Applied Statistics Division, Indian Statistical Institute, Kolkata, India.
Tata Translational Cancer Research Center, Tata Medical Center, Kolkata, India.
Lifetime Data Anal. 2024 Jul;30(3):680-699. doi: 10.1007/s10985-024-09622-1. Epub 2024 Mar 1.
Linear mixed models are traditionally used for jointly modeling (multivariate) longitudinal outcomes and event-time(s). However, when the outcomes are non-Gaussian a quantile regression model is more appropriate. In addition, in the presence of some time-varying covariates, it might be of interest to see how the effects of different covariates vary from one quantile level (of outcomes) to the other, and consequently how the event-time changes across different quantiles. For such analyses linear quantile mixed models can be used, and an efficient computational algorithm can be developed. We analyze a dataset from the Acute Lymphocytic Leukemia (ALL) maintenance study conducted by Tata Medical Center, Kolkata. In this study, the patients suffering from ALL were treated with two standard drugs (6MP and MTx) for the first two years, and three biomarkers (e.g. lymphocyte count, neutrophil count and platelet count) were longitudinally measured. After treatment the patients were followed nearly for the next three years, and the relapse-time (if any) for each patient was recorded. For this dataset we develop a Bayesian quantile joint model for the three longitudinal biomarkers and time-to-relapse. We consider an Asymmetric Laplace Distribution (ALD) for each outcome, and exploit the mixture representation of the ALD for developing a Gibbs sampler algorithm to estimate the regression coefficients. Our proposed model allows different quantile levels for different biomarkers, but still simultaneously estimates the regression coefficients corresponding to a particular quantile combination. We infer that a higher lymphocyte count accelerates the chance of a relapse while a higher neutrophil count and a higher platelet count (jointly) reduce it. Also, we infer that across (almost) all quantiles 6MP reduces the lymphocyte count, while MTx increases the neutrophil count. Simulation studies are performed to assess the effectiveness of the proposed approach.
线性混合模型传统上用于联合建模（多变量）纵向结局和事件时间（s）。然而，当结局是非正态分布时，更适合使用分位数回归模型。此外，在存在一些时变协变量的情况下，了解不同协变量的效应如何从一个分位数水平（结局）到另一个分位数水平变化，以及事件时间如何在不同分位数之间变化可能会很有趣。对于这种分析，可以使用线性分位数混合模型，并可以开发出有效的计算算法。我们分析了来自加尔各答 Tata 医疗中心进行的急性淋巴细胞白血病（ALL）维持研究的数据集。在这项研究中，ALL 患者在前两年接受两种标准药物（6MP 和 MTx）治疗，并且纵向测量了三种生物标志物（例如淋巴细胞计数、中性粒细胞计数和血小板计数）。治疗后，对患者进行了近三年的随访，并记录了每位患者的复发时间（如果有）。对于这个数据集，我们为三个纵向生物标志物和复发时间开发了一个贝叶斯分位数联合模型。我们考虑为每个结果使用不对称拉普拉斯分布（ALD），并利用 ALD 的混合表示来开发 Gibbs 采样算法来估计回归系数。我们提出的模型允许不同的分位数水平用于不同的生物标志物，但仍同时估计特定分位数组合对应的回归系数。我们推断，较高的淋巴细胞计数加速了复发的机会，而较高的中性粒细胞计数和较高的血小板计数（联合）则降低了复发的机会。此外，我们推断，在（几乎）所有分位数上，6MP 降低了淋巴细胞计数，而 MTx 增加了中性粒细胞计数。进行了模拟研究以评估所提出方法的有效性。
