Biostatistics Case Studies 2010

1. Biostatistics Case Studies 2010 Session 1: Study Size Tutorial Peter D. Christenson Biostatistician http://gcrc.labiomed.org/biostat

2. First, Use software for three papers.Then, Discuss some logic.

3. Paper #1

5. How was N=498 determined? What reduction in CVD events can 224 + 224 subjects detect? Nevertheless How many subjects would be needed to detect this Δ?

6. Software Output for % of CVD Events 224 + 224 → detect 6.7% vs. 1.13%, i.e., 88% ↓. Need 3115 + 3115 to detect 25% ↓ from 6.7% to 5%, i.e., a total of (3115+3115)/0.9 = 6922.

7. From earlier design paper (Russell 2007): Δ = 0.85(0.05)mm = 0.0425 mm

8. Software Output for Mean IMT Each group N for 10% Dropout → 0.9N = 224 → N = 224/0.9 = 249. Total study size = 2(249)=498

9. Paper #2

11. Williamson paper

12. Software Output - Percentages Slightly larger Ns due to slightly different test to be used.

13. Software Output - Means Can detect 0.4 SDs. Units? Since normal range =~ 6SD, this corresponds to ~0.4/6=7% shift in normal range. Applies to any continuously measured outcome.

14. Paper #3

16. From Nance paper Δ = ~8% Δ SD√(1/N1 + 1/N2) = 2.82 Solve for SD to get SD =~ 6.8%

17. Software Output for Gilchrist Paper

18. Some Logic

19. Back to: How was 498 determined?

20. How IMT Change Comparison Will be Made Strength of Treatment Effect: Signal:Noise Ratio t= Observed Δ SD√(1/N1 + 1/N2) Δ = Aggressive - Standard Mean Diff in IMT changes SD = Std Dev of within group IMT changes N1 = N2 = Group size | t | > ~1.96 ↔ p<0.05

21. Could Solve for N Observed Δ SD√(1/N1 + 1/N2) t = ≥~1.96 if (with N = N1 = N2): 2SD2 Δ2 Δ ≥ 1.96SD√(2/N) or N ≥ (1.96)2 This is not quite right. The Δ is the actual observed difference. This sample Δ will vary from the real Δ in “everyone”. Need to increase N in case the sample happens to have a Δ that is lower than the real Δ (50% possibility).

22. Need to Increase N for Power Power is the probability that p<0.05 if Δ is the real effect, incorporating the possibility that the Δ in our sample could be smaller. 2SD2 Δ2 (1.96)2 N = for 50% power. Need to increase N to: 2SD2 Δ2 N = (1.96 + 0.842)2 for 80% power. 2SD2 Δ2 N = (1.96 + 1.282)2 for 90% power. from Normal Tables

23. Info Needed for Study Size: Comparing Means 2SD2 Δ2 N = (1.96 + 0.842)2 • Effect • Subject variability • p-value (1.96 for p=0.05; 2.58 for p=0.01) • Power (0.842 for 80% power; 1.645 for 95% power) Same four quantities, but different formula, if comparing %s, hazard ratios, odds ratios, etc.

24. 2SD2 Δ2 N = (1.96 + 0.842)2 2(0.16)2 (0.0425)2 N = (1.96 + 0.842)2 = 224 Each group N for 10% Dropout → 0.9N = 224 → N = 224/0.9 = 249. Total study size = 2(249)=498

25. Change Effect Size to be Detected

26. SD Estimate Could be Wrong Should examine SD as study progresses. May need to increase N if SD was underestimated.

27. Recall: Software Output for % of CVD Events 224 + 224 → detect 6.7% vs. 1.13%, i.e., 88% ↓. Need 3115 + 3115 to detect 25% ↓ from 6.7% to 5%, i.e., a total of (3115+3115)/0.9 = 6922.

28. Comparing Survival We just saw that: Need 3115 + 3115 to detect 25% ↓ from 6.7% to 5%, i.e., a total of (3115+3115)/0.9 = 6922. This does not use the 10% of 6922 = 692 subjects lost to follow-up (in the analysis). Recall that survival analysis, e.g., Kaplan-Meier curves, does use the info from these 692 subjects for as long as they were observed. So, fewer than 6922 subjects are needed using survival analysis - we calculate that N now.

29. Comparing Survival Really 0. This software requires >0.

30. Comparing Survival Total of 6304, includes 10% loss, compared to 6922.

31. Some Study Size Software

32. Free Study Size Software www.stat.uiowa.edu/~rlenth/Power

33. Study Size Software in GCRC Lab ncss.com ~$500

34. nQuery - Used by Most Drug Companies