1. 1 PH 240A: Chapter 11 Alan Hubbard University of California Berkeley (Slides by Nick Jewell)

2. 2 Pancreatic Cancer by Multiple Levels of Coffee Consumption Disease Status Dnot D Coffee drinking (cups/day) 02088108 1--2153271424 3--4106154260 5+88130218 3676431010

3. 3 Generic Symbols for Entries in 2 x K Table Disease Status Dnot D Exposure Level 1a1a1 b1b1 m1m1 2a2a2 b2b2 m2m2... KaKaK bKbK mKmK nDnD a1a1 n

4. 4 Overall Test of Association

5. 5  Population-based & Cohort   Case-Control: 

6. 6 Overall Test of Association  Extension of  2 test of association  K-1 degrees of freedom under H 0  Same as standard  2 test of association when K = 2

7. 7 Coffee Drinking and Pancreatic Cancer Disease Status Dnot D Coffee drinking (cups/day) 02088108 1--2153271424 3--4106154260 5+88130218 3676431010 3 d. of f. p = 0.0003 (Pooled  2 = 16.6, p =0.00005)

8. 8 Test for Trend in Risk  High degree of freedom test low power  Limit set of alternative hypotheses   i.e. risks systematically increase or decrease

9. 9 Test for Trend: Quantified Exposure Levels x x x x X, numerical measure of Exposure E P(D|E=x) x1x1 x2x2 xKxK x3x3 Typical H 0 Typical H A2 (2 degrees of freedom)

10. 10 Test for Trend  Weighted linear regression of estimated risks against X  Qualitatively ordered exposure variables  Choose a suitable scale (One d. of f.)

11. 11 Coffee Drinking and Pancreatic Cancer Disease Status Dnot D Coffee drinking (cups/day) 02088108 1--2153271424 3--4106154260 5+88130218 3676431010 1 dof p = 0.0008 2 dof, p = 0.026

12. 12 Goodness of Fit  How well is variation in risk explained by linear pattern of increase (or decrease)  K-2 degree of freedom test (be cautious about power)

13. 13 Coffee Drinking and Pancreatic Cancer Disease Status Dnot D Coffee drinking (cups/day) 02088108 1--2153271424 3--4106154260 5+88130218 3676431010 1 dof p = 0.0008 2 dof, p = 0.026

14. 14 Western Collaborative Group Study CHD Event Dnot D Body Weight (lbs) 15032558590 150 + -16031505536 160 + -17050594644 170 + -18066501567 >18078739817 25728973154

15. 15 WCGS—CHD Incidence against Body Weight Any increasing trend will tend to be detected by the test for trend (based on a linear trend)

16. 16 Pancreatic Cancer Incidence Against Coffee Drinking Consumption Same graph, but case-control-so use log odds and ignore scale on Y-axis