Zhao Yang
Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, Canada.
Biom J. 2025 Oct;67(5):e70070. doi: 10.1002/bimj.70070.
Partially linear models are commonly used in observational studies of the causal effect of treatment and/or exposure when there are observed confounding variables. The models are robust and asymptotically distribution-free for testing the causal null hypothesis. In this research, we investigate methods for estimating the partially linear models with data missing at random in all the variables, including the response, the treatment, and the confounding variables. We develop a general estimation method for inference in partially linear models with nonmonotone missing at random data. It proposes using partially linear working models to improve the estimation efficiency of the standard complete case method. It can be shown that the new estimator is consistent, which does not depend on the correctness of the working models. In addition, we recommend bootstrap estimates for the asymptotic variances and semiparametric models for the missing data probabilities. It is computationally simple and can be directly implemented in standard software. Simulation studies are provided to examine its performance. A real data example with sparsely observed missingness patterns is used to illustrate the method.
当存在观测到的混杂变量时，部分线性模型常用于治疗和/或暴露因果效应的观察性研究。这些模型对于检验因果零假设具有稳健性且渐近无分布。在本研究中，我们研究了在所有变量（包括响应变量、治疗变量和混杂变量）中随机缺失数据的情况下估计部分线性模型的方法。我们开发了一种通用估计方法，用于对具有非单调随机缺失数据的部分线性模型进行推断。它建议使用部分线性工作模型来提高标准完全病例法的估计效率。可以证明，新的估计量是一致的，且不依赖于工作模型的正确性。此外，我们建议对渐近方差进行自助估计，并对缺失数据概率采用半参数模型。它计算简单，可直接在标准软件中实现。提供了模拟研究来检验其性能。使用一个具有稀疏观测缺失模式的实际数据示例来说明该方法。
