A response-adaptive multi-arm design for continuous endpoints based on a weighted information measure

TL;DR

A response-adaptive design for continuous endpoints which explicitly allows to control the trade-off between the number of patients allocated to the "optimal"arm and the statistical power is presented.

Abstract

Multi-arm trials are gaining interest in practice given the statistical and logistical advantages they can offer. The standard approach uses a fixed allocation ratio, but there is a call for making it adaptive and skewing the allocation of patients towards better-performing arms. However, it is well-known that these approaches might suffer from lower statistical power. We present a response-adaptive design for continuous endpoints which explicitly allows to control the trade-off between the number of patients allocated to the "optimal" arm and the statistical power. Such a balance is achieved through the calibration of a tuning parameter, and we explore robust procedures to select it. The proposed criterion is based on a context-dependent information measure which gives greater weight to treatment arms with characteristics close to a pre-specified clinical target. We establish conditions under which the procedure consistently selects the target arm and derive the corresponding limiting allocation ratios. We also introduce a simulation-based hypothesis testing procedure which focuses on selecting the target arm and discuss strategies to effectively control the type-I error rate. The practical implementation of the proposed criterion and its potential advantage over currently used alternatives are illustrated in the context of early Phase IIa proof-of-concept oncology trials.

Figures (26)

• Figure 1: Information gain $\Delta_{n_j}$ in \ref{['eq:infoGainSymm']} as function of (a) sample mean $\bar{x}_{n_j}$ (left), (b) standard deviation $\sigma_j^p$ (center) and (c) sample size $n_j^\kappa$ of the $j$-th arm (right).
• Figure 2: WE($p$,$\kappa$) design's allocation ratios for increasing sample sizes, for four arms and different values of $p$ and $\kappa$: asymptotic allocation ratios (dashed lines); mean allocation ratios across simulations (solid lines); variation observed across replicates (light-shaded areas) under scenario $\bm{\mu}=(1,1.1,1.2,3)$, $\bm{\sigma}=(1,1,1,2)$, $\gamma=0$.
• Figure 3: Empirical distribution of differences $d_j-d_{j^*}=|\mu_j-\gamma|-|\mu_{j^*}-\gamma|$, $j\neq j^*$ relative to the best arm $j^*$. Panels show $j=j^{**}$ (left), $j=j^{***}$ (middle) and $j=j^{****}$ (right), across the $S=500$ alternative scenarios randomly generated for the simulation study in Section 5.1. The vertical dashed and dotted lines indicate the thresholds below which all scenarios have differences $d_j-d_{j^*}$ smaller than $\epsilon=0.1$ and $\epsilon=0.5$, respectively.
• Figure 4: Type-I error rates for a grid of values of $c:\,\mu_j-\gamma=c,\,\forall j,\,c\geq0$ and for several designs. Design-specific cut-off probabilities are calibrated both in the case of strong (left) and average (right) control of the type-I error rate at level $\alpha=5\%$.
• Figure 5: Empirical distribution of $\widehat{\pi}_{\widehat{j}^*,\widehat{j}^{**}}$ for FR and WE$(p,\kappa)$ designs under $H_0:\mu_j-\gamma=c,\,\forall j$, for (i) $c=0$, (ii) $c=0.82$ and (iii) $c=3.27$, and (iv) under the scenario characterized by $\bm\mu=(1.91,-3.36,-0.37,3.99)$, with $\bm\sigma=(2,2,2,4)$, $\gamma=0$, $B=5$; the cut-off $\eta_{0.05}$ (black dot) corresponds to $\alpha=5\%$, with $\eta_{0.05}^{\text{max}}$ (dashed line) approximately controlling type-I error below $5\%$ across all designs and null scenarios.

Theorems & Definitions (13)

• Theorem 1
• Theorem 2
• Theorem 3
• Corollary 1
• Theorem 4
• Theorem 5
• proof
• proof
• proof
• proof