Measures of Association

1. Week 3
Measures of association
EPID 504D
Emory Rollins School of Public Health

2. 2x2 table
Disease No disease
Exposed a b
Unexposed c d

3. Estimating risk - cohort
Disease No disease Risk/Rate
Exposed a b a/(a+b)
Unexposed c d c/(c+d)
Table 9-1. Design of a Cohort Study
Table 11-9. Calculating in a Cohort Study
• Risk ratio = risk (exposed) / risk (unexposed)
• Rate ratio = rate (exposed) / rate (unexposed)

4. Estimating risk - cohort
Diarrhea No diarrhea Total Risk (attack rate)
Ate egg salad 45 9 54 45/54 (83%)
Did not eat egg salad 18 41 60 18/60 (30%)
• Risk ratio = risk (exposed) / risk (unexposed)
= 83% / 30%
= 2.8
• Risk difference = 83% - 30% = 53%

5. Estimating “risk” – case-control
• Can’t estimate risk directly
– Have cases and controls
– Can vary the number of controls
– Estimate risk using odds

6. Estimating risk – case-control
Disease No disease
Exposed a b
Unexposed c d
Table 10-1. Design of a Case-control Study
Table 11-5. Risk Calculations in a Cohort Study
• Odds = probability/(1-probability)
• Odds ratio = odds exposure (diseased) / odds
exposure (non-diseased)
• Odds ratio = (a/c)/(b/d)
= (ad)/(bc)

7. Estimating risk

8. Doll and Hill, 1950
• Odds of exposure (case) = 688/21
• Odds of exposure (control) = 650/59
• Odds ratio = (ad)/(bc)=~3.0
Case Control Total
Smoker 688 650 1338
Non-smoker 21 59 80
Total 709 709 1418
Smoking and carcinoma of the lung. Br Med J. 1950; 2(4682): 739–748

9. Summary
• Odds ratio generally approximates risk
ratio if the disease is “rare”
• If RR, OR = 1 then no association
• If RR, OR > 1 then positive association
• If RR, OR < 1 then negative association

10. Potential for prevention
• Attributable risk
• Population attributable risk
Background risk
Risk due to exposure

11. Attributable risk
• In the exposed, how much of the disease
is due to exposure?
• Attributable risk =
(Incidence exposed) – (Incidence unexposed)
Incidence exposed

12. Population attributable risk
• In the total population, how much disease
is due to exposure?
• Population attributable risk =
(Incidence total popn)-(Incidence non-exposed)
Incidence total popn

13. Example
JAMA. 2004;291(10):1238-45.

14. Readings
• Chapters 11&12
• Chapter 13 (review)