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Abstract:
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We show how to give rigorous Type I Error proofs for clinical trial designs using simulation. In principle, this can be done for designs with highly adaptive sampling, censored survival data, or complex null hypothesis spaces. The methods can also support mid-course re-design of complex trials, including unplanned addition or deletion of treatment arms. We require a well-specified exponential family model for observations (or, asymptotically, test statistics with a Brownian limit), a design with prespecified rules for sampling and hypothesis rejection, a compact region of interest in the null hypothesis space, and (lots of) simulations over a grid of parameter values within that region. Computational scale is a limiting factor, especially for hard-to-simulate trials or models with many parameters. We also propose a technique for tuning rejection thresholds to guarantee satisfaction of a fixed Type I Error upper bound. In this talk we will discuss the key ideas: large-scale Monte Carlo simulation, Taylor expansions, and some mathematical bounding arguments. We also discuss software implementation, aiming to shorten regulatory negotiations and reduce risk for new designs.
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