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Meeting on Futility Analysis London, 11 November 2008 Simple approaches to futility analysis

Medical and Pharmaceutical Statistics Research Unit. Meeting on Futility Analysis London, 11 November 2008 Simple approaches to futility analysis John Whitehead. Medical and Pharmaceutical Statistics Research Unit MPS Research Unit

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Meeting on Futility Analysis London, 11 November 2008 Simple approaches to futility analysis

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  1. Medical and Pharmaceutical Statistics Research Unit Meeting on Futility Analysis London, 11 November 2008 Simple approaches to futility analysis John Whitehead Medical and Pharmaceutical Statistics Research Unit MPS Research Unit Director: Professor John Whitehead Department of Mathematics and Statistics Tel: +44 1524 592350 Fylde College Fax: +44 1524 592681 Lancaster University E-mail: j.whitehead@lancaster.ac.uk Lancaster LA1 4YF, UK

  2. Example: A study in stroke Patients: Have suffered an ischaemic stroke no more than 6 hours earlier Treatments: E: Experimental drug, administered for 5 days C: Placebo Primary Modified Rankin score after 90 days Response: SUCCESS = score of 0 or 1 FAILURE = score of 2 – 6 Success rates on E and C are pE and pC Futility meeting

  3. Intended analysis The data can be summarised as and will be analysed using Pearson’s c2-test: Futility meeting

  4. It can be shown that where and To a good level of approximation, Z ~ N(qV, V) where q is the log-odds ratio Futility meeting

  5. Power requirement E will be claimed better than C if Z  u where and and qR represents a clinically worthwhile improvement Thus u and V must satisfy and Futility meeting

  6. This leads to where zg is the 100g percentage point of N(0, 1), and to where Futility meeting

  7. Suppose that a = 0.05, 1 – b = 0.90 and pC = 0.45 Attainment of pE = 0.55 would be clinically worthwhile Then qR = 0.40 and A sample size of 1052 could be adopted (V = 65.75) Run the trial until 1052 patients have been recruited, treated and followed up to 90 days Futility meeting

  8. The one-stage design claim E > C Z 15.893 V 65.75 Futility meeting

  9. The two-stage design claim E > C Z u1 u2 continue V1 V2 V 1 abandon Futility meeting

  10. The futility design Z claim E > C u2 continue V1 V2 V 1 abandon Futility meeting

  11. Power requirement E will be claimed better than C if Z11and Z2u2 where and Futility meeting

  12. Let F2 denote the bivariate standard normal distribution function where Then F2 is the PROBBNRM function of SAS, and so can easily be evaluated Futility meeting

  13. Thus 1, u2, V1 and V2 must satisfy and There are 2 equations and 4 unknowns, so some constraints can be imposed Let us require that : futility will be assessed when half of the information is available Futility meeting

  14. Some feasible designs -u2 = 15.890 in all cases 1 n2 V2a 1 - b fut0 fut1 cpower -2.0 1052 65.75 0.0249 0.902 0.364 0.0040 0.206 -1.5 1052 65.75 0.0249 0.901 0.397 0.0052 0.232 -1.0 1052 65.75 0.0249 0.901 0.431 0.0067 0.260 -0.5 1052 65.75 0.0248 0.901 0.465 0.0085 0.289 0.0 1054 65.88 0.0248 0.901 0.500 0.0106 0.321 0.5 1056 66.00 0.0248 0.901 0.535 0.0133 0.354 1.0 1058 66.13 0.0248 0.900 0.569 0.0164 0.389 1.5 1062 66.38 0.0249 0.900 0.603 0.0201 0.426 2.0 1066 66.63 0.0248 0.900 0.636 0.0244 0.464 Futility meeting

  15.  fut0 = P(Z1 1 q = 0); fut1 = P(Z1 1 q = 0.40)  u2 = 15.890 for all designs, compared with u = 15.893 for a one-stage design  Search is to three decimal places in u2and to the nearest even integer in n2  No design exists for 1= 2.5 Futility meeting

  16. cpower is the conditional power: P(Z2 u2 Z1= 1; q = 0.40) So, when q = qR: fut1is the probability of falling into the hole (of false stopping) cpoweris the probability of getting out of the hole fut1  cpoweris the probability of falling into the hole and then of getting out of it again (loss of power) For 1 = 0.0, fut1 = 0.0106, cpower = 0.321 and fut1 cpower = 0.0034 Futility meeting

  17. Preferred design: 1 u2 n2 V2a 1 - b fut0 fut1 0.0 15.890 1054 65.88 0.0248 0.901 0.500 0.0106  Only two extra patients needed  50% chance of stopping if no effect  Very simple futility criterion -stop if the treatment isn’t working Futility meeting

  18. Recommended design: 1 u2 n2 V2a 1 - b fut0 fut1 0.0 15.893 1052 65.75 0.0247 0.8999 0.500 0.0107  This is the one-stage design with an added futility look  Tiny loss of power  Avoids misunderstanding and difficulties with regulators  Analyse as if there was no futility analysis - conservative Futility meeting

  19. General recommendations 1. In lengthy trials in serious conditions, perform an interim analysis half way through 2. Abandon the study if the estimated treatment effect is negative 3. Ignore the futility rule in the final analysis 4. Design the futility rule into the protocol, and consider absolute properties, not conditional ones 5. You can adjust for prognostic factors and deal with complicated endpoints 6. Also useful when there are multiple active treatments 7. Can check through exact calculation or simulation Futility meeting

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