Modelling multilevel nonlinear treatment‐by‐covariate interactions in cluster randomized controlled trials using a generalized additive mixed model

协变量 多级模型 混合模型 随机效应模型 相互作用 广义线性混合模型 统计 数学 线性模型 分层数据库模型 随机对照试验 星团(航天器) 计算机科学 荟萃分析 数据挖掘 医学 内科学 外科 程序设计语言
作者
Sun‐Joo Cho,Kristopher J. Preacher,Haley E. Yaremych,Matthew Naveiras,Douglas Fuchs,Lynn S. Fuchs
出处
期刊:British Journal of Mathematical and Statistical Psychology [Wiley]
卷期号:75 (3): 493-521 被引量:5
标识
DOI:10.1111/bmsp.12265
摘要

A cluster randomized controlled trial (C-RCT) is common in educational intervention studies. Multilevel modelling (MLM) is a dominant analytic method to evaluate treatment effects in a C-RCT. In most MLM applications intended to detect an interaction effect, a single interaction effect (called a conflated effect) is considered instead of level-specific interaction effects in a multilevel design (called unconflated multilevel interaction effects), and the linear interaction effect is modelled. In this paper we present a generalized additive mixed model (GAMM) that allows an unconflated multilevel interaction to be estimated without assuming a prespecified form of the interaction. R code is provided to estimate the model parameters using maximum likelihood estimation and to visualize the nonlinear treatment-by-covariate interaction. The usefulness of the model is illustrated using instructional intervention data from a C-RCT. Results of simulation studies showed that the GAMM outperformed an alternative approach to recover an unconflated logistic multilevel interaction. In addition, the parameter recovery of the GAMM was relatively satisfactory in multilevel designs found in educational intervention studies, except when the number of clusters, cluster sizes, and intraclass correlations were small. When modelling a linear multilevel treatment-by-covariate interaction in the presence of a nonlinear effect, biased estimates (such as overestimated standard errors and overestimated random effect variances) and incorrect predictions of the unconflated multilevel interaction were found.
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