Group sequential design for randomized trials using “first hitting time” model

Abstract

Group sequential design (GSD) has become a popular choice in recent clinical trials as it improves trial efficiency by providing options for early termination. The implementation of traditional tests for survival analysis (eg, the log‐rank test and the Cox proportional hazard (PH) model) in the GSD setting has been widely discussed. The PH assumption is required for conventional (sequential) design, it is, however, often violated in practice. As an alternative, some generalized tests have been proposed (eg, the Max‐Combo test) and their efficacies have been established. In this article, we explore the application of a more flexible, “first hitting time” based threshold regression (TR) model to GSD. TR assumes that subjects' health status is a latent (unobservable) process, and the clinical event of interest occurs when the latent health process hits a pre‐specified boundary. The simulation results supported our findings that, in most cases, this comparable new method can successfully control type I error while providing higher early stopping opportunities in the sequential design, even when non‐proportional hazard presents.

Causal Inference in Threshold Regression and the Neural Network Extension (TRNN)

“…The Cox model may lose power significantly when the PH assumption is violated, not to mention the lack of collapsibility and interpretation issues. Alternatively, TR is capable of addressing distinct hazard types [10]. As we have shown in Section 5, the genotype or other baseline characteristics can be adjusted as part of the initial health status.…”

“…When µ < 0, a convenient and exact computational formula for evaluating RMST(τ) is given by RMST(τ) = τS(τ|µ, y 0 ) + (y 0 /|µ|)S(1/τ| − y 0 , −µ). (10) Two other formulas when µ = 0 and µ > 0 can be easily obtained by variable transformation [27].…”

“…In this application, we would like to consider sigmoid and tanh activation functions for the hidden layer. Additional hyperparameters we tuned included hidden unit number for µ network (10,15,20), hidden unit number for y 0 network (2, 5, 10), learning rate (0.002, 0.005), and delta for early stopping (0.01, 0.02). There are many other hyperparameters, such as batch size, to be tuned.…”

“…The first-hitting-time (FHT)-based threshold regression (abbreviated as TR) [7,8] is a well-accepted alternative method to analyze covariate effects on time-to-event endpoints while allowing for clinically meaningful interpretations [9][10][11]. We show in Section 4 that estimators from a TR Model using a Wiener process with linear predictors are collapsible and, hence, the TR model can be easily adapted for causal survival analysis.…”