An adaptive treatment length strategy is a sequential stage-wise treatment strategy where a subject's treatment begins at baseline and one chooses to stop or continue treatment at each stage provided the subject has been continuously treated. The effects of treatment are assumed to be cumulative and, therefore, the effect of treatment length on clinical endpoint, measured at the end of the study, is of primary scientific interest. At the same time, adverse treatment-terminating events may occur during the course of treatment that require treatment be stopped immediately. Because the presence of a treatment-terminating event may be strongly associated with the study outcome, the treatment-terminating event is informative. In observational studies, decisions to stop or continue treatment depend on covariate history that confounds the relationship between treatment length on outcome. We propose a new risk-set weighted estimator of the mean potential outcome under the condition that time-dependent covariates update at a set of common landmarks. We show that our proposed estimator is asymptotically linear given mild assumptions and correctly specified working models. Specifically, we study the theoretical properties of our estimator when the nuisance parameters are modeled using either parametric or semiparametric methods. The finite sample performance and theoretical results of the proposed estimator are evaluated through simulation studies and demonstrated by application to the Enhanced Suppression of the Platelet Receptor IIb/IIIa with Integrilin Therapy (ESPRIT) infusion trial data.

中文翻译：

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连续时间自适应治疗长度策略下的平均潜在结果估计

适应性治疗长度策略是一种连续的分阶段治疗策略，其中受试者的治疗从基线开始，并且如果受试者已连续接受治疗，则选择在每个阶段停止或继续治疗。假设治疗的效果是累积的，因此，在研究结束时测量的治疗时间对临床终点的影响是主要的科学兴趣。同时，治疗过程中可能发生不良的终止治疗事件，需要立即停止治疗。由于治疗终止事件的存在可能与研究结果密切相关，因此治疗终止事件可提供信息。在观察性研究中，停止或继续治疗的决定取决于混淆治疗时间与结果之间关系的协变量历史。我们提出了一种新的平均潜在结果的风险集加权估计量，条件是时间相关的协变量在一组共同的地标处更新。我们表明，我们提出的估计量在给定温和假设和正确指定的工作模型的情况下是渐近线性的。具体来说，当使用参数或半参数方法对有害参数建模时，我们研究了估计器的理论特性。所提出的估计器的有限样本性能和理论结果通过模拟研究进行评估，并通过应用于使用整合素疗法 (ESPRIT) 输注试验数据增强抑制血小板受体 IIb/IIIa 来证明。