Subgroup analysis evaluates treatment effects across multiple sub-populations. When subgroups are defined by latent memberships inferred from imperfect measurements, the analysis typically involves two inter-connected models, a latent class model and a subgroup outcome model. The classical one-stage framework, which models the joint distribution of the two models, may be infeasible with observational data containing many confounders. The two-stage framework, which first estimates the latent class model and then performs subgroup analysis using estimated latent memberships, can accommodate potential confounders but may suffer from bias issues due to misclassification of latent subgroup memberships. This paper focuses on latent subgroups inferred from binary item responses and addresses when and how a valid two-stage latent subgroup analysis can be made with observational data. We investigate the maximum misclassification rate that a valid two-stage framework can tolerate. Introducing a spectral method perspective, we propose a two-stage approach to achieve the desired misclassification rate with the blessing of many item responses. Our method accommodates high-dimensional confounders, is computationally efficient and robust to noninformative items. In observational studies, our methods lead to consistent estimation and valid inference on latent subgroup effects. We demonstrate its merit through simulation studies and an application to educational assessment data.

翻译：亚组分析用于评估不同亚群体间的治疗效果。当亚组由不完美测量推断出的潜在成员关系定义时，分析通常涉及两个相互关联的模型：潜在类别模型和亚组结果模型。经典的单一阶段框架对两个模型的联合分布进行建模，但在包含众多混杂因素的观测数据中可能不可行。两阶段框架首先估计潜在类别模型，然后使用估计的潜在成员关系进行亚组分析，能够容纳潜在的混杂因素，但可能因潜在亚组成员关系的错误分类而产生偏差问题。本文聚焦于从二元项目反应推断出的潜在亚组，探讨在观测数据下何时以及如何进行有效的两阶段潜在亚组分析。我们研究了有效两阶段框架所能容忍的最大错误分类率。通过引入谱方法视角，我们提出了一种两阶段方法，借助大量项目反应的优势达到期望的错误分类率。我们的方法能够处理高维混杂因素，计算效率高且对无信息项目具有鲁棒性。在观测性研究中，我们的方法能够实现对潜在亚组效应的一致估计和有效推断。我们通过模拟研究和教育评估数据的应用展示了该方法的优势。