1. 1 PH 241: Chapter 7 Nicholas P. Jewell University of California Berkeley February 10, 2006

2. 2 2 x 2 Table Notation Disease Status Dnot D Exposure Eaba+b not Ecdc+d a+cb+dn

3. 3 Cohort Study Example (Population OR = 1) Disease Status DNot D Exposure status E84250 not E113950 1981100 Typical Study      p = 0.44

4. 4 Cohort Study Example (Population OR = 1)  1,000 typical studies  Smallest OR estimate = 0.15  Largest OR estimate = 7.58  Average of OR estimates = 1.16 (bias)  Median of OR estimates = 1

5. 5 Sampling Distribution of Odds Ratio Estimate not Normal--skewed

6. 6 Cohort Study Example (Population OR = 1)  1,000 typical studies  Smallest log(OR) estimate = -1.90 =log(0.15)  Largest log(OR) estimate = 2.03 = log(7.58)  Average of OR estimates = -0.011 (little bias)  Median of OR estimates = 0 =log(1) I always use natural logarithms

7. 7 Sampling Distribution of Log Odds Ratio Estimate

8. 8 Confidence Intervals for the Odds Ratio Disease Status Dnot D Exposure Eaba+b not Ecdc+d a+cb+dn 95% CIs for log(OR) and OR

9. 9 Case-Control Study of Pancreatic Cancer Sex Disease Status Coffee Drinking (cups/day) Total 01-23-45+ Men Case Control 9 32 94 119 53 74 60 82 216 307 Women Case Control 11 56 59 152 53 80 28 48 151 336 Total1084242602181010

10. 10 Case-Control Study of Pancreatic Cancer Pancreatic Cancer CasesControls Coffee Drinking (cups/day) 347555902 02088108 3676431010

11. 11 Estimate & Confidence Intervals for the Relative Risk Disease Status Dnot D Exposure Eaba+b not Ecdc+d a+cb+dn 95% CIs for log(RR) and RR

12. 12 Western Collaborative Group Study Occurrence of CHD YesNo Behavior Type Type A17814111589 Type B7914861565 25728973154

13. 13 Estimate & Confidence Intervals for the Excess Risk Disease Status Dnot D Exposure Eaba+b not Ecdc+d a+cb+dn 95% CIs for ER:

14. 14 Western Collaborative Group Study Occurrence of CHD YesNo Behavior TypeType A17814111589 Type B7914861565 25728973154

15. 15 Estimate & Confidence Intervals for the Attributable Risk: Population-Based Study Disease Status Dnot D Exposure Eaba+b not Ecdc+d a+cb+dn 95% CIs for log(1-AR) and AR

16. 16 Western Collaborative Group Study Occurrence of CHD YesNo Behavior TypeType A17814111589 Type B7914861565 25728973154

17. 17 Small sample adjustments  Odds Ratio  Estimate:  CIs:  Relative Risk  Estimate:  Exact tests/CIs

18. 18 Case-Control Study of Pancreatic Cancer Pancreatic Cancer CasesControls Coffee Drinking (cups/day) 347555902 02088108 3676431010 An exact 95% CI for OR is (1.64, 4.80)

19. 19 Small Sample Ideas  Be aware when you have entered “small sample world” where approximations may not be accurate and adjustments/exact methods may be required