Online Program

Principal Surrogacy in a Time-to-Event Setting

*Michael Elliott, University of Michigan 
Xin Gao, FDA 

Keywords: Causal modeling; Potential outcome; Principal stratification; Principal surrogacy; gamma frailty

Surrogate evaluation receives considerable attention in the recent years due to the possibility to lower medical costs or shorten the duration of medical studies. However, conventional surrogate evaluation methods fail to provide a causal interpretation, as surrogate markers that are conditioned on in regression modeling are post- randomization variables. Principal surrogacy, defined based on the concept of principal stratification (Frangakis and Rubin, 2002), overcomes such shortcomings. The principal surrogacy literature focuses on normally distributed continuous primary outcomes or binary outcomes. In this article, we propose a shared gamma frailty proportional hazard causal model to study principal surrogacy for time-to-event outcomes. The proposed model is constructed under the potential outcome framework with a principal stratication approach, and a gamma frailty model is used to associate the potential outcomes of an individual under different treatment arms. We define the principal hazard ratio, expected associative effect and expected dissociative effect to evaluate principal surrogacy. A Bayesian estimation method using a Markov chain Monte Carlo algorithm is adopted for model estimation due to the complicated missing data structure. We illustrate the proposed model within a randomized clinical trial of colorectal cancer to study disease free survival as a principal surrogate for an overall survival primary outcome.