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Design

Simulation methods for calculating the conditional power in interim analysis: The case of an interim result opposite to the initial hypothesis in a life-threatening disease. Somatostin plus Isosorbide-5-Mononitrate vs Somatostatin in the control of acute gastro-oesophageal variceal bleeding:

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Design

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  1. Simulation methods for calculating the conditional power in interim analysis:The case of an interim result opposite to the initial hypothesis in a life-threatening disease.

  2. Somatostin plus Isosorbide-5-Mononitrate vs Somatostatin in the control of acute gastro-oesophageal variceal bleeding: a double blind, randomized, placebo-controlled clinical trial. Junquera F, et al. GUT 2000; 46 (1) 127-132.

  3. Design • Disease • Acute variceal bleeding in cirrhotic patients • Objective • To test whether the addition of oral Isosorbide 5-Mononitrate (Is-5-Mn) improved the efficacy of Somatostatine (SMS) alone in the control of bleeding.

  4. Design • Treatments • Group 1: SMS + PLB (Control) • Group 2: SMS + Is-5-Mn (Experimental) • Working hypothesis • The rate of success would increase from 60% to 90%.

  5. Sample size: Pre-determination n=n per group s2 = variance q = effect size f(a , b) = function of type I and II errors n = s2 / q2 * f(a , b)

  6. Statistical errors: f(,)

  7. Fixed sample size ALPHA = 0.05 POWER = 0.90 P1 = 0.90 P0 = 0.60 Case sample size for uncorrected chi-squared test: 42

  8. Introduction: interim analyses • Often ethical concerns on these situations, specially in life-threatening diseases. • Sometimes, pre-defined working hypothesis may not adjust to reality. • Treatments may be better than expected • Treatments may be worse than expected (safety and/or efficacy) • Long studies or big sample sizes make advisable some kind of interim control.

  9. Introduction • At some fixed times, cumulated data can be analysed and decisions may be taken in base to the findings. • Multiple analysis can lead to statistical errors and mistaken clinical decisions. • Several methods deal with multiplicity issues.

  10. Design • For ethical reasons the design allows an interim analysis, when half of the sample size is recruited. • Pocock’s group sequentialmethod (1977) a = 0.05 b = 0.1 (power 90%) p0= 60%, p1=90%

  11. Group Sequential Methods

  12. a adjusted sample size ALPHA = 0.029 POWER = 0.90 P1 = 0.90 P0 = 0.60 Case sample size for uncorrected chi-squared test: 48

  13. Internal Participants Monitoring Comittee Digestive System Research Unit Pharmacist Statistician Clinical Pharmacologist Liver Unit

  14. 50% Sample size with evaluated outcome Data for Interim analysis Statistical analysis: • 50 patients finalised

  15. Interim analysis Chi-square=2.427, p-value=0.119 OR1 (observed): 3.11 (0.72 –13.51) ORr (design): 0.17

  16. Problem statement • Evidence from interim analysis against working hypothesis • Although no statistical evidence supporting study termination, clinical criteria suggested so. • Search for objective support to clinical intuition.

  17. 50% Sample size with evaluated outcome Data for Interim analysis Statistical analysis: • 50 patients finalised Recruitment: • 10 patients

  18. Possible solutions 1) Group sequential methods 2) Alpha spending function approach 3) Repeated confidence intervals 4) Stochastic curtailing methods 5) Bayesian methods 6) Boundaries approach (likelihood function)

  19. Conditional power • Negative results: • CAST (I-II) study. NEJM (1989 & 1992) • Group sequential testing using permutation distribution & stochastic curtailment methods • HPMPC trial, Ann Intern Med 1997 • ACTG Study 243. NEJM 1998

  20. Conditional power • Positive results: • CRYO-ROP Arch Ophthalmology,1988 • Grable el al. Am J Obstet Gynecol, 1996 • Extension of trial: • Proschan MA, Biometrics, 1995

  21. Stochastic curtailment Lan, Simon y Halperin (1982) Stop if in i inspection: • 0, P(reject H0| ) is high at the end • 0, P(reject H0 | ) is small at the end

  22. Application to real data • design: p(ctr) = 60% p(exp) = 90% • 1st Inspection (50 patients): p(ctr) = 87.5% p(exp) = 69.2% • Probability of proving the working hypothesis at the end (100 patients) projecting the results from this inspection

  23. Methods: • OR design: 0.17 => qr= log(OR) = -1.792 • Simulations: • Fortran 90 • 1,000,000 studies =>precision < 0.01% • 15 possibilities ranging from –1.5xqrto +1.5xqr

  24. Effect Size Design Observed +1 x qr -0.63 xqr -1.5 x qr +1.5 xqr 0 q/qr ORr design: 0.17 qr= log(OR) = -1.79

  25. Obs H0 H1

  26. Conditional power calculation

  27. Conditional power calculation q1(1st inspection) qr(design)

  28. P(q < q1 | q/qr= 1.00) = 53/1,000,000 P(q < q1 | q/qr= 1.25) = 2/1,000,000 P(q < q1 | q/qr= 1.50) = 0/1,000,000

  29. Interim analysis after completion of 10 more patients Chi-square=4.794, p-value=0.029 OR1’ (observed): 4.00 ORr (design): 0.17

  30. Final Interpretation • The study was interrupted not based in the sequential pre-defined rule. • The clinical intuition was confirmed by the conditional power calculation. • The study was finished due to: • The low likeliness of the working hypothesis • The high probability of a worse outcome with the experimental treatment

  31. Conclusions • Simulations may be a very useful tool in some design and analysis situations, as it has been shown in this case of the conditional power calculation.

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