Knafl George J, Meghani Salimah H
School of Nursing, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA.
Department of Biobehavioral Health Sciences, School of Nursing, University of Pennsylvania, Philadelphia, PA, USA.
Open J Stat. 2021 Oct;11(5):633-654. doi: 10.4236/ojs.2021.115038. Epub 2021 Sep 30.
The purpose of this article is to investigate approaches for modeling individual patient count/rate data over time accounting for temporal correlation and non-constant dispersions while requiring reasonable amounts of time to search over alternative models for those data. This research addresses formulations for two approaches for extending generalized estimating equations (GEE) modeling. These approaches use a likelihood-like function based on the multivariate normal density. The first approach augments standard GEE equations to include equations for estimation of dispersion parameters. The second approach is based on estimating equations determined by partial derivatives of the likelihood-like function with respect to all model parameters and so extends linear mixed modeling. Three correlation structures are considered including independent, exchangeable, and spatial autoregressive of order 1 correlations. The likelihood-like function is used to formulate a likelihood-like cross-validation (LCV) score for use in evaluating models. Example analyses are presented using these two modeling approaches applied to three data sets of counts/rates over time for individual cancer patients including pain flares per day, as needed pain medications taken per day, and around the clock pain medications taken per day per dose. Means and dispersions are modeled as possibly nonlinear functions of time using adaptive regression modeling methods to search through alternative models compared using LCV scores. The results of these analyses demonstrate that extended linear mixed modeling is preferable for modeling individual patient count/rate data over time, because in example analyses, it either generates better LCV scores or more parsimonious models and requires substantially less time.
本文的目的是研究对个体患者计数/率随时间变化的数据进行建模的方法，该方法要考虑时间相关性和非恒定离散度，同时需要合理的时间来搜索这些数据的替代模型。本研究探讨了两种扩展广义估计方程（GEE）建模方法的公式。这些方法使用基于多元正态密度的似然函数。第一种方法是扩充标准GEE方程，使其包含离散度参数估计方程。第二种方法基于由似然函数关于所有模型参数的偏导数确定的估计方程，从而扩展了线性混合建模。考虑了三种相关结构，包括独立、可交换和一阶空间自回归相关。似然函数用于制定一个似然交叉验证（LCV）分数，用于评估模型。给出了使用这两种建模方法应用于个体癌症患者随时间变化的计数/率的三个数据集的示例分析，包括每天的疼痛发作次数、每天按需服用的止痛药物以及每天每剂量的全天候止痛药物。使用自适应回归建模方法将均值和离散度建模为时间的可能非线性函数，以便通过使用LCV分数比较的替代模型进行搜索。这些分析结果表明，扩展线性混合建模对于随时间变化的个体患者计数/率数据建模更可取，因为在示例分析中，它要么生成更好的LCV分数，要么生成更简约的模型，并且所需时间大大减少。
