Knafl George J, Meghani Salimah H
School of Nursing, University of North Carolina at Chapel Hill, Chapel Hill, USA.
Department of Biobehavioral Health Sciences, School of Nursing, University of Pennsylvania, Philadelphia, USA.
Open J Stat. 2022 Aug;12(4):456-485. doi: 10.4236/ojs.2022.124029. Epub 2022 Aug 11.
To formulate and demonstrate methods for regression modeling of probabilities and dispersions for individual-patient longitudinal outcomes taking on discrete numeric values.
Three alternatives for modeling of outcome probabilities are considered. Multinomial probabilities are based on different intercepts and slopes for probabilities of different outcome values. Ordinal probabilities are based on different intercepts and the same slope for probabilities of different outcome values. Censored Poisson probabilities are based on the same intercept and slope for probabilities of different outcome values. Parameters are estimated with extended linear mixed modeling maximizing a likelihood-like function based on the multivariate normal density that accounts for within-patient correlation. Formulas are provided for gradient vectors and Hessian matrices for estimating model parameters. The likelihood-like function is also used to compute cross-validation scores for alternative models and to control an adaptive modeling process for identifying possibly nonlinear functional relationships in predictors for probabilities and dispersions. Example analyses are provided of daily pain ratings for a cancer patient over a period of 97 days.
The censored Poisson approach is preferable for modeling these data, and presumably other data sets of this kind, because it generates a competitive model with fewer parameters in less time than the other two approaches. The generated probabilities for this model are distinctly nonlinear in time while the dispersions are distinctly non-constant over time, demonstrating the need for adaptive modeling of such data. The analyses also address the dependence of these daily pain ratings on time and the daily numbers of pain flares. Probabilities and dispersions change differently over time for different numbers of pain flares.
Adaptive modeling of daily pain ratings for individual cancer patients is an effective way to identify nonlinear relationships in time as well as in other predictors such as the number of pain flares.
制定并演示针对呈现离散数值的个体患者纵向结局的概率和离散度进行回归建模的方法。
考虑了三种结局概率建模的替代方法。多项概率基于不同结局值概率的不同截距和斜率。有序概率基于不同结局值概率的不同截距和相同斜率。删失泊松概率基于不同结局值概率的相同截距和斜率。使用扩展线性混合模型估计参数，该模型基于考虑患者内相关性的多元正态密度最大化一个似然函数。提供了用于估计模型参数的梯度向量和海森矩阵的公式。似然函数还用于计算替代模型的交叉验证分数，并控制用于识别概率和离散度预测变量中可能的非线性函数关系的自适应建模过程。给出了一名癌症患者在97天内每日疼痛评分的示例分析。
删失泊松方法对于这些数据以及可能的其他此类数据集的建模更可取，因为它比其他两种方法在更短的时间内生成一个参数更少的竞争模型。该模型生成的概率在时间上明显是非线性的，而离散度在时间上明显是非恒定的，这表明需要对这类数据进行自适应建模。分析还探讨了这些每日疼痛评分对时间和每日疼痛发作次数的依赖性。不同疼痛发作次数下，概率和离散度随时间的变化不同。
对个体癌症患者的每日疼痛评分进行自适应建模是一种有效的方法，可用于识别时间以及其他预测变量（如疼痛发作次数）中的非线性关系。
