An estimation method of marginal treatment effects on correlated longitudinal and survival outcomes

Abstract

This paper concerns treatment effects on correlated longitudinal and time to event processes. The marginal mean of the longitudinal outcome in the presence of event occurrence is often of interest from clinical and epidemiological perspectives. When the probability of the event is treatmentdependent, differences between treatment-specific longitudinal outcome means are usually not constant over time. In this paper, we propose a measure to quantify treatment effects using time-varying differences in longitudinal outcome means, which accounts for the constantly changing population composition due to event occurrences. Generalized linear mixed models (GLMM) and proportional hazards (PH) models are employed to construct the proposed measure. The proposed method is applied to analyze the motivating data arising from the study of weight loss in the Diabetes Prevention Program where weights after diabetes occurrence are systematically different from diabetes-free weights.

A likelihood based approach for joint modeling of longitudinal trajectories and informative censoring process

“…More complex models were also proposed by having the longitudinal process follow smooth trajectories including splines and some mean-zero stochastic process that allow trends to vary with time (Taylor 1994; Henderson et al 2000; Wang and Taylor 2001; Xu and Zeger 2001). Other models included the work of Ding and Wang 2008; Nathoo and Dean 2008; Rizopoulos, Verbeke, Lesaffre 2009; Wu, Liu, and Hu 2010; Jacqmin-Gadda et al 2010; Pan and Yi 2011). Most of these approaches were built on the concept of having mixed-effects longitudinal models and Cox model for the survival components and both parts are joined by shared random effects and the likelihood function is maximized using EM algorithms.…”