ABSTRACT In biomedical studies, patients' reaction to the treatment can be different depending on their health condition at baseline. In this paper, we develop a bivariate varying-coefficient regression model for longitudinal data with the baseline outcome. The proposed model enables the exploration of the dynamic trend of response variables over time and to provide an effective treatment based on an individual's baseline level of disease by allowing the coefficients to vary with time and baseline. The varying coefficients are modelled through basis function approximation and a set of basis functions is selected by the proposed criterion based on the empirical loglikelihood. After the proposed model is fitted to data, the hypothesis test is designed to evaluate the efficacy of treatments across baseline levels. Theoretical and empirical studies confirm that the proposed methods choose the most parsimonious model consistently and compare the treatment effects successfully across baseline levels. The entire procedure is illustrated with depression data analysis.

中文翻译：

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在使用双变量变系数模型比较治疗效果时调整基线信息

摘要 在生物医学研究中，患者对治疗的反应可能会因他们在基线时的健康状况而有所不同。在本文中，我们为具有基线结果的纵向数据开发了一个双变量变系数回归模型。所提出的模型能够探索响应变量随时间的动态趋势，并通过允许系数随时间和基线变化，根据个人的基线疾病水平提供有效的治疗。变化的系数通过基函数近似建模，并通过基于经验对数似然的建议标准选择一组基函数。在建议的模型与数据拟合后，假设检验旨在评估跨基线水平的治疗效果。理论和实证研究证实，所提出的方法始终选择最简约的模型，并在基线水平上成功地比较治疗效果。整个过程通过抑郁症数据分析进行了说明。