A 2018 publication in the Biometrical Journal by Cytel’s Cyrus Mehta, Lingyun Liu and Sam Hsiao, ‘Optimal Promising Zone Designs’ (1) marks a new milestone for adaptive sample size re-estimation. Inspired by insights from the team's work with a number of Cytel's strategic consulting clients, it presents an easy to implement and new iteration of the popular promising zone design. The basic principle? That any investment of sample size at an interim analysis should be contingent on a minimal acceptable return on the investment. This return is expressed in terms of guaranteed conditional power, By identifying a minimum rate of return upfront, the new design offers greater efficiency to clinical trial planners. Importantly, the design concept is both easy to communicate, and easily understood among statistical and clinical stakeholders alike. In this blog, Cytel Co-Founder and Fellow of the American Statistical Association, Cyrus Mehta shares his insights with us on the goals and key takeaways of the publication, and how it adds to the growing toolkit of intuitive adaptive designs available to drug developers today. We also share full access to the publication itself.
What was the objective of the publication? Cyrus Mehta Our consulting experience with various clients gave us the following insight -- in many cases, sponsors were prepared to increase the sample size based on unblinded interim results only if by doing so they could be guaranteed at least a minimum amount of conditional power, say 80%, at the smallest clinically meaningful treatment effect. That is, they expected a minimum return on investment before they were prepared to invest additional subjects into the trial. This insight enabled us to identify the promising zone that would meet their needs. In the meantime, Jennison and Turnbull published a paper (2) in which they showed how one could benchmark any adaptive design with sample size re-estimation against the best that could be achieved; i.e., against the optimal adaptive design. Using their technique we discovered to our surprise that the promising zone design that we were proposing to meet our clients' needs was, in fact, an optimal design. We felt that this was an important discovery with practical implications for our clients and should be published.
How does it add to previous work in sample size re-estimation designs? Cyrus Mehta Previously, we and others had proposed that the promising zone should be identified differently. The criteria that we used was that the range of the interim data for identifying the promising zone should be restricted such that it would be unnecessary to make any statistical adjustments at the time of the final analysis. This was felt to be more efficient than using an adjusted test statistic based on pre-specified weights that corrected for the fact that the sample size had been increased. This is still a valid and useful approach. But if the client is able to specify a minimum rate of return, then the new approach that we have proposed in the current paper is more efficient.
What would you like readers of the publication to take away? The main message for any sponsor contemplating a promising zone design is the following:
(a) Can you specify the smallest treatment effect that is still clinically meaningful? (i.e., if the true treatment effect were smaller than this specification, the sponsor would no longer be interested in the new intervention.)
(b) Can you specify the minimum rate of return (in terms of conditional power) that you require before you will invest any additional subjects into this trial?
(c) What is the maximum increase in sample size you can afford, based on your budgetary and other constraints?
If you can answer all three questions, then you can construct a decision rule for increasing the sample size that is optimal.
Thank you to Cyrus Mehta for his insights.
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1) Hsiao, S., Liu, L. and Mehta, C. (2018). Optimal promising zone designs. Biometrical Journal.
2) Jennison, C. and Turnbull, B. (2015). Adaptive sample size modification in clinical trials: start small then ask for more?. Statistics in Medicine, 34(29), pp.3793-3810.