Bayesian enrichment strategies for randomized discontinuation trials

Abstract

We propose optimal choice of the design parameters for random discontinuation designs (RDD) using a Bayesian decision-theoretic approach. We consider applications of RDDs to oncology phase II studies evaluating activity of cytostatic agents. The design consists of two stages. The preliminary open-label stage treats all patients with the new agent and identifies a possibly sensitive subpopulation. The subsequent second stage randomizes, treats, follows, and compares outcomes among patients in the identified subgroup, with randomization to either the new or a control treatment. Several tuning parameters characterize the design: the number of patients in the trial, the duration of the preliminary stage, and the duration of follow-up after randomization. We define a probability model for tumor growth, specify a suitable utility function, and develop a computational procedure for selecting the optimal tuning parameters.

Figure 1

Boxplots of the a priori distribution of the proportion p_e of patients eligible for the second stage of the trial across discontinuation trials having alternative durations of the first stage. The a priori distributions are computed through a simple data driven procedure; the adopted procedure for specifying the prior is discussed in Section 4. The lines in boxplots indicate the 5th, 25th, 50th, 75th, and 95th percentiles.

Figure 2

Panel (i): The upper trajectory shows observed historical tumor growth data (∎) under the control regimen. The lower trajectory shows imputed measurements and trajectory under the treatment regimen. Panels (ii) and (iii): Median trajectories, 80% confidence bands and 50% confidence bands of $X_{i,t}^1\sim \mathbf{GP}({\tilde{a}}_j-{\tilde{\psi }}_j{\tilde{b}}_j,{\tilde{b}}_j,{\tilde{\sigma }}_j\mid X_{i,t_0}^1={\tilde{X}}_{j,t_0}^1,\dots ,X_{i,t_k}={\tilde{X}}_{j,t_k}^1)$ under two alternative prior distributions for ${\left\{\tilde{\psi }\right\}}_{j=1}^M$.

Figure 3

Summary curves showing the distribution of projected tumor growth during the first 250 days after the tumor reaches the minimal threshold ε = 0.02. Solid lines: the median function and the 80% confidence band of the growth process X_t. Dashed lines: the 80% confidence band of the conditional expectations E(X_t|θ).

Figure 4

Optimal RDDs. Orthogonal sections of expected utility surfaces corresponding to alternative utility functions.