Curtailed two-stage design for comparing two arms in randomized phase II clinical trials

Abstract

In phase II clinical trials, patients are recruited sequentially and consequently the time required to complete the clinical trial will become long if the accrual rate is low. To speed up the drug development process and account for ethical issues, stochastically and non-stochastically curtailed two-stage designs have been proposed in single-arm phase II clinical trials. More recently, randomized phase II clinical trials are being increasingly recommended to avoid biased evaluation of the treatment effect when compared with a historical control. The current patient population and the historical one may be quite heterogeneous. Moreover, it is impossible to randomly assign patients for treatments. Consequently, various two-stage designs have been presented for comparing two arms. Since the sample size required in a randomized phase II trial is usually larger than that required in a single-arm phase II trial, we introduce the concept of curtailed sampling procedure to develop curtailed two-stage design for two-armed, randomized phase II clinical trials. The proposed design does not require pairwise patient response comparison, yet it allows a trial to be stopped early as soon as the difference in therapeutic effect of the experimental therapy and the standard at the end of a trial is foreknown.

A stochastically curtailed two‐arm randomised phaseIItrial design for binary outcomes

“…A no go decision, that is, a decision to not reject H 0 , is made as soon as the final difference in responses is guaranteed to not be r or greater in favour of the treatment arm; this occurs before the end of a trial if m − X T ( m ) + X C ( m ) ≥ N /2 − r + 1. These decision rules are the NSC boundaries used by Chen et al, 12 though we relax their requirement for continuous monitoring. Jung, Carsten and Chen and Chen et al also include an explicit interim analysis, that is, an interim analysis at which point a go/no go decision is made regardless of whether or not the final pre‐specified stopping boundary may be reached 10,11,12 .…”

“…These decision rules are the NSC boundaries used by Chen et al, 12 though we relax their requirement for continuous monitoring. Jung, Carsten and Chen and Chen et al also include an explicit interim analysis, that is, an interim analysis at which point a go/no go decision is made regardless of whether or not the final pre‐specified stopping boundary may be reached 10,11,12 . However, such an approach may result in a no go decision even when there is a high probability of correctly identifying that the null hypothesis is false.…”

“…For existing design approaches that permit early stopping to reject H 0 under NSC only, such as Carsten and Chen and Chen et al, the upper bound for rejecting the null hypothesis in terms of CP is always fixed at θ E = 1 . 11,12 That is, the CP must be equal to one in order to reject the null hypothesis, and this value may not be altered. Further, the designs of Jung, Carsten and Chen and Chen et al include an explicit interim analysis, containing some stopping boundary that does not take into account the probability of reaching the final stopping boundary.…”

“…The trial stops as soon as the required difference in the number of responses is guaranteed to be reached, or cannot be reached (again, either at the interim or by the end of the trial). Thus the designs of Carsten and Chen and Chen et al require continuous or almost continuous monitoring 11,12 …”

“…We note that other two‐arm approaches have been proposed 17,18,19,20,21,22 . However, it is impractical to compare all randomised two‐arm designs, and so our approach will be compared only to Jung's design, as this is the two‐arm analogue to the popular Simon design, and Carsten and Chen and Chen et al's designs, as these designs use curtailment and as such are similar to our approach 10,11,12 . Table 1 shows the main differences between the designs to be compared.…”