A simulation study of methods for selecting subgroup-specific doses in phase 1 trials

Abstract

Patient heterogeneity may complicate dose-finding in phase 1 clinical trials if the dose-toxicity curves differ between subgroups. Conducting separate trials within subgroups may lead to infeasibly small sample sizes in subgroups having low prevalence. Alternatively,it is not obvious how to conduct a single trial while accounting for heterogeneity. To address this problem,we consider a generalization of the continual reassessment method on the basis of a hierarchical Bayesian dose-toxicity model that borrows strength between subgroups under the assumption that the subgroups are exchangeable. We evaluate a design using this model that includes subgroup-specific dose selection and safety rules. A simulation study is presented that includes comparison of this method to 3 alternative approaches,on the basis of nonhierarchical models,that make different types of assumptions about within-subgroup dose-toxicity curves. The simulations show that the hierarchical model-based method is recommended in settings where the dose-toxicity curves are exchangeable between subgroups. We present practical guidelines for application and provide computer programs for trial simulation and conduct.

Keywords: Bayesian study design; conditionally independent hierarchical model; continual reassessment method; phase 1 clinical trial; subgroup-specific dose-finding.

Figure 1

An example of three patient subgroups with different true dose-toxicity curves (y-axis: toxicity probability, x-axis: dose). Given the fixed target toxicity probability, π^*=0.30, the three subgroups have different true optimal doses.

Figure 2

Subgroup-specific dose-toxicity curves assumed in the simulations, presented in terms of the true dose-toxicity probabilities ${\pi }_{1,k}^{\mathit{true}},\cdots ,{\pi }_{6,k}^{\mathit{true}}$ for each subgroup (Sg): Sg 1, diamond and solid; Sg 2, square and dashed; Sg 3, triangle and dashed-dotted; Sg 4, star and dotted. Figures 1a, 1b, 1c, and 1d correspond to scenarios 1, 2, 3, and 4, respectively. Optimal doses are indicated by open circles.

Figure 3

Subgroup-specific weighted probability of selection (WPS) of optimal dose and probability of correctly selecting (PCS) the optimal dose for HB-CRM (diamond and solid), K-CRM-1-trial (square and dashed), and 1-CRM-K-trials (triangle and dashed-dotted), and CRM (star and dotted) when the total sample size N_max = 96 with assuming equal subgroup proportions ξ = (ξ₁, …, ξ₄) = (.25, .25, .25, .25).

Figure 4

Subgroup-specific weighted probability of selection (WPS) of optimal dose and probability of correctly selecting (PCS) the optimal dose for K-CRM-1-trial (square and dashed), and 1-CRM-K-trials (triangle and dashed-dotted), and CRM (star and dotted) when the total sample size N_max = 96 under the dose-toxicity scenarios 2 to 4 with assuming different subgroup proportions ξ = (.40, .30, .20, .10).

Figure 5

Subgroup-specific weighted probability of selection (WPS) of optimal dose for HB-CRM, K-CRM-1-trial, 1-CRM-K-trials, and CRM under the dose-toxicity scenarios 1 to 4 (from the first raw to the bottom), for maximum sample sizes N_max = 48, 72, 96, 120, in subgroups 1: diamond and solid, 2: square and dashed, 3: triangle and dashed-dotted, 4: star and dotted. (a) Assume equal subgroup proportions ξ = (ξ₁, …, ξ₄) = (.25, .25, .25, .25), and (b) assume different subgroup proportions ξ = (.40, .30, .20, .10).

Figure 5

Subgroup-specific weighted probability of selection (WPS) of optimal dose for HB-CRM, K-CRM-1-trial, 1-CRM-K-trials, and CRM under the dose-toxicity scenarios 1 to 4 (from the first raw to the bottom), for maximum sample sizes N_max = 48, 72, 96, 120, in subgroups 1: diamond and solid, 2: square and dashed, 3: triangle and dashed-dotted, 4: star and dotted. (a) Assume equal subgroup proportions ξ = (ξ₁, …, ξ₄) = (.25, .25, .25, .25), and (b) assume different subgroup proportions ξ = (.40, .30, .20, .10).