Oncology Clinical Trial Design Planning Based on a Multistate Model That Jointly Models Progression-Free and Overall Survival Endpoints

Abstract

When planning an oncology clinical trial, the usual approach is to assume proportional hazards and even an exponential distribution for time-to-event endpoints. Often, besides the gold-standard endpoint overall survival (OS), progression-free survival (PFS) is considered as a second confirmatory endpoint. We use a survival multistate model to jointly model these two endpoints and find that neither exponential distribution nor proportional hazards will typically hold for both endpoints simultaneously. The multistate model provides a stochastic process approach to model the dependency of such endpoints neither requiring latent failure times nor explicit dependency modeling such as copulae. We use the multistate model framework to simulate clinical trials with endpoints OS and PFS and show how design planning questions can be answered using this approach. In particular, nonproportional hazards for at least one of the endpoints are a consequence of OS and PFS being dependent and are naturally modeled to improve planning. We then illustrate how clinical trial design can be based on simulations from a multistate model. Key applications are coprimary endpoints and group-sequential designs. Simulations for these applications show that the standard simplifying approach may very well lead to underpowered or overpowered clinical trials. Our approach is quite general and can be extended to more complex trial designs, further endpoints, and other therapeutic areas. An R package is available on CRAN.

FIGURE 1

Multistate model for oncology endpoints PFS and OS.

FIGURE 2

Transition hazards, survival functions, and hazard ratios for the Scenario 1. The black dashed line is the time‐averaged OS HR, cf. Table 1.

FIGURE 3

Transition hazards, survival functions, and hazard ratios for the Scenario 2. The blue dashed line is the time‐averaged OS HR, cf. Table 1.

FIGURE 4

Transition hazards, survival functions, and hazard ratios for the Scenario 3. The blue dashed line is the time‐averaged OS HR, cf. Table 1.

FIGURE 5

Transition hazards, survival functions, and hazard ratios for the Scenario 4. The blue dashed line is the time‐averaged OS HR, cf. Table 1.

FIGURE 6

Simulation steps for simple study design with two coprimary endpoints. Results are shown for Scenario 1.

FIGURE 7

Simulation steps for the group‐sequential design with the results of Scenario 1. IA: interim analysis; FA: final analysis.

FIGURE 8

Comparison of survival functions of OS: as specified by the IDM versus fulfilling the assumption of constant OS hazards.