Recent works have proposed optimal subsampling algorithms to improve computational efficiency in large datasets and to design validation studies in the presence of measurement error. Existing approaches generally fall into two categories: (i) designs that optimize individualized sampling rules, where unit-specific probabilities are assigned and applied independently, and (ii) designs based on stratified sampling with simple random sampling within strata. Focusing on the logistic regression setting, we derive the asymptotic variances of estimators under both approaches and compare them numerically through extensive simulations and an application to data from the Vanderbilt Comprehensive Care Clinic cohort. Our results reinforce that stratified sampling is not merely an approximation to individualized sampling, showing instead that optimal stratified designs are often more efficient than optimal individualized designs through their elimination of between-stratum contributions to variance. These findings suggest that optimizing over the class of individualized sampling rules overlooks highly efficient sampling designs and highlight the often underappreciated advantages of stratified sampling.

翻译：近期研究提出了最优子抽样算法，以提高大型数据集的计算效率，并在存在测量误差的情况下设计验证研究。现有方法主要分为两类：(i) 优化个体化抽样规则的设计，即分配并独立应用单元特定概率；(ii) 基于分层抽样的设计，在各层内采用简单随机抽样。聚焦于逻辑回归设定，我们推导了两种方法下估计量的渐近方差，并通过大量模拟及范德比尔特综合护理诊所队列数据的应用进行了数值比较。我们的结果进一步证实分层抽样不仅仅是个体化抽样的近似，相反，通过消除层间方差贡献，最优分层设计通常比最优个体化设计更高效。这些发现表明，在个体化抽样规则类别上进行优化会忽略高效抽样设计，并凸显了分层抽样常被低估的优势。