1. Biostatistics Case Studies 2008 Peter D. Christenson Biostatistician http://gcrc.labiomed.org/biostat Session 2: Statistical Adjustment: How it Works

2. Study Goal Diabetic Atherogenic FPG HbA1c HOMA-IR CRP PWV Adiponectin Pioglitizone ?

3. Conclusions 1.808=Actual Pio-Control Diff 1.522=Expected Diff if all subjects had the same ΔHbA1c

4. Question #1

5. Question #2

6. Question #3

7. From Table 2:

8. Question #4, but for Adiponectin Post-Pre HbA1c -42

9. Question #4, but for Adiponectin Post-Pre HbA1c -42

10. Question #4, but for Adiponectin Post-Pre HbA1c -42

11. Question #6

12. Adiponectin and HbA 1c Changes: Changes: HbA1c -0.1 -1.0 Adiponectin -0.02 1.79 Mean HbA1c = -0.56 Table 4 →1.81 = 1.79 - (-0.02) Question #6

13. Look back at the graphs from Questions 4 and 5 We examine the two possible most extreme associations between adiponectin and HbA1c changes, and then a typical association. Question #7

14. Suppose A Perfect Correlation Between Changes in Adiponectin and HbA 1c Obviously, changes in adiponectin are completely explained by changes in HbA 1c. The predicted adiponectin change for every subject at the mean HbA 1c change is the same. The difference in group means(0) is what is not explained by HbA 1c.

15. Suppose Zero Correlation Between Changes in Adiponectin and HbA 1c Changes in adiponectin are completely unrelated to changes in HbA 1c. The predicted adiponectin change for each subject at the mean HbA 1c change is unchanged. The difference in group means (1.82) is what is not explained by HbA 1c.

16. Adjustment Results from Table 4: 1.808 = actual diff in mean adiponectin changes (=1.79--0.02) 1.522 = diff in mean adiponectin changes, adjusted for HbA 1c. We now use simulated data to demonstrate how 1.522 is determined.

17. Simulated Data to Match Table 4

18. Typical ANOCOV Software Results

19. Parameter Std Variable DF Estimate Error t Value Pr > |t| Intercept 1 -0.00868 0.31260 -0.03 0.9779 Treatment 1 1.52086 0.43890 3.47 0.0007 a1c 1 -0.97902 0.17848 -5.49 <.0001 Parameter Std Variable DF Estimate Error t Value Pr > |t Intercept 1 -0.02046 0.34485 -0.06 0.9528 Treatment 1 1.81078 0.48068 3.77 0.0002 Unadjusted: Adjusted:

20. Question #8

21. ~60 50 =SEM Normal Range: 1680 ± 2SD SD ≈ 50x√66 ≈ 400 → Normal Range 4x400=1600 wide i.e., ~ 900 to 2500 Effect is ~ 60/1600 ≈ 4% of normal range

22. Question #9 0.04 ? Error in Paper