1. Chapter 6: Incidence & Prevalence Chapter 3 Epidemiologic Measures
4/19/2017
Epi Kept Simple
Chapter 3
Epidemiologic Measures
(c) B. Gerstman
Epidemiology 1

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
All are loosely called “rates,” but only the second is a true mathematical rate
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4. Types of Populations We measure disease frequency in:
Closed populations  “cohorts”
Open populations
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5. Closed Population ≡ Cohort
Cohort (Latin cohors, meaning “enclosure”; also the basic tactical unit of a Roman legion
Epidemiologic cohort ≡ a group of individuals followed over time
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6. Open Populations Inflow (immigration, births)
Outflow (emigration, death)
An open population in “steady state” (constant size and age) is said to be stationary
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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
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8. Denominators
Denominators  a measure of population size or person-time*
* Person-time ≈ (no. of people) × (time of observation)
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9. Incidence Proportion (IP)
Can be calculated in cohorts only
Requires follow-up of individuals
Synonyms: risk, cumulative incidence, attack rate
Interpretation: average risk
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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
10-year average risk is .011 or 1.1%.
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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
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12. Rate is .00111 per year or 11.1 per 10,000 years
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
Rate is per year or 11.1 per 10,000 years
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13. Individual follow-up in a Cohort
PY = “person-year”
25 PYs
50 PYs
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14. Incidence Rate, Open Population
Example: 2,391,630 deaths in 1999 (one year)
Population size = 272,705,815
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15. Prevalence Interpretation A: proportion with condition
Interpretation B: probability a person selected at random will have the condition
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16. Example: Prevalence of hysterectomy
Recruit 1000 women
Ascertain: 100 had hysterectomies
Prevalence is 10%
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17. Dynamics of Prevalence Cistern Analogy
Ways to increase prevalence
Increase incidence  increase inflow
Increase average duration of disease  decreased outflow
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18. Relation Between Incidence and Prevalence
When disease rare & population stationary
Example:
Incidence rate = 0.01 / year
Average duration of the illness = 2 years.
Prevalence ≈ 0.01 / year × 2 years = 0.02
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19. 3.2 Measures of Assocation
Chapter 8: Association & Impact
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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
In epidemiology it is common to use the term exposure to denote any explanatory variable
i.E we may speak of smoking as an exposure that causes lung cancer or advanced maternal age at pregnancy as an exposure that causes Down Syndrome
(Prof. G. could you please help me understand the inactive lifestyle E+??)){We arbitrary define the risk factor as “exposure” to an inactive lifestyle. Then we compare the mortality rate in the exposed (inactive lifestyle) and nonexposed (active lifestyle) groups. I’ve added a third bullet to this effect.}
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20. Arithmetic (αριθμός) Comparisons
Chapter 8: Association & Impact
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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
We compare the weight of a man of 100 kg to the weight of a woman of 50 kg.
-Absolute comparisons are derived by subtraction and using (original units of measure kg)
-{Relative comparisons are derived by division (the division cancels out units, making a unit-free comparison}
"For the things of this world cannot be made known without a knowledge of mathematics."- Roger Bacon
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21. Chapter 8: Association & Impact
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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…
We compare the weight of a man of 100 kg to the weight of a woman of 50 kg.
-Absolute comparisons are derived by subtraction and using (original units of measure kg)
-{Relative comparisons are derived by division (the division cancels out units, making a unit-free comparison}
Gerstman
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22. Relative Comparison Recall that I have $2 and you have $1.
Chapter 8: Association & Impact
4/19/2017
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
We compare the weight of a man of 100 kg to the weight of a woman of 50 kg.
-Absolute comparisons are derived by subtraction and using (original units of measure kg)
-{Relative comparisons are derived by division (the division cancels out units, making a unit-free comparison}
Gerstman
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23. Absolutes Comparisons Applied to Risks
Chapter 8: Association & Impact
4/19/2017
Absolutes Comparisons Applied to Risks
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.
In absolute terms, I have 2% MINUS 1% = 1% greater risk of the disease
This is the risk difference
We compare the weight of a man of 100 kg to the weight of a woman of 50 kg.
-Absolute comparisons are derived by subtraction and using (original units of measure kg)
-{Relative comparisons are derived by division (the division cancels out units, making a unit-free comparison}
Gerstman
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24. Relative Comparisons Applied to Risks
Chapter 8: Association & Impact
4/19/2017
Relative Comparisons Applied to Risks
In relative terms I have
2% ÷ 1% = 2  twice your risk
This is the relative risk associated with the exposure
We compare the weight of a man of 100 kg to the weight of a woman of 50 kg.
-Absolute comparisons are derived by subtraction and using (original units of measure kg)
-{Relative comparisons are derived by division (the division cancels out units, making a unit-free comparison}
Gerstman
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25. Chapter 8: Association & Impact
4/19/2017
Terminology
For simplicity sake, the terms “risk” and “rate” will be applied to all incidence and prevalence measures.
Let’s apply arithmetic to risks. These are the formulas. {The formulas are simple: RD is a subtraction and RR is a division. The key is to understand how we interpret the RR and the RD. They both quantify the relation between E and D, but they tell you something different about the association. Going through lots of examples in the book will help understand subtleties.}
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26. Rate or Risk Difference
Chapter 8: Association & Impact
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Rate or Risk Difference
Let RD represent the rate or risk difference
where
R1 ≡ the risk or rate in the exposed group R0 ≡ the risk or rate in the non-exposed group
Let’s apply arithmetic to risks. These are the formulas. {The formulas are simple: RD is a subtraction and RR is a division. The key is to understand how we interpret the RR and the RD. They both quantify the relation between E and D, but they tell you something different about the association. Going through lots of examples in the book will help understand subtleties.}
Interpretation: Excess risk associated with the exposure in absolute terms
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27. Rate or Risk Ratio Let RR represent the rate or risk ratio
Chapter 8: Association & Impact
4/19/2017
Rate or Risk Ratio
Let RR represent the rate or risk ratio
where
R1 ≡ the risk or rate in the exposed group R0 ≡ the risk or rate in the non-exposed group
Let’s apply arithmetic to risks. These are the formulas. {The formulas are simple: RD is a subtraction and RR is a division. The key is to understand how we interpret the RR and the RD. They both quantify the relation between E and D, but they tell you something different about the association. Going through lots of examples in the book will help understand subtleties.}
Interpretation: excess risk associated with the exposure in relative terms.
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28. Example Fitness & Mortality (Blair et al., 1995)
Chapter 8: Association & Impact
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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 = per 100,000 PYs
{See p. 159 for details.}
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29. Fitness and Mortality: RD
Chapter 8: Association & Impact
4/19/2017
Fitness and Mortality: RD
What is the effect of improved fitness on mortality in absolute terms?
{See p. 159 for details.}
The effect of improved fitness was to decrease mortality by 54.4 per 100,000 person-years
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30. Chapter 8: Association & Impact
4/19/2017
Example Relative Risk
What is the effect of improved fitness on mortality in relative terms?
{See p. 159 for details.}
The effect of the improved fitness was to almost cut the rate of death in half.
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31. Designation of Exposure
Chapter 8: Association & Impact
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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 = / = (1.8 times or “almost twice the rate”)
{See p. 159 for details.}
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32. 2-by-2 Table Format Disease + Disease − Total Exposure + A1 B1 N1
For person-time data: let N1 ≡ person-time in group 1 and N0 ≡ person-time in group 0, and ignore cells B1 and B0
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33. Fitness Data, table format
Fitness Improved?
Died
Person-years
Yes 25 --
4054 No 32
2937
Rates per 10,000 person-years
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34. Food borne Outbreak Example
Exposure ≡ eating a particular dish
Disease ≡ gastroenteritis
Disease +
Disease −
Total
Exposure + 63 25 88
Exposure – 1 6 7 64 31 95
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35. Food borne Outbreak Data
Disease +
Disease −
Total
Exposure + 63 25 88
Exposure – 1 6 7 64 31 95
Exposed group had 5 times the risk
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36. Comparison of RR and RD RR  strength of effect
Chapter 8: Association & Impact
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Comparison of RR and RD
RR  strength of effect
RD  effect in absolute terms
Rates (per ) of Lung CA & CHD assoc. w/smoking
Smoker
Nonsmoke RR RD
LungCA
104 10
10.40 94
CHD
565
413
1.37
152
Smoking causes more heart disease even though the association between smoking a heart disease is weaker than the association between smoking an lung cancer. This is because heart disease is more common in the population.
Smoking  Stronger effect for LungCA
Smoking  Causes more CHD
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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
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38. The Odds Ratio Similar to a RR, but based on odds rather than risks D+
Total E+ A1 B1 N1 E− A0 B0 N0 M1 M0 N
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
“Cross-product ratio”
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39. Odds Ratio, Example Milunsky et al, 1989, Table 4 NTD = Neural Tube Defect
Folic Acid+ 10
10,703
Folic Acid− 39
11,905
Exposed group had 0.29 times (about a quarter) the risk of the nonexposed group
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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
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41. Attributable Fraction Exposed Cases (AFe)
Proportion of exposed cases averted with elimination of the exposure
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42. Example: AFe
RR of lung CA associated with moderate smoking is approx Therefore:
Interpretation: 90.4% of lung cancer in moderate smokers would be averted if they had not smoked.
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43. Attributable Fraction, Population (AFp)
Proportion of all cases averted with elimination of exposure from the population
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44. AFp equivalent formulas
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45. AFp for Cancer Mortality, Selected Exposures
Doll & Peto, 1981
Miller, 1992
Tobacco
30%
29%
Dietary
35%
20%
Occupational 4% 9%
Repro/Sexual 7%
Sun/Radiation 3% 1%
Alcohol 6%
Pollution 2% -
Medication
Infection
10%
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