Precision Bayesian phase I-II dose-finding based on utilities tailored to prognostic subgroups

Abstract

A Bayesian phase I-II design is presented that optimizes the dose of a new agent within predefined prognostic subgroups. The design is motivated by a trial to evaluate targeted agents for treating metastatic clear cell renal carcinoma, where a prognostic risk score defined by clinical variables and biomarkers is well established. Two clinical outcomes are used for dose-finding, time-to-toxicity during a prespecified follow-up period, and efficacy characterized by ordinal disease status evaluated at the end of follow-up. A joint probability model is constructed for these outcomes as functions of dose and subgroup. The model performs adaptive clustering of adjacent subgroups having similar dose-outcome distributions to facilitate borrowing information across subgroups. To quantify toxicity-efficacy risk-benefit trade-offs that may differ between subgroups, the objective function is based on outcome utilities elicited separately for each subgroup. In the context of the renal cancer trial, a design is constructed and a simulation study is presented to evaluate the design's reliability, safety, and robustness, and to compare it to designs that either ignore subgroups or run a separate trial within each subgroup.

Keywords: Bayesian phase I-II clinical trial design; adaptive randomization; clustering; dose finding; patient prognostic subgroups.

FIGURE 1

Illustration of subgroup-specific utilities U_g. A, The utility of toxicity for subgroup g, U_T,g(Y_T), $Y_{\text{T}}\in {ℝ}^{+}$. B-D, The utilities of a bivariate outcome, U_g(Y) with Y = (Y_T, Y_E), for subgroups 1, 2, and 3, respectively. Y_E = 0, 1, 2, and 3 represent PD, SD, PR, and CR, respectively

FIGURE 2

Comparison between D-Sub and D-Comb. A-C, Histograms of differences in $p_m^{\text{sel}}(g)$ between D-Sub and D-Comb. D-F, Histograms of differences in $p_m^{\text{unacc}}(g)$ between D-Sub and D-Comb for the truly unacceptable doses and those between D-Comb and D-Sub for the truly acceptable doses. G-I, Histograms of differences in $n_m^{\text{ptrt}}(g)$ between D-Sub and D-Comb for the truly unacceptable doses. The left, middle, and right columns are for subgroups g = 1 (favorable), g = 2 (intermediate), and g = 3 (poor). A positive value indicates better performance of D-Sub than D-Comb in Panels A-F, and a worse performance in Panels G-I

FIGURE 3

Comparison between D-Sub and D-Sep. A-C, Histograms of differences in $p_m^{\text{sel}}(g)$ between the D-Sub and D-Sep designs. D-F, Histograms of differences in $p_m^{\text{unacc}}(g)$ between D-Sub and D-Sep for the truly unacceptable doses and those between D-Sep and D-Sub for the truly acceptable doses. G-I, Histograms of differences in $n_m^{\text{ptrt}}(g)$ between D-Sub and D-Sep for the truly unacceptable doses. The left, middle, and right columns are for subgroups g = 1 (favorable), g = 2 (intermediate), and g = 3 (poor). A positive value indicates better performance of D-Sub than D-Sep in Panels A-F, and a worse performance in Panels G-I