测量约束下基于替代辅助的最优抽样用于风险预测
Surrogate-assisted optimal sampling for risk prediction under measurement constraints
AI总结：
针对真实响应测量成本高且有限的问题，提出一种利用替代变量辅助的最优抽样框架，通过最小化期望交叉熵损失来分配测量预算，并构建逆概率加权估计器，实现预测性能提升与鲁棒性。
摘要：
在许多风险预测问题中，协变量和响应替代变量通常可在大规模目标人群中常规获取，而真实响应则成本高昂且仅对有限子集观测。这产生了一个设计问题：在固定测量预算下，必须决定哪些观测应接受响应测量以构建预测模型。我们提出了一种在测量约束下用于风险预测的替代辅助最优抽样框架。在目标设定中，替代变量识别出已确认的阳性病例，而替代阴性观测的响应未被观测且可选择性地测量，因此抽样设计决定了响应测量预算的分配方式。我们的框架构建了最小化期望样本外交叉熵损失主导项的最优抽样设计，并将所得设计纳入逆概率加权交叉熵估计量。所提出的设计仅依赖于协变量、替代变量和初步估计量，因此在设计阶段不需要未标记观测的响应。我们建立了所得估计量的一致性、渐近正态性和前导阶预测最优性。广泛的模拟研究和两个真实数据应用表明，所提出的设计提高了预测性能，并在替代变量错误设定和罕见结局设定下表现出鲁棒性。
英文摘要：
In many risk prediction problems, covariates and a response surrogate are routinely available for a large target population, whereas the true response is costly to ascertain and is observed only for a limited subset. This creates a design problem: one must decide which observations should receive response measurement in order to build a prediction model under a fixed measurement budget. We propose a surrogate-assisted optimal sampling framework for risk prediction under measurement constraints. In the target setting, the surrogate identifies confirmed positive cases, while responses for surrogate-negative observations remain unobserved and can be selectively measured, and thus the sampling design determines how the response measurement budget is allocated. Our framework constructs an optimal sampling design minimizing the leading term of the expected out-of-sample cross-entropy loss and incorporates the resulting design into an inverse-probability-weighted cross-entropy estimator. The proposed design depends only on covariates, the surrogate, and a preliminary estimator, and therefore does not require responses from unlabeled observations at the design stage. We establish consistency, asymptotic normality, and leading-order prediction optimality of the resulting estimator. Extensive simulation studies and two real data applications demonstrate that the proposed design improves prediction performance and exhibits robustness under surrogate misspecification and rare outcome settings.
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