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 (CKD), the effect of a treatment is often demonstrated on a surrogate outcome, the longitudinal trajectory of glomerular filtration rate (GFR). However, estimating the effect of a treatment on the GFR trajectory 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 outcome of GFR, and the terminal event process. Available estimation methods either impose restrictive parametric assumptions with corresponding maximum likelihood estimation that is computationintensive or other assumptions not appropriate for the GFR setting. 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, and the relationship between the longitudinal outcome and the terminal event is nonparametric. The proposed semiparametric joint model is flexible and can be extended to include nonlinear trajectory of the longitudinal outcome easily. An estimating equation based method is proposed to estimate the treatment effect on the slope of the longitudinal outcome (e.g., GFR slope). Theoretical properties of the proposed estimators are derived. Finite sample performance of the proposed method 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) trail to examine the effect of Losartan on GFR slope.

翻译：在需要长期随访以测量主要结局指标的临床试验中，利用可更早测量或成本更低的公认替代结局来估计治疗效应具有重要价值。例如，在慢性肾脏病（CKD）临床试验中，治疗效应常通过替代结局——肾小球滤过率（GFR）的纵向轨迹来验证。然而，由于GFR测量可能因死亡或肾衰竭等终点事件的发生而终止，估计治疗对GFR轨迹的影响变得复杂。因此，为估计该效应，必须同时考虑GFR的纵向结局与终点事件过程。现有估计方法要么采用限制性参数假设及计算密集的相应最大似然估计，要么采用不适用于GFR场景的其他假设。本文构建了一个半参数框架来联合建模纵向结局与终点事件，其中纵向结局模型为半参数形式，而纵向结局与终点事件的关系为非参数形式。所提出的半参数联合模型具有灵活性，可轻松扩展至包含非线性纵向轨迹的情形。我们提出了一种基于估计方程的方法来估计治疗对纵向结局斜率（如GFR斜率）的效应，推导了所提估计量的理论性质，并通过模拟研究评估了该方法的有限样本表现。最后，我们应用"血管紧张素II拮抗剂氯沙坦降低非胰岛素依赖型糖尿病终点事件研究（RENAAL）"的数据，演示了所提方法在检验氯沙坦对GFR斜率效应中的应用。