The Cox proportional hazards model is typically used to analyze time‐to‐event data. If the event of interest is rare and covariates are difficult or expensive to collect, the nested case‐control (NCC) design provides consistent estimates at reduced costs with minimal impact on precision if the model is specified correctly. If our scientific goal is to conduct inference regarding an association of interest, it is essential that we specify the model a priori to avoid multiple testing bias. We cannot, however, be certain that all assumptions will be satisfied so it is important to consider robustness of the NCC design under model misspecification. In this manuscript, we show that in finite sample settings where the functional form of a covariate of interest is misspecified, the estimates resulting from the partial likelihood estimator under the NCC design depend on the number of controls sampled at each event time. To account for this dependency, we propose an estimator that recovers the results obtained using using the full cohort, where full covariate information is available for all study participants. We present the utility of our estimator using simulation studies and show the theoretical properties. We end by applying our estimator to motivating data from the Alzheimer's Disease Neuroimaging Initiative.

中文翻译：

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嵌套案例控制设计中错误指定协变量函数形式的鲁棒估计

Cox比例风险模型通常用于分析事件时间数据。如果感兴趣的事件很少发生，并且协变量难以收集或昂贵，那么如果正确指定模型，则嵌套案例控制（NCC）设计将以降低的成本提供一致的估计，并且对精度的影响最小。如果我们的科学目标是对感兴趣的关联进行推断，则必须事先指定模型以避免多重测试偏差。但是，我们不能确定是否满足所有假设，因此重要的是考虑模型错误指定下NCC设计的稳健性。在这份手稿中，我们证明了在有限的样本设置中，错误指定了感兴趣的协变量的函数形式，在NCC设计下，由部分似然估计器得出的估计值取决于每个事件时间采样的控件数量。为了解决这种依赖性，我们提出了一种估计器，该估计器可以恢复使用完整队列获得的结果，其中所有研究参与者都可以获得完整的协变量信息。我们通过仿真研究介绍了估算器的效用，并显示了理论特性。最后，我们将估算器应用于来自阿尔茨海默氏病神经成像计划的数据。我们通过仿真研究介绍了估算器的效用，并显示了理论特性。最后，我们将估算器应用于来自阿尔茨海默氏病神经成像计划的数据。我们通过仿真研究介绍了估算器的效用，并显示了理论特性。最后，我们将估算器应用于激发阿尔茨海默氏病神经影像学计划的数据。