Arizona State University, Tempe, AZ, USA.
Phoenix Children's Hospital, Phoenix, AZ, USA.
Prev Sci. 2023 Apr;24(3):505-516. doi: 10.1007/s11121-021-01262-3. Epub 2021 Jul 7.
Growth mixture models (GMMs) are applied to intervention studies with repeated measures to explore heterogeneity in the intervention effect. However, traditional GMMs are known to be difficult to estimate, especially at sample sizes common in single-center interventions. Common strategies to coerce GMMs to converge involve post hoc adjustments to the model, particularly constraining covariance parameters to equality across classes. Methodological studies have shown that although convergence is improved with post hoc adjustments, they embed additional tenuous assumptions into the model that can adversely impact key aspects of the model such as number of classes extracted and the estimated growth trajectories in each class. To facilitate convergence without post hoc adjustments, this paper reviews the recent literature on covariance pattern mixture models, which approach GMMs from a marginal modeling tradition rather than the random effect modeling tradition used by traditional GMMs. We discuss how the marginal modeling tradition can avoid complexities in estimation encountered by GMMs that feature random effects, and we use data from a lifestyle intervention for increasing insulin sensitivity (a risk factor for type 2 diabetes) among 90 Latino adolescents with obesity to demonstrate our point. Specifically, GMMs featuring random effects-even with post hoc adjustments-fail to converge due to estimation errors, whereas covariance pattern mixture models following the marginal model tradition encounter no issues with estimation while maintaining the ability to answer all the research questions.
增长混合模型(GMM)应用于具有重复测量的干预研究中,以探索干预效果的异质性。然而,传统的 GMM 很难估计,尤其是在单中心干预研究中常见的样本量下。强制 GMM 收敛的常用策略涉及对模型进行事后调整,特别是将协方差参数约束为类间相等。方法学研究表明,尽管事后调整可以提高收敛性,但它们会将更多脆弱的假设嵌入到模型中,从而对模型的关键方面产生不利影响,例如提取的类别数量和每个类别的估计增长轨迹。为了在不进行事后调整的情况下促进收敛,本文回顾了协方差模式混合模型的最新文献,该模型从边缘建模传统而不是传统 GMM 使用的随机效应建模传统来接近 GMM。我们讨论了边缘建模传统如何避免具有随机效应的 GMM 遇到的估计复杂性,我们使用了一项生活方式干预的肥胖 90 名拉丁裔青少年胰岛素敏感性增加(2 型糖尿病的危险因素)的数据来证明我们的观点。具体来说,具有随机效应的 GMM——即使进行了事后调整——也由于估计误差而无法收敛,而遵循边缘模型传统的协方差模式混合模型在保持回答所有研究问题的能力的同时,不会遇到估计问题。