Semiparametric joint modeling to estimate the treatment effect on a longitudinal surrogate with application to chronic kidney disease trials

In clinical trials where long follow-up is required to measure the primary outcome of interest, there is substantial interest in using an accepted surrogate outcome that can be measured earlier in time or with less cost to estimate a treatment effect. For example, in clinical trials of chronic kidney disease, the effect of a treatment is often demonstrated on a longitudinal surrogate, the change of the longitudinal outcome (glomerular filtration rate, GFR) per year or GFR slope. However, estimating the effect of a treatment on the GFR slope is complicated by the fact that GFR measurement can be terminated by the occurrence of a terminal event, such as death or kidney failure. Thus, to estimate this effect, one must consider both the longitudinal GFR trajectory and the terminal event process. In this paper, we build a semiparametric framework to jointly model the longitudinal outcome and the terminal event, where the model for the longitudinal outcome is semiparametric, the relationship between the longitudinal outcome and the terminal event is nonparametric, and the terminal event is modeled via a semiparametric Cox model. The proposed semiparametric joint model is flexible and can be easily extended to include a nonlinear trajectory of the longitudinal outcome. An estimating equation based method is proposed to estimate the treatment effect on the longitudinal surrogate outcome (eg, GFR slope). Theoretical properties of the proposed estimators are derived, and finite sample performance is evaluated through simulation studies. We illustrate the proposed method using data from the Reduction of Endpoints in NIDDM with the Angiotensin II Antagonist Losartan (RENAAL) trial to examine the effect of Losartan on GFR slope.