Exact confidence limits for the response rate in two-stage designs with over- or under-enrollment in the second stage

Abstract

Simon’s two-stage design has been widely used in early phase clinical trials to assess the activity of a new investigated treatment. In practice, the actual sample sizes do not always follow the study design precisely, especially in the second stage. When over- or under-enrollment occurs in a study, the original critical values for the study design are no longer valid for making proper statistical inference in a clinical trial. The hypothesis for such studies is always one-sided, and the null hypothesis is rejected when only a few responses are observed. Therefore, a one-sided lower interval is suitable to test the hypothesis. The commonly used approaches for confidence interval construction are based on asymptotic approaches. These approaches generally do not guarantee the coverage probability. For this reason, Clopper-Pearson approach can be used to compute exact confidence intervals. This approach has to be used in conjunction with a method to order the sample space. The frequently used method is based on point estimates for the response rate, but this ordering has too many ties which lead to conservativeness of the exact intervals. We propose developing exact one-sided intervals based on the p-value to order the sample space. The proposed approach outperforms the existing asymptotic and exact approaches. Therefore, it is recommended for use in practice.

Correlation Coefficients for a Study with Repeated Measures

“…Because these estimated variances and covariance are very close between these two methods, the final estimated correlations are very similar. When a study has different number of follow-up for each participant, ρ I and ρ CS differ from each other [18,[24][25][26]. For a study with some possible outliers as seen in the data testing association between pH and PaCO 2 [6], their difference is substantial.…”

Accurate confidence intervals for risk difference in meta-analysis with rare events

“…Exact confidence intervals are preferable for statistical inference. However, it is often computationally intensive, such as the aforementioned the exact interval by Buehler [28,[30][31][32]. For these reasons, simulation based intervals are proposed for use in practice, including the proposed interval here, the Tian interval, and the interval based on confidence distribution [24,[33][34][35].…”

Response to the letter by Guogen Shan, Hua Zhang, and Tao Jiang

“…We thank Drs. Shan, Zhang, and Jiang for their interest in our article and for drawing our attention to Buehler's method for constructing exact one‐sided confidence limits through enumeration of all possible datasets under the unconditional framework 1‐5 . This approach can be applied to the current setting of making inference for the location parameter, μ 0 , of the beta‐binomial (BB) model when both the number of studies, K , and the study‐specific sample sizes, n i , are small.…”