1. Summary of Measures and Design 3h
“A haunting tale of risk, rate and odds”
Hein Stigum
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09:00 09:45 1 DAGs
10:00 10:45 1 DAGs
11:00 11:45 1 DAGs
11:45 12:30 1 Lunch
12:30 13:15 1 Measures
13:30 14:15 1 Design
14:30 15:15 1 Design
15:30 16: Design
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Hi, Handouts for Wednesday's lectures on DAGs and Summary of Measures and Design are now on Fronter under Lectures>Hein Stigum. If you print out you may want to use colors as it conveys a lot of information in these presentations.
Jun-19
H.S.

2. Concepts Risk Rate Odds probability, proportion, %
Km/h, cases/person-time
2 math quatities
prop: fraction, numerator (top) is part of denominator (bottom)
ex: colds in class=2/30=7% , no dimension, 0-1
rate: change in one quantity per change in another (time),
ex: speed, drive 100 km in 2 h then average speed is 50 km/h, dimension, no upper bound
Odds: disease per healthy person
Statistical concept:
risk: probability, no dimension,
ex: flip coin
Jun-19
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H.S. 2 2 2

3. Cohorts Closed cohort Open cohort Count persons, risk
Count person-time, rate
Closed cohort with time varying covariates
Line= follow up
Circle=event (disease)
Red line=exposed
Count person-time, rate
Jun-19
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4. Epidemiological measures
Frequency
prevalence
incidence
Association
Risk difference
Risk ratio
Odds ratio
Potential impact
Attributable fraction
How much disease?
More disease
among exposed?
We have covered ..
We turn now to Association measures
Does smoking cause lung cancer? We measure the strength of the association between the risk factor (smoking) and the disease.
assoc. measures are calculated from freq measures
Important cause?
Jun-19
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5. Frequency measures May convert rate to risk: Name Equation Type
Cohorts
Prevalence
Incidence Proportion
(Cumulative Incidence)
Incidence Rate
Odds
risk
rate
odds -
closed cohort
any cohort
Show extra animation here
May convert rate to risk:
Jun-19
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6. Disease frequency depicted
Show:
Prevalence
Incidence proportion, closed pop, no loss to follow up
Incidence rate, takes observation time into account, (could also have loss to follow up)
H.S.

7. Exercise: Risk, Rate and Odds
Cohort of 200 subject followed for 10 years
Calculate the 10-year risk of disease
Calculate the rate of disease
Calculate the 10-year odds of disease
Explain the results in words
5 minutes
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8. Frequency measures existing cases Prevalence Incidence proportion risk
Incidence rate
existing cases
risk
new cases
rate
odds
Prevalence odds
Incidence odds
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9. Association measures More disease among exposed?
Compare frequency among exposed1 and unexposed0
Difference: RD=risk1-risk0 0=no effect
Ratio: RR=risk1/risk0 1=no effect
Frequency
Association or Effect
Difference
Ratio
Risk
Rate
Odds
Difference
Risk Difference, RD
Rate Difference -
Ratio
Risk Ratio, RR
Rate Ratio, RR, IRR, (HRR)
Odds Ratio, OR
Dekoder til bakkenett: 1 kr vs 0.5 kr
Situation 0-1
Can use all 3 types of measures, ex=incidence prop
2 types:
null value=no association
RR=2 means exposed twize the risk
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10. Designs
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11. The 2 by 2 table The lowest number sets the precisiond
The lowest number sets the precision
=.13
To increase power:
In a cohort study: oversample unexposed
In a case control study: oversample disease
To increase power:
Cohort: balance exposure (north-south)
Case-Control: balance disease (east-west)
Jun-19
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12. Time E,D no time cross-section E → D prospective
cohort, nested CC, Case-Cohort
E ← D
retrospective
traditional CaseControl
Present time
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13. Designs Aims Designs Disease occurrence Exposure-Disease association
Cross-sectional studies
Cohort studies
Case-control studies
Case-Cohort
Nested Case Control
Traditional Case Control
Inside an existing cohort
Aim: find association
Designs: unit of analysis, time for finding exposure and disease
At the end of an imaginary cohort
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14. 3 examples What design should we use? Gender and Smoking
Do girls smoke more than boys?
Exercise and Coronary Heart Disease (CHD)
Does exercise reduce the risk?
Genes and Diabetes type 1
Does gene-type increase the risk?
Consider:
Reversed Causality
Frequency of outcome
Recall bias
What design
should we use?
Jun-19
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15. Cross-section
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16. Prevalence depicted Prevalence risk Exposed: P1 Unexposed: P0
Prevalence odds
Exposed: O1
Unexposed: O0
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17. Cross-sectional example
Pro: fast and inexpensive
Con: reversed causality
Interpretations in the two last slides
Adolescents age 16-18
95% CI
Ex 2: Reversed causality: right after disease, CHD->little exercise, later may have CHD->much exercise OK
Typical problems:
Rev. Caus.
Size
Recall
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18. Cohort
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19. Incidence risk, rate and odds depicted
Exposed: R1
Unexposed: R0
Show:
Prevalence
Incidence proportion, closed pop, no loss to follow up
Incidence rate, takes observation time into account, (could also have loss to follow up)
H.S.

20. Exercise: Cohort Full Cohort, 3 year follow up
Calculate the 3-year risk of disease for exposed and unexposed
Calculate the rate of disease for exposed and unexposed
Calculate the 3-year odds of disease for exposed and unexposed
Calculate the difference and ratio association measures, use no exercise as reference.
Explain the results in words
Exercise-CHD: OR=0.5 significant down to 2000 subjects
Gene-Diabetes: OR=2.4 significant down to subjects (power 80%)
subject followed for 3 years
95% CI
Gene-Diabetes as cohort:
Gene freq 5% * dis freq 1%=0.05%
Number in exposed, diseased cell= *0.05%=50
10 minutes
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21. Case Control studies
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22. Traditional Case-Control
Full Cohort:
Case-Control:
Sampling fraction f=0.1
N % N   Contr/Case Power
Full cohort % %
Trad. Case-Control % %
In practice: All cases, 1-5 controls per case
Sample controls independent of exposure
Sample controls from base population of cases
Money saved?
Jun-19
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23. Traditional Case-Control cont.
One Control per Case:
Sampling fraction f=?
Typical problems:
Rev. Caus.
Size
Recall
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24. Nested studies: case-control inside a cohort
Exposure information:
relatively cheap store blood, questionnaire full cohort
relatively expensive analyze blood cases+controls
Cohort
start
Cohort
end
store blood
quest.
quest.
quest.
Cases
analyze
blood
Expensive: money or limited amount of blood
→ prospective study →
Controls
exposure
Jun-19
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25. Nested studies cont. for rare outcomes
Cohort problems
Trad. Case-Control problems
Poor balance 
large study
Recall bias
Selection of controls
Nested studies:
Case-Cohort
Nested case-control
Expensive: money or limited amount of blood
Efficient design (balanced)
Prospective (no recall bias)
Easy selection of controls
Jun-19
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26. Case-Control studies of (imaginary) cohort E → D prospective E ← D
Design
Nested
Direction
Sample controls
Case-Cohort
Nested Case-Control
Traditional Case-Control
Yes No
Prospective
Retrospective
At start
During follow up
At end
of (imaginary) cohort
E → D
prospective
E ← D
retrospective
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27. Case-Cohort .
controls
Show extra animation
Prospective
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28. . . . . Nested Case-Control case case controls controls risk set
Prospective
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29. Traditional Case-Control.
controls
Retrospective
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30. Exercise: Case-Control studies
Full cohort
10 year
follow up
Sampling fraction f=0.1
Include all cases from the full cohort. Sample controls as in 2-4 below:
Case-Cohort: sample 10% disease free (independent of exposure) at the start of the cohort. Calculate the pseudo risks of disease.
Nested Case-Control: sample 10% of the risk time (independent of exposure) as control. Calculate the pseudo rates of disease.
Traditional Case-Control: sample 10% disease free (independent of exposure) at the end of the cohort. Calculate the pseudo odds of disease.
Calculate risk-, rate- and odds ratios.
20 minutes
Jun-19
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31. Case-Cohort vs. Nested Case-Control
Design
Loss to follow up
Tailored sampling
Reuse controls
Estimation
Case-Cohort:
Nested Case-Control:
Low efficacy if much
loss to follow up
Good
Simple random
Stratified sampling.
Counter matching.
Yes
Not straight
forward
Modified Cox
Stratified Cox or
Conditional logistic
Case-Cohort: generalist
Nested Case-Control: specialist
Jun-19
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32. Measures and regression model
Outcome
Exposed
Unexposed
Regression
Continuous
mean1
mean0
Linear regression
Binary
risk1
rate1
odds1
risk0
rate0
odds0 ?
Jun-19
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33. Adjusted measures
Remove the effect of confounders in regression models
Frequency
Association or Effect
Difference
Ratio
Risk
RD:
RR:
Rate
IRR:
Odds -
OR:
Linear-binomial
Log-binomial
Linear-Poisson
Cox, Poisson
Logistic
Generalized linear models
Family (y|x)
Link
Measure
Alternative
binomial
Standardize freq measures on sex and age
Remove effect of sex and age on association measures in regression
logit
log
identity OR RR RD
Poisson regression with robust variance
Linear regression with robust variance
Poisson
identity
RateDiff
Jun-19
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34. Summing up Frequency Association Designs risk, rate, odds
risk, rate, odds in exposed vs unexposed
Designs
Cross-sectional
Cohort
Case-control
Case-Cohort
Nested Case Control
Traditional Case Control
no time
prospective
nested prospective
retrospective
Logistic regression is not the only model!
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35. Extra Material
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36. Interpretations of Difference and ratio measures
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37. Cross-sectional example, interpretations
Risk Difference=0.16: Among boys 14% smoke, girls smoke 16 percetagepoints more
Risk Ratio=2.1: Among boys 14% smoke, girls smoke 2.1 times more
Rate Difference:
Adolescents age 16-18
95% CI
Ex 2: Reversed causality: right after disease, CHD->little exercise, later may have CHD->much exercise
Rate Ratio:
Odds Ratio=2.6: The odds of smoking is 2.6 higher for girls than for boys
Jun-19
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38. Cohort exercise, interpretations
Full Cohort, 3 year follow up
Risk among unexposed=0.10: If no exercise the 3 years risk of coronary heart disease is 10%,
Risk Difference=-0.05: those who exercise have 5 percentage points less risk
Risk Ratio=0.5: those who exercise have half the risk
Exercise-CHD: OR=0.5 significant down to 2000 subjects
Gene-Diabetes: OR=2.4 significant down to subjects (power 80%)
subject followed for 3 years
95% CI
Gene-Diabetes as cohort:
Gene freq 5% * dis freq 1%=0.05%
Number in exposed, diseased cell= *0.05%=50
Rate among unexposed=0.035: If no exercise the rate of CHD is 35 new cases per 1000 person years
Rate Difference=-0.018: those who exercise will have 18 cases less per 1000 py
Rate Ratio=0.49: those who exercise will have half the rate of CHD
Odds Ratio=0.47: The odds of CHD is appr. half among subject who exercise compared to no exercise
Jun-19
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