Li Wei, Chen Sophie Yu-Pu, Rong Alan
a Data Science , Astellas Pharma Global Development, Inc ., Northbrook , Illinois , USA.
b Department of Biostatistics , University of Michigan , Ann Arbor , Michigan , USA.
J Biopharm Stat. 2019;29(2):229-243. doi: 10.1080/10543406.2018.1534857. Epub 2018 Oct 25.
In randomized controlled trials with delayed treatment effect, there is a delay period before the experimental therapy starts to exhibit a beneficial effect. The phenomenon of delayed treatment effect is often observed in the emerging and important field of immuno-oncology. It is important to estimate the duration of delay as this information helps in characterizing the pattern of comparative treatment effect, understanding the mechanism of action of the experimental therapy, and forming optimal treatment strategies. For a fixed delay time, we propose a maximum likelihood estimator and evaluate its asymptotic properties via simulation. We further evaluate two functions that link the pre- and postdelay hazard ratios to the average hazard ratio given a fixed delay time. For the case of random delay time, where the delay time may vary from patient to patient, we propose a semiparametric joint survival model for delay time and event time to estimate the mean delay time and the postdelay hazard ratio, assuming a Beta distribution for the delay time. We describe an extension of the model to estimate subgroup-specific mean delay times. Simulation study and application to data from a clinical trial in colon cancer patients demonstrate the robustness of the proposed model.
在具有延迟治疗效果的随机对照试验中，在实验性治疗开始呈现有益效果之前存在一个延迟期。延迟治疗效果现象在免疫肿瘤学这个新兴且重要的领域中经常被观察到。估计延迟持续时间很重要，因为该信息有助于刻画比较治疗效果的模式、理解实验性治疗的作用机制以及形成最优治疗策略。对于固定的延迟时间，我们提出一种最大似然估计器，并通过模拟评估其渐近性质。我们进一步评估两个函数，它们在给定固定延迟时间的情况下将延迟前和延迟后的风险比与平均风险比联系起来。对于随机延迟时间的情况，即延迟时间可能因患者而异，我们提出一个用于延迟时间和事件时间的半参数联合生存模型，以估计平均延迟时间和延迟后的风险比，假设延迟时间服从贝塔分布。我们描述了该模型的一个扩展，用于估计亚组特定的平均延迟时间。模拟研究以及对结肠癌患者临床试验数据的应用证明了所提出模型的稳健性。
