Optimal inference for Simon's two-stage design with over or under enrollment at the second stage

Abstract

Simon’s two-stage designs are widely used in clinical trials to assess the activity of a new treatment. In practice, it is often the case that the second stage sample size is different from the planned one. For this reason, the critical value for the second stage is no longer valid for statistical inference. Existing approaches for making statistical inference are either based on asymptotic methods or not optimal. We propose an approach to maximize the power of the study while maintaining the type I error rate where the type I error rate and power are calculated exactly from binomial distributions. The critical values of the proposed approach are numerically searched by an intelligent algorithm over the complete parameter space. It is guaranteed that the proposed approach is at least as powerful as the conditional power approach which is a valid but non-optimal approach. The power gain of the proposed approach can be substantial as compared to the conditional power approach. We apply the proposed approach to a real Phase II clinical trial.

Correlation Coefficients for a Study with Repeated Measures

“…e objective of this manuscript is to conduct extensive simulation studies to compare the existing correlations for repeated measures with regard to the average of correlation and the mean squared error (MSE) and identify the correlation method that has the best performance to be used in practice. In addition to the parameter of interest (correlation for repeated measures), there are several nuisance parameters in the variance-covariance matrix: variances, correlations within each outcome, and correlation between outcomes from different visits [17][18][19][20]. It is computationally intensive for these comparisons.…”

Exact confidence limits for the probability of response in two-stage designs

“…An additional critical response value was introduced for the first stage termination due to efficacy, and they developed a statistical software package to compute these designs [2]. Recently, other modified Simon’s designs, such as adaptive two-stage designs [3–7], have been developed to improve the flexibility and efficiency of a trial by allowing the second stage sample size to be changed as the observed first stage responses.…”