1. Biostatistics Case Studies 2009 Peter D. Christenson Biostatistician http://gcrc.labiomed.org/biostat Session 4: The Logic Behind Statistical Adjustment

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

3. Conclusions 1.808=Actual Pioglitizone-Control Difference in adiponectin. 1.522=Expected Diff if all subjects had the same ΔHbA1c

4. Question #1

5. Question #2 In Figure 1D, the before and after error bars for Both groups are very wide and overlap considerably, yet the changes are very significant (p<0.01). Why is this?

6. Question #2

7. Adjustment by Stratification

8. Question #3 The first method to look for a direct effect on atherogenic markers is subgrouping subjects by high and low HbA1c changes (Figure 1). Is it compelling? What other subgroupings (stratifications) could be examined?

9. Question #3 Adjustment of CRP and PWV Effects by Stratification on HbA1c

10. Question #3 From Table 2: Negligible Treatment by Responder Interaction Interaction = Responder Δ minus Non Responder Δ

11. Question #4 Fig 1D divides subjects into only 2 subgroups (strata) of high and low HbA1c change. Suppose 10 subgroups, from greatest to least HbA1c decrease were used. What pattern of pre and post differences would strongly support the authors’ conclusion? What pattern would contradict the authors?

12. Question #4, but for Adiponectin Post-Pre HbA1c -42 Interaction = 0

13. Question #4, but for Adiponectin Post-Pre HbA1c -42 Interaction is negligible

14. Question #5, but for Adiponectin Post-Pre HbA1c -42 Interaction is very strong, would give p<0.001

15. Adjustment by Regression

16. Question #6 In Table 4, the unadjusted difference between pioglitizone and control groups for change in adiponectin is 1.808. Reproduce this number using Table 2.

17. Question #6

18. 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

19. We now want to see how 1.808 was adjusted to 1.522 in Table 4. 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

20. 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.

21. 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.

22. 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.

23. Simulated Data to Match Table 4

24. Typical ANOCOV Software Results

25. 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:

26. Question #8 Peripheral question: Most of us are not familiar with units for PWV, unlike the other measures. How would you describe the pioglitizone effect on PWV in Figure 1B using some relative or percentage basis rather than scientific units?

27. Question #8

28. ~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

29. Question #9 Peripheral question: In the first paragraph between Tables 2 and 3, the authors claim that changes in CRP were greater in responders. Do you believe this from Figure 1C?

30. Question #9 0.04 ? Error in Paper