In the realm of clinical trial design, particularly within early-phase studies, the ability to make informed decisions about whether to proceed to larger, more definitive trials is paramount. Researchers have introduced a refined approach to three-outcome designs in external pilot trials, integrating progression criteria that allow for more nuanced decision-making. This framework not only streamlines the trial process but also enhances the accuracy of go/no-go decisions.
Three-Outcome Designs: A Closer Look
Traditional two-outcome designs often categorize trial results into simple 'go' or 'stop' decisions. However, three-outcome designs introduce an intermediate 'pause' outcome, allowing for a more cautious and adaptive approach. This is particularly useful in scenarios where initial results are promising but not definitive. The refined methodology builds upon existing three-outcome designs, such as those proposed by Sargent et al. and Storer, by reformulating the operating characteristics and error rates associated with each outcome.
Sargent et al.'s design defines operating characteristics relevant to the three-outcome setting. These include measures akin to type I and type II error rates, denoted as (\alpha _a) and (\beta _a), respectively. The design also considers the probabilities of obtaining a pause decision under both null (\(\lambda\)) and alternative (\(\delta\)) hypotheses. The goal is to set constraints on these characteristics and choose \(n, x_0,\) and \(x_1\) to minimize n while satisfying these constraints.
Storer's three-outcome design takes a similar approach but uses a different set of operating characteristics. Here, the type I error rate (\alpha _b) is the probability of exceeding the lower threshold, \(x_0\), under the null, and the type II error rate (\beta _b) is the probability of failing to exceed the upper threshold under the alternative. The remaining operating characteristics are the probabilities of incorrectly obtaining a stop or a go decision when the true parameter is at some midpoint \(\rho _m \in (\rho _0, \rho _1)\). These operating characteristics, denoted by \(\gamma _L\) and \(\gamma _U\) respectively, reflects the motivation of this design to encourage an intermediate outcome when the true parameter value is between the null and alternative.
Adjustments Following a 'Pause' Outcome
A key innovation of this refined approach is the allowance for adjustments to be made following a 'pause' outcome. This could involve modifying the intervention, refining the trial design, or gathering additional data before making a final decision. By incorporating the potential impact of these adjustments into the error rate calculations, the framework provides a more realistic assessment of the trial's overall success probability. The effect of this adjustment is denoted by \(\tau\), such that the parameter in the main trial will equal \(\rho ' = \rho\) if no adjustment is made and \(\rho ' = \rho + \tau\) if it is.
Implementation and Error Rate Reformulation
To facilitate the implementation of these designs, the researchers have developed the R package 'tout'. This package provides tools for determining optimal values for key trial parameters, such as sample size and decision thresholds, while adhering to pre-specified error rate constraints. The method estimates the probability \(\eta\), sets constraints on the type I and II error rates \(\alpha , \beta\), and finally searches for the values of \(n, x_0, x_1\) which minimise n whilst satisfying the constraints.
The error rates \(\alpha\) and \(\beta\) are refined as follows:
$$\begin{aligned} \alpha = \max \left[ \underset{\rho \le \rho _0}{\max} \Pr (x_1< \hat{\rho }), \underset{\rho + \tau \le \rho _0}{\max} \eta \Pr (x_0< \hat{\rho } \le x_1) + \Pr (x_1 < \hat{\rho }) \right] . \end{aligned}$$
$$\begin{aligned} \beta = \max \left[ \underset{\rho > \rho _1}{\max} \Pr (\hat{\rho } \le x_0), \underset{\rho + \tau > \rho _1}{\max} \Pr (\hat{\rho } \le x_0) + \eta \Pr (x_0 < \hat{\rho } \le x_1) \right] . \end{aligned}$$
Impact and Future Directions
By providing a more flexible and accurate framework for designing and analyzing pilot trials, this research has the potential to improve the efficiency of pharmaceutical R&D. The ability to adapt trial designs based on interim results, while maintaining rigorous control over error rates, could lead to more informed decisions about which therapies to advance to later-stage development. This unified framework for designing and analysing three-outcome pilot studies doesn’t allow for adjustments to the intervention or trial design prior to the definitive trial.
