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Abstract:
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Group sequential designs allow stopping a clinical trial for its efficacy objectives based on interim evaluation of the accumulating data while controlling the probability of crossing the boundary at any analysis. To monitor trials with uncertainty in group sizes at each analysis, error spending functions are often used to derive stopping boundaries. Although flexible, most spending functions are generic increasing functions with parameters that are difficult to interpret. They are often selected arbitrarily, sometimes using trial and error, so that the corresponding boundaries approximate the desired behavior numerically. Lan and DeMets proposed a spending function that approximates in a natural way the O'Brien-Fleming boundary based on the Brownian motion process. We extend this approach to a general family which has an additive boundary for the Brownian motion process. The spending function and the group sequential boundary share a common parameter which regulates how fast the error is spent. In a special case, the parameter has an interpretation as the conditional error rate, which is the conditional probability to reject the null hypothesis at the final analysis.
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