We propose a regression framework to analyze outcomes that are indirectly observed via one or multiple proxies. Semiparametric transformation models, including Cox proportional hazards regression, turn out to be well suited to model the association between the covariates and the unobserved outcome. By coupling this regression model to a semiparametric measurement model, we can estimate these associations without requiring calibration data and without imposing strong functional assumptions on the relationship between the unobserved outcome and its proxy. When multiple proxies are available, we propose a data‐driven aggregation resulting in an improved proxy. We empirically validate the proposed methodology in a simulation study, revealing good finite sample properties, especially when multiple proxies are aggregated. The methods are demonstrated on two case studies.

中文翻译：

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间接观测结果的半参数线性变换模型

我们提出了一种回归框架来分析通过一个或多个代理间接观察到的结果。半参数转换模型（包括Cox比例风险回归）证明非常适合于建模协变量和未观察到的结果之间的关联。通过将此回归模型耦合到半参数测量模型，我们可以估计这些关联，而无需校准数据，也无需对未观察到的结果与其代理之间的关系强加强有力的功能假设。当有多个代理可用时，我们建议进行数据驱动的聚合，从而改进代理。我们在仿真研究中以经验方式验证了所提出的方法，揭示了良好的有限样本属性，尤其是当多个代理聚合时。