目的:通常建议使用带有广义估计方程(GEE)的边际模型来分析相关的序数结果,这在纵向研究或集群随机试验(CRT)中很常见。集群内关联通常在纵向研究或CRT中感兴趣,并且可以用成对的估计方程来估计。然而,当聚类数量较小时,聚类内关联参数和方差的估计器可能会受到有限样本偏差的影响。本文的目的是介绍一种新开发的R包ORTH。使用具有有限样本偏差校正的GEE模型分析相关序数结果的Ord。
方法:R包ORTH。Ord实现了基于正交残差(ORTH)的估计的交替逻辑回归的修改版本,在边际均值和关联模型中,使用配对估计方程联合估计参数。序数响应之间的聚类内关联通过全局成对比值比(POR)建模。R包还根据矩阵乘法调整的正交化残差(MMORTH)对POR参数估计进行了有限样本偏差校正,以校正估计方程,以及具有不同协方差估计选项的偏差校正三明治估计。
结果:一项模拟研究表明,与未校正的ORTH相比,MMORTH提供的全局POR估计偏差较小,其95%置信区间的覆盖率更接近标称水平。对患者报告的正颌手术临床试验结果的分析说明了ORTH的特征。Ord.
结论:本文概述了ORTH方法,对估计方程和三明治估计器进行了偏差校正,以分析相关的序数数据,描述了ORTH的功能。OrdR包,使用仿真研究评估软件包的性能,最后说明了其在临床试验分析中的应用。
OBJECTIVE: Marginal models with generalized estimating equations (GEE) are usually recommended for analyzing correlated ordinal outcomes which are commonly seen in a longitudinal study or clustered randomized trial (CRT). Within-cluster association is often of interest in longitudinal studies or CRTs, and can be estimated with paired estimating equations. However, the estimators for within-cluster association parameters and variances may be subject to finite-sample biases when the number of clusters is small. The objective of this article is to introduce a newly developed R package ORTH.Ord for analyzing correlated ordinal outcomes using GEE models with finite-sample bias corrections.
METHODS: The R package ORTH.Ord implements a modified version of alternating logistic regressions with estimation based on orthogonalized residuals (ORTH), which use paired estimating equations to jointly estimate parameters in marginal mean and association models. The within-cluster association between ordinal responses is modeled by global pairwise odds ratios (POR). The R package also provides a finite-sample bias correction to POR parameter estimates based on matrix multiplicative adjusted orthogonalized residuals (MMORTH) for correcting estimating equations, and bias-corrected sandwich estimators with different options for covariance estimation.
RESULTS: A simulation study shows that MMORTH provides less biased global POR estimates and coverage of their 95% confidence intervals closer to the nominal level than uncorrected ORTH. An analysis of patient-reported outcomes from an orthognathic surgery clinical trial illustrates features of ORTH.Ord.
CONCLUSIONS: This article provides an overview of the ORTH method with bias-correction on both estimating equations and sandwich estimators for analyzing correlated ordinal data, describes the features of the ORTH.Ord R package, evaluates the performance of the package using a simulation study, and finally illustrates its application in an analysis of a clinical trial.