-time*

* Person-time ≈ (no. of people) × (time of observation)

Incidence Proportion (IP)

• Synonyms: risk, cumulative incidence, attack rate

• Interpretation: average risk

(c) B. Gerstman Chapter 3 9

Can be calculated in cohorts only

Requires follow-up of individuals

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

women900

women10

risk @ no.

onsets of no.IP

10-year average risk is .011 or 1.1%.10-year average risk is .011 or 1.1%.

0111.0

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

(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 yearsRate is .00111 per year or 11.1 per 10,000 years

years 9000

10

years 10 women900

women10

year

.00111

(c) B. Gerstman 13(c) B. Gerstman 13

Individual follow-up in a Cohort

years 50 years 25

onsets 2

years 75

onsets 2

PY = “person-year”

25 PYs

50 PYs

Incidence Rate, Open Population

(c) B. Gerstman Chapter 3 14

years-person 100,000per 877

nobservatio ofduration size population Avg

onsetsIR

-1year deaths 008770.0

Example: 2,391,630 deaths in 1999 (one year)Population size = 272,705,815

year 1persons 5272,705,81

deaths 2,391,630IR

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

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%

10.0people 1000

people 100

Dynamics of PrevalenceCistern Analogy

(c) B. Gerstman Chapter 3 17

Increase incidence increase inflow

Increase average duration of disease decreased outflow

Ways to increase prevalence

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 stationaryWhen disease rare & population stationary

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

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

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…

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

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 ComparisonsApplied to Risks

• In absolute terms, I have 2% MINUS 1% = 1% greater risk of the disease

• This is the risk difference

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

Gerstman Chapter 8 25

Terminology

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

Gerstman Chapter 8 26

Rate or Risk DifferenceLet RD represent the rate or risk Let RD represent the rate or risk

differencedifference

01 RRRD

where where

RR11 ≡ the risk or rate in the exposed group ≡ the risk or rate in the exposed group

RR00 ≡≡ the risk or rate in the non-exposed risk or rate in the non-exposed groupgroupInterpretation: Interpretation: ExcessExcess risk associated risk associated

with the exposure in absolute termswith the exposure in absolute terms

Gerstman Chapter 8 27

Rate or Risk RatioLet RR represent the rate or risk ratioLet RR represent the rate or risk ratio

0

1

R

RRR

where where

RR11 ≡ the risk or rate in the exposed group ≡ the risk or rate in the exposed group

RR00 ≡≡ the risk or rate in the non-exposed risk or rate in the non-exposed groupgroupInterpretation: excess risk associated Interpretation: excess risk associated with the exposure in relative termswith the exposure in relative terms..

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

Gerstman 29

Fitness and Mortality: RD

01 RRRD

The effect of improved fitness was to decrease mortality by 54.4 per 100,000 person-years

Gerstman 30

Example

Relative Risk

0

1

R

RRR 55.0yrs-p 100,000per 0.122

yrs-p 100,000per 7.67

The effect of the improved fitness was to almost cut the rate of death in half.

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”)

Gerstman Chapter 8 32

2-by-2 Table FormatDisease + 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

11 N

AR

0

00 N

AR

Gerstman Chapter 8 33

Fitness Data, table formatFitness Improved?

Died Person-years

Yes 25 -- 4054

No 32 -- 2937

67.61000,104054

25

1

11

N

AR

95.108000,102937

32

0

00

N

AR

Rates per 10,000 person-years

Gerstman Chapter 8 34

Food borne Outbreak Example

Disease + Disease − Total

Exposure + 63 25 88

Exposure –

1 6 7

Total 64 31 95

7159.088

63

1

11 N

AR 1429.0

7

1

0

00 N

AR

Exposure ≡ eating a particular dishDisease ≡ gastroenteritis

Gerstman Chapter 8 35

Food borne Outbreak Data

71

8863

0

1 R

RRR

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

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

2.501

25

0

11

R

RRR 6.10

01

106

0

22 R

RRR

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

01

01

00

11

AB

BA

BA

BAOR

“Cross-product ratio”

Similar to a RR, but based on odds rather than risks

Gerstman Chapter 8 39

Odds Ratio, ExampleMilunsky et al, 1989, Table 4

NTD = Neural Tube DefectNTD+ NTD−

Folic Acid+ 10 10,703

Folic Acid− 39 11,905

01

01

AB

BAOR

Exposed group had 0.29 times (about a quarter) the risk of the nonexposed group

39703,10

905,1110

29.0

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

Gerstman Chapter 8 41

Attributable Fraction Exposed Cases (AFe)

RR

RRAFe

1 :formula Equivalent

1

01 :formula alDefinitionR

RRAFe

Proportion of exposed cases averted with elimination of the exposure

Gerstman Chapter 8 42

Example: AFe

RR of lung CA associated with moderate smoking is approx. 10.4. Therefore:

RR

RRAFe

1

Interpretation: 90.4% of lung cancer in moderate smokers would be averted if they had not smoked.

904.4.10

14.10

Gerstman Chapter 8 43

Attributable Fraction, Population (AFp)

population nonexposedin rate

rate overall

where

:formula alDefinition

0

0

R

R

R

RRAFp

Proportion of all cases averted with elimination of exposure from the population

Gerstman Chapter 8 44

AFp equivalent formulas

populationin exposure of prevalence where

)1(1

)1(

e

e

ep

p

RRp

RRpAF

exposed are that cases of proportion where

c

cep

p

pAFAF

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% -