The failure-time outcome-dependent sampling (ODS) design is a cost-effective sampling scheme, which can improve the efficiency of the studies by selectively including certain failures to enrich the observed sample. In modeling process, taking some prior constraints on parameters into account may lead to more powerful and efficient inferences. In this paper, we study how to fit the proportional hazards model with parameter constraints to data from a failure-time ODS design. We propose constrained weighted estimation by conducting an optimization problem on a working likelihood function. The asymptotic properties of the proposed estimator are established.We develop a restricted minorization-maximization (MM) algorithm for the numerical calculation of the proposed estimator. Simulation studies are conducted to evaluate the finite-sample performance of the proposed estimator. An application to a data set from a Wilms tumor study is illustrated for the utility of the proposed method.

中文翻译：

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故障时间结果依赖抽样设计下 Cox 模型中的约束估计

故障时间结果依赖抽样 (ODS) 设计是一种具有成本效益的抽样方案，它可以通过选择性地包括某些故障来丰富观察样本来提高研究效率。在建模过程中，考虑对参数的一些先验约束可能会导致更强大和更有效的推理。在本文中，我们研究如何将具有参数约束的比例风险模型拟合到来自故障时间 ODS 设计的数据。我们通过对工作似然函数进行优化问题来提出约束加权估计。建立了所提出的估计量的渐近性质。我们开发了一种限制性的最小化-最大化(MM)算法来对所提出的估计量进行数值计算。进行模拟研究以评估所提出的估计器的有限样本性能。对来自 Wilms 肿瘤研究的数据集的应用说明了所提出方法的实用性。