Partial least squares (PLS) regression is a popular alternative to ordinary least squares regression because of its superior prediction performance demonstrated in many cases. In various contemporary applications, the predictors include both continuous and categorical variables. A common practice in PLS regression is to treat the categorical variable as continuous. However, studies find that this practice may lead to biased estimates and invalid inferences (Schuberth et al., 2018). Based on a connection between the envelope model and PLS, we develop an envelope-based partial PLS estimator that considers the PLS regression on the conditional distributions of the response(s) and continuous predictors on the categorical predictors. Root-n consistency and asymptotic normality are established for this estimator. Numerical study shows that this approach can achieve more efficiency gains in estimation and produce better predictions. The method is applied for the identification of cytokine-based biomarkers for COVID-19 patients, which reveals the association between the cytokine-based biomarkers and patients' clinical information including disease status at admission and demographical characteristics. The efficient estimation leads to a clear scientific interpretation of the results.

中文翻译：

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基于包络的偏偏最小二乘法应用于基于细胞因子的 COVID-19 生物标志物分析


偏最小二乘 (PLS) 回归是普通最小二乘回归的流行替代方案，因为它在许多情况下表现出卓越的预测性能。在各种当代应用中，预测变量包括连续变量和分类变量。 PLS 回归的常见做法是将分类变量视为连续变量。然而，研究发现这种做法可能会导致估计偏差和无效推论（Schuberth et al., 2018）。基于包络模型和 PLS 之间的联系，我们开发了一种基于包络的部分 PLS 估计器，该估计器考虑响应条件分布的 PLS 回归和分类预测器的连续预测器。为此估计量建立了根 n 一致性和渐近正态性。数值研究表明，这种方法可以提高估计效率并产生更好的预测。该方法应用于识别 COVID-19 患者基于细胞因子的生物标志物，揭示了基于细胞因子的生物标志物与患者临床信息（包括入院时的疾病状况和人口统计特征）之间的关联。有效的估计可以对结果进行清晰的科学解释。