Cumulative incidence regression for dynamic treatment regimens

Abstract

Recently dynamic treatment regimens (DTRs) have drawn considerable attention, as an effective tool for personalizing medicine. Sequential Multiple Assignment Randomized Trials (SMARTs) are often used to gather data for making inference on DTRs. In this article, we focus on regression analysis of DTRs from a two-stage SMART for competing risk outcomes based on cumulative incidence functions (CIFs). Even though there are extensive works on the regression problem for DTRs, no research has been done on modeling the CIF for SMART trials. We extend existing CIF regression models to handle covariate effects for DTRs. Asymptotic properties are established for our proposed estimators. The models can be implemented using existing software by an augmented-data approximation. We show the improvement provided by our proposed methods by simulation and illustrate its practical utility through an analysis of a SMART neuroblastoma study, where disease progression cannot be observed after death.

Keywords: Competing risks; Fine and Gray; Inverse probability weighting; Scheike model; Sequential Multiple Assignment Randomized Trial.

Fig. 1.

A two-stage SMART setup.

Fig. 2.

The estimated CIFs over time using six models. The black solid line is the true function. Gray lines for Fine–Gray-related models. Black stepwise curves for Scheike-related models. The native methods are dashed lines, the fixed weight methods are dotted lines, and the time-varying weight are long dashed lines.

Fig. 3.

The estimated CIFs for the four regimens obtained by using the WFG method with four cases while controlling for Age = 3 years, Stage4dx = 0, and Bonedx = 0. The plots in the upper row are for Ferritindx = 0, and the plots in the lower row are for Ferritindx = 1. The plots in the left column are for MYCNdx = 0, and the plots in the right column are for MYCNdx = 1.