Department of Biostatistics, Princess Margaret Cancer Centre, 7989University Health Network, Toronto, Ontario, Canada.
Dalla Lana School of Public Health, 7938University of Toronto, Toronto, Ontario, Canada.
Stat Methods Med Res. 2022 Feb;31(2):361-371. doi: 10.1177/09622802211061634. Epub 2021 Dec 6.
Functional regression has been widely used on longitudinal data, but it is not clear how to apply functional regression to microbiome sequencing data. We propose a novel functional response regression model analyzing correlated longitudinal microbiome sequencing data, which extends the classic functional response regression model only working for independent functional responses. We derive the theory of generalized least squares estimators for predictors' effects when functional responses are correlated, and develop a data transformation technique to solve the computational challenge for analyzing correlated functional response data using existing functional regression method. We show by extensive simulations that our proposed method provides unbiased estimations for predictors' effect, and our model has accurate type I error and power performance for correlated functional response data, compared with classic functional response regression model. Finally we implement our method to a real infant gut microbiome study to evaluate the relationship of clinical factors to predominant taxa along time.
功能回归已被广泛应用于纵向数据，但对于如何将功能回归应用于微生物组测序数据，目前还不清楚。我们提出了一种新的功能响应回归模型，用于分析相关的纵向微生物组测序数据，该模型扩展了经典的功能响应回归模型，仅适用于独立的功能响应。我们推导了在功能响应相关时，用于预测器效应的广义最小二乘估计量的理论，并开发了一种数据转换技术，以解决使用现有功能回归方法分析相关功能响应数据的计算挑战。通过广泛的模拟，我们表明，与经典的功能响应回归模型相比，我们提出的方法为预测器效应提供了无偏估计，并且我们的模型对于相关的功能响应数据具有准确的Ⅰ型错误和功效性能。最后，我们将我们的方法应用于真实的婴儿肠道微生物组研究中，以评估临床因素与随着时间推移的主要分类群之间的关系。
