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Changing the Test Statistic After an Interim Analysis

Changing the Test Statistic After an Interim Analysis. John Lawrence, DBI. I. Motivation II. Outline of procedure III. Simulation results. Outline. What is required to show efficacy?. 2-arm study to show that a drug is superior to placebo on survival or time to event

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Changing the Test Statistic After an Interim Analysis

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  1. Changing the Test Statistic After an Interim Analysis John Lawrence, DBI MCP2002 Bethesda, MD

  2. I. Motivation II. Outline of procedure III. Simulation results Outline MCP2002 Bethesda, MD

  3. What is required to show efficacy? • 2-arm study to show that a drug is superior to placebo on survival or time to event • S0 and S1 are the survival curves • Necessary to show S0 and S1 are not the same MCP2002 Bethesda, MD

  4. Initial Design of Study • H0: S0 S1 vs. H1: S0 S1 and the difference represents a clinically meaningful benefit in favor of the treatment. • In practice, usually assume proportional hazards and use logrank statistic to test H0: l 1vs. H1: l 1 MCP2002 Bethesda, MD

  5. MCP2002 Bethesda, MD

  6. Other Statistics • Covariate-adjusted logrank statistic • Wilcoxon statistic or other weighted version of logrank type statistic (Gr or Beta family). • Difference in survival curves at fixed time (e.g. 6-month survival rates) • Difference in median survival times MCP2002 Bethesda, MD

  7. A procedure that maintains type I error rate • LetZ1 = interim observed Z-statistic using original test statistic.Z1*= interim observed Z-statistic using new test statistic.Z* = observed Z-statistic using new test statistic at end of study • In many cases, pairs are bivariate normal MCP2002 Bethesda, MD

  8. Final test statistic Z2* = unique linear combination of (Z1*, Z*) that is standard normal (under H0) and independent of Z1* is normal with mean 0 under H0.See also Bauer (1989), Cui et al. (1999), Fisher (1998), Lehmacher & Wassmer (1999) for sample size adaptation. MCP2002 Bethesda, MD

  9. Simulation 50 patients/arm recruited over 2 years 2 years follow-up. Interim look after 1.5 years. S0(t) = exp(-1.5 t) S1(t) = exp(-1.05 t) Prop. Hazards alternative = exp(-1.33 t^1.75) NPH alternative MCP2002 Bethesda, MD

  10. Four rules for changing r • Rule 1: always change the statistic to r2 = 4 • Rule 2: always change the statistic to r2 = 4 and increase recruitment/follow-up. • Rule 3: change to r2 = 4 iff the test of proportional hazards rejects at level 0.2. • Rule 4: change to the value of r2 in {0, 1, 2, 3, 4} which has smallest p-value at interim look. MCP2002 Bethesda, MD

  11. MCP2002 Bethesda, MD

  12. Summary • Can change statistic after looking at part of data. • Can improve power without inflating type I error rate • Other design changes (sample size, etc.) and testing at multiple time points allowed. MCP2002 Bethesda, MD

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