Is Promising Zone Design Optimal?
In traditional clinical trial design, the sample size is often determined to detect the target treatment effect with enough power. However, it is not always easy to define the target treatment effect size. Treatment effect is typically estimated based on limited prior trial data, and thus admits huge uncertainties. If the effect size is over-estimated, the sample size could be too small resulting in an underpowered study. On the other hand, sample size could be too large leading to an unnecessarily overpowered study if the effect size is underestimated at design stage.
Two main streams of strategies have been developed to mitigate the risk of such uncertainties. One strategy is to target a small and conservative treatment effect with a larger sample size. Interim analysis can be built in to cut down the sample size if overwhelming efficacy is observed at interim. In group sequential designs, the Type I error can be controlled using spending function approaches such as Lan and DeMets (1983).
Group sequential design is not always feasible since it might be challenging for the sponsor to commit a large sample size upfront without assurance of success. The other strategy to mitigate the risk of the uncertainty about treatment effect at design stage is to start with a smaller sample size targeting a more optimistic treatment effect. Interim data can be reviewed to check if sample size increase is warranted to increase the likelihood of success. A few approaches have been proposed to control the Type I error in case of sample size adaptation based on unblinded sample size re-estimation. These methods include Cui, Hung & Wang 1999; Lehmacher & Wassmer 1999, Chen DeMets and Lan 2006; Müller & Schäfer 2001; Mehta & Pocock 2011.
Although Type I error control has been well addressed by published methods, there is limited research on the optimality of sample size adaptation rules. Two important questions are yet to be answered: when to increase the sample size and how much to increase. Mehta & Pocock 2011 introduced the idea of sample size increase in a predefined promising zone. In this approach, the interim results are categorized into favorable, promising, and unfavorable zones in case of no early stopping at interim. The sample size would be increased only if the interim results fall into the promising zone which is commonly defined by conditional power. For example, if the conditional power is between 30% and 90%, sample size would be increased to reach target conditional power 90%. If the conditional power is greater than 90%, interim results are considered favorable, and the trial can continue to the end with the planned sample size. On the other hand, if the conditional power is less than 30%, it doesn’t warrant a sample size increase since a huge sample size increase would be needed to reach good conditional power, which might not be feasible.
Jennison and Turnbull 2015 developed another approach based on maximizing expected utility. This approach also results in a promising zone design. In this approach, a promising zone and a corresponding decision rule for sample size increase are derived implicitly by solving an optimization problem which is characterized by an objective function and constrained. The objective function balances the tradeoff between conditional power gain and sample size increase. This design is optimal in terms of unconditional power among all the promising zone designs that have the same initial sample size, maximum sample size and expected sample size.
Jennison and Turnbull 2015 set up a gold-standard optimal design to benchmark other alternative promising zone designs. Hsiao, Liu, and Mehta 2019 present a constrained promising zone design where the constrained is imposed to ensure a minimal conditional power. This constrained promising zone design is evaluated against the optimal unconstrained Jennison and Turnbull (2015) design and against a constrained version of the Jennison and Turnbull design. The constrained promising zone design has comparable performance to the constrained Jennison and Turnbull design. The unconstrained Jennison and Turnbull design has slightly better unconditional power. Compared to the constrained design, the promising zone of the unconstrained Jennison and Turnbull design starts early. This means that sample size increase could be triggered with lower conditional power. On the other hand, the constrained design only increases sample size if a decent conditional power can be reached with the additional investment of sample size.
Keeping the Promise Anniversary Celebrations reflects on the past achievements of this design, while also engaging ideas about how this design will continue to transform the industry in years to come. We invite you to celebrate along by clicking on the below:
About the Guest Author of Blog:
Lingyun Liu is a Director of Biostatistics at Vertex Pharmaceuticals, but spent over a decade as a Cytel statistician. She is a leading scholar on promising zones.