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Biostatistics Case Studies 2005

Biostatistics Case Studies 2005. Session 1: Study Design for Demonstrating Lack of Treatment Effect: Equivalence or Non-inferiority. Peter D. Christenson Biostatistician http://gcrc.humc.edu/Biostat. Case Study. p ASA+PPI = 1.5%. Demonstrate: p clop – p ASA+PPI ≤ 4%.

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Biostatistics Case Studies 2005

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  1. Biostatistics Case Studies 2005 Session 1: Study Design for Demonstrating Lack of Treatment Effect: Equivalence or Non-inferiority Peter D. Christenson Biostatistician http://gcrc.humc.edu/Biostat

  2. Case Study

  3. pASA+PPI = 1.5% Demonstrate: pclop – pASA+PPI ≤ 4% N=145/group Power=80% for what?

  4. Typical Analysis: Inferiority or Superiority [Not used in this paper] H0: pclop – pASA+PPI= 0% H1: pclop – pASA+PPI≠ 0% H1 → therapies differ α = 0.05 Power = 80% for Δ=|pclop - pASA+PPI|=? = 95% CI for pclop – pASA+PPI Clop inferior pclop – pASA+PPI 0 Clop superior pclop – pASA+PPI 0 No diff detected* pclop – pASA+PPI 0 * and 80% chance that a Δ of (?) or more would be detected.

  5. Typical Analysis: Inferiority or Superiority [Not used in this paper] H0: pclop – pASA+PPI= 0% H1: pclop – pASA+PPI≠ 0% H1 → therapies differ α = 0.05 Power = 80% for Δ=|pclop - pASA+PPI|=? Detectable Δ = 5.5%-1.5%=4% So, N=331/group → 80% chance that a Δ of 4% or more would be detected.

  6. Typical Analysis: Inferiority or Superiority [Not used in this paper] H0: pclop – pASA+PPI= 0% H1: pclop – pASA+PPI≠ 0% H1 → therapies differ α = 0.05 Power = 80% for Δ=|pclop - pASA+PPI|=4% Note that this could be formulated as two one-sided tests (TOST): H0: pclop – pASA+PPI≤ 0% H1: pclop – pASA+PPI> 0% H1 → clop inferior α = 0.025 Power = 80% for pclop - pASA+PPI =4% H0: pclop – pASA+PPI≥ 0% H1: pclop – pASA+PPI< 0% H1 → clop superior α = 0.025 Power = 80% for pclop - pASA+PPI =-4%

  7. Demonstrating Equivalence [Not used in this paper] H0: |pclop – pASA+PPI| ≥ E% H1: |pclop – pASA+PPI|< E% H1 → therapies “equivalent”, within E Note that this could be formulated as two one-sided tests (TOST): H0: pclop – pASA+PPI≤ -4% H1: pclop – pASA+PPI> -4% H1 → clop non-superior α = 0.025 Power = 80% for pclop - pASA+PPI = 0% H0: pclop – pASA+PPI≥ 4% H1: pclop – pASA+PPI< 4% H1 → clop non-inferior α = 0.025 Power = 80% for pclop - pASA+PPI = 0%

  8. Demonstrating Equivalence H0: |pclop – pASA+PPI | ≥ 4% H1: |pclop – pASA+PPI | < 4% H1 → equivalence α = 0.05 Power = 80% for pclop - pASA+PPI = 0 = 95% CI for pclop – pASA+PPI pclop – pASA+PPI Clop non-superior -4 0 4 pclop – pASA+PPI Clop non-inferior -4 0 4 pclop – pASA+PPI Equivalence* -4 0 4 * both non-superior and non-inferior.

  9. This Paper: Inferiority and Non-Inferiority Apparently, two one-sided tests (TOST), but only one explicitly powered: H0: pclop – pASA+PPI≤ 0% H1: pclop – pASA+PPI> 0% H1 → clop inferior α = 0.025 Power = 80% for pclop - pASA+PPI = ?% H0: pclop – pASA+PPI≥ 4% H1: pclop – pASA+PPI< 4% H1 → clop non-inferior α = 0.025 Power = 80% for pclop - pASA+PPI = 0% The authors chose E=4% as the maximum therapy difference that therapies are considered equivalent.

  10. This Paper: Inferiority and Non-Inferiority = 95% CI for pclop – pASA+PPI Decisions: pclop – pASA+PPI Clop inferior -4 0 4 pclop – pASA+PPI Clop non-inferior -4 0 4 “Non-clinical” inferiority* pclop – pASA+PPI -4 0 4 * clop is statistically inferior, but not enough for clinical significance. Observed Results: pclop = 8.6%; pASA+PPI = 0.7%; 95% CI = 3.4 to 12.4 pclop – pASA+PPI Clop inferior -4 0 4 12

  11. Power for Test of ClopidrogrelNon-Inferiority H0: pclop – pASA+PPI≥ 4% H1: pclop – pASA+PPI < 4% H1 → clop non-inferior α = 0.025 Power = 80% for pclop - pASA+PPI = 0%

  12. Power for Test of Clopidrogrel Inferiority H0: pclop – pASA+PPI≤ 0% H1: pclop – pASA+PPI > 0% H1→ clop inferior α = 0.025 Power = 80% for pclop - pASA+PPI = 7.3% Detectable Δ = 8.8%-1.5%=7.3%

  13. Conclusions: This Paper • In this paper, clop was so inferior that investigators were apparently lucky to have enough power for detecting it. The CI was too wide with this N for detecting a smaller therapy difference. • Investigators justify testing non-inferiority of clop only (and not of Aspirin + Nexium) with the lessened desirability of combination therapy (?). • I feel that this is a good approach for size and power for a new competing therapy against a standard, if the N for clop inferiority had been considered also. • Note that power calculations were based on actual %s of subjects, whereas cumulative 12-month incidence was used in the analysis. There are not power calculations for equivalency tests using survival analysis, that I know of.

  14. Conclusions: General • “Negligibly inferior” would be better than non-inferior. • All inference can be based on confidence intervals. • Pre-specify the comparisons to be made, which can be defined as where confidence intervals lie. • Ns are smaller for equivalence tests, but study may be underpowered to detect differences if that is the case, unless specifically designed for that. • Power for only one or for multiple comparisons. Power can be different for different comparisons. • For large N, reversing α and β=1-power for the typical test gives the same N as for equivalence test.

  15. Appendix: Possible Errors in Study Conclusions Typical study to demonstrate superiority/inferiority Truth: Study Claims: H0: No Effect H1: Effect No Effect Correct Error (Type II) Specificity Sensitivity Effect Error (Type I) Correct Set α=0.05 Specificity=95% Power: Maximize Choose N for 80%

  16. Typical study to demonstrate superiority/inferiority Appendix: Graphical Representation of Power H0: true effect=0 HA: true effect=3 Effect in study=1.13 N=100 per Group Larger Ns give narrower curves 41% HA H0 5% Effect (Group B mean – Group A mean) \\\ = Probability of concluding HA if H0 is true. /// = Probability of concluding H0 if HA is true. Power=100-41=59% Note greater power if larger N, and/or if true effect>3, and/or less subject heterogeneity.

  17. Appendix: Online Study Size / Power Calculator www.stat.uiowa.edu/~rlenth/Power Does NOT include tests for equivalence or non-inferiority or non-superiority

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