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Parameter Estimation Approaches in Adaptive Group Sequential Clinical Trials

The promising zone design is an adaptive design which allows for sample size re-estimation based on the results of an interim analysis. Since its introduction 10 years ago by Cytel co-founder Professor Cyrus Mehta and Professor Stuart Pocock of the London School of Hygiene and Tropical Medicine, it has been widely debated and explored. During the first webinar of ‘Keeping the Promise Anniversary Celebrations’, Professor Mehta presented on a unified approach to controlling the type-1 error.

Statistical methods for controlling the type-I error of hypothesis tests in adaptive group sequential clinical trials are well-established and well-understood. However, methods for obtaining statistically valid point estimates and confidence intervals are not as well-established or as well-understood. For classical group sequential trials involving no adaptation, one can compute a repeated confidence interval at each interim look and a stage-wise adjusted confidence interval at the final look.

In the fourth webinar of the ‘Keeping the Promise’ webinar series, Professor Mehta generalizes these methods so as to accommodate adaptive sample size re-estimation and adaptive changes in the number and spacing of the interim looks. The estimation methods are consistent with corresponding hypothesis tests and the confidence interval at the final analysis provides exact coverage of the unknown treatment effect.

Below is a brief overview of the two types of parameter estimation methods:

The Repeated Confidence Interval (RCI) Method

This method is an extension of the repeated confidence intervals (RCIs) proposed by Jennison and Turnbull (J. Roy. Statist. Soc. B 1989; 51:301-361). It can be used to compute conservative confidence intervals for a group sequential test in which an adaptive design change is made one or more times over the course of the trial. The key idea, due to Müller and Schäfer (Biometrics 2001; 57:886-891), is that by preserving the null conditional rejection probability of the remainder of the trial at the time of each adaptive change, the overall type I error rate, taken unconditionally over all possible design modifications, is also preserved. [1] During the webinar, Cyrus illustrates RCI for group sequential design (GSD) if there is no adaptation and RCI for adaptive GSD.

The Stage-Wise Adjusted (SWCI or BWCI) Methods

Tsiatis, Rosner and Mehta (1984) introduced the Stage-Wise Adjusted Confidence Intervals (SWACIs) for constructing confidence intervals following group sequential tests of a normal mean. If no adaptive change is made, the classical group sequential SWACI may be adopted. The SWACI method is not applicable in adaptive sample space design. During the webinar, Cyrus shares an example to illustrate the use of the SWACI in which the conditional error rate is projected backwards from the adapted to the original design, also known as the backward image confidence interval (BWCI). The BWCI method produces median unbiased point estimates and confidence intervals with exact coverage at any desired level at the end of an adaptive group sequential trial. [2]

RCI Vs. BWCI Methods

RCI has a conservative coverage of δ and positively biased point estimate. Whereas, BWCI provides exact coverage and median unbiased point estimate. RCI is available after each interim look and is valid even if the trial continues after the boundary is crossed. On the contrary, BWCI is available only at the final analysis where it exhausts the entire α.

Click below to watch the on demand webinar.


[1] Mehta, Cyrus & Bauer, Peter & Posch, Martin & Brannath, Werner. (2007). Repeated confidence intervals for adaptive group sequential trials. Statistics in medicine. 26. 5422-33. 10.1002/sim.3062.

[2] Bhatt DL, Mehta C. Adaptive Designs for Clinical Trials. N Engl J Med. 2016 Jul 7;375(1):65-74. doi: 10.1056/NEJMra1510061. PMID: 27406349.

About the Author of Blog:


Mansha Sachdev specializes in content creation and knowledge management. She holds an MBA degree and has 11 years of experience in handling various facets of marketing, across industries. At Cytel, Mansha is a Content Marketing Manager and is responsible for producing informative content that is related to the pharmaceutical and medical devices industries.