PubMed · 12579130
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Yossef Aelony. 2003. Missing data from mesothelioma study.. https://doi.org/10.1067/mtc.2003.244
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In clinical trials success rates of two treatments to be compared often range from 10 to 90 per cent. When the comparison probabilities are (much) smaller than 10 per cent, standard methods for sample size and power calculations may provide invalid results. This situation may occur when there is interest in safety rather than in efficacy. In such trials, no more patients should be included than strictly necessary. We compared the results of maximum likelihood methods for the computation of sample sizes in a non-inferiority trial, including exact procedures and considered unequal sample sizes for experimental and reference treatment. An exact, unequal sample size maximum likelihood procedure is advocated when the specified non-zero risk difference under the null hypothesis is not too large. Such a procedure is also indicated when the parameter of interest is the relative risk, rather than the risk difference.
Due to the optional sampling effect in a sequential design, the maximum likelihood estimator (MLE) following sequential tests is generally biased. In a typical two-stage design employed in a phase II clinical trial in cancer drug screening, a fixed number of patients are enrolled initially. The trial may be terminated for lack of clinical efficacy of treatment if the observed number of treatment responses after the first stage is too small. Otherwise, an additional fixed number of patients are enrolled to accumulate additional information on efficacy as well as on safety. There have been numerous suggestions for design of such two-stage studies. Here we establish that under the two-stage design the sufficient statistic, i.e. stopping stage and the number of treatment responses, for the parameter of the binomial distribution is also complete. Then, based on the Rao-Blackwell theorem, we derive the uniformly minimum variance unbiased estimator (UMVUE) as the conditional expectation of an unbiased estimator, which in this case is simply the maximum likelihood estimator based only on the first stage data, given the complete sufficient statistic. Our results generalize to a multistage design. We will illustrate features of the UMVUE based on two-stage phase II clinical trial design examples and present results of numerical studies on the properties of the UMVUE in comparison to the usual MLE.