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Chapter 12 of @JTBook walks through how to design and analyze such a study using a fixed or group sequential design.
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Chapter 12 of @JTBook walks through how to design and analyze such a study using a fixed or group sequential design.
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The time-to-event approximation provides an initial approximation to computing bounds; more importantly, it provides sample size and study duration approximations that are not given by the Jennison and Turnbull approach.
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# The time-to-event approach
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```
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Now we convert this to a design with integer event counts at analyses.
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This is achieved by rounding interim analysis event counts from the above design and rounding up the final analysis event count.
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This is achieved by rounding interim analysis event counts from the above design and rounding up the final analysis event count.
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This will result in a slight change in event fractions at interim analyses as well as a slight change from the targeted 90% power.
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We now explain the rationale behind the spending function choices.
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Recall that the hazard ratio (HR) is 1 minus the VE.
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The vaccine efficacy at bounds should be checked to see if the evidence is convincing enough to be accepted as a clinically relevant benefit in addition to statistical benefit (efficacy bounds) or a less than relevant benefit for futility bounds.
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The vaccine efficacy at bounds should be checked to see if the evidence is convincing enough to be accepted as a clinically relevant benefit in addition to statistical benefit (efficacy bounds) or a less than relevant benefit for futility bounds.
cumsum(as.numeric(gsBinomialExact(k = xb$k, theta = xb$theta, n.I = xb$n.I, b = b, a = xb$lower$bound)$upper$prob[,2]))
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}
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excess_beta_spend
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# Summary
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We have provided an extended example to show that a @ChanBohidar exact binomial using spending function bounds can be derived in a two-step process that delivers sample size and bounds by 1) deriving a related time-to-event design using asymptotic methods and then 2) converting to an exact binomial design.
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Adjustments were made to target Type I and Type II error probabilities in the asymptotic approximation to ensure the exact binomial Type I and Type II error rates were achieved. The method seems a reasonable and straightforward approach to develop a complete design that accounts for the impact of enrollment, failure rates dropout rates, and trial duration.
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Adjustments were made to target Type I and Type II error probabilities in the asymptotic approximation to ensure the exact binomial Type I and Type II error rates were achieved. The method seems a reasonable and straightforward approach to develop a complete design that accounts for the impact of enrollment, failure rates dropout rates, and trial duration.
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