Motivated by an empirical analysis of ecological momentary assessment data (EMA) collected in a smoking cessation study, we propose a joint modeling technique for estimating the time-varying association between two intensively measured longitudinal responses: a continuous one and a binary one. A major challenge in joint modeling these responses is the lack of a multivariate distribution. We suggest introducing a normal latent variable underlying the binary response and factorizing the model into two components: a marginal model for the continuous response, and a conditional model for the binary response given the continuous response. We develop a two-stage estimation procedure and establish the asymptotic normality of the resulting estimators. We also derived the standard error formulas for estimated coefficients. We conduct a Monte Carlo simulation study to assess the finite sample performance of our procedure. The proposed method is illustrated by an empirical analysis of smoking cessation data, in which the question of interest is to investigate the association between urge to smoke, continuous response, and the status of alcohol use, the binary response, and how this association varies over time.

中文翻译：

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用于联合建模纵向数据中的二元和连续结果的时变系数模型

受戒烟研究中收集的生态瞬时评估数据 (EMA) 的实证分析的启发，我们提出了一种联合建模技术，用于估计两个密集测量的纵向响应之间的时变关联：连续响应和二元响应。联合建模这些响应的一个主要挑战是缺乏多元分布。我们建议在二元响应的基础上引入一个正常的潜在变量，并将模型分解为两个部分：连续响应的边际模型和给定连续响应的二元响应的条件模型。我们开发了一个两阶段的估计程序，并建立了所得估计量的渐近正态性。我们还推导出了估计系数的标准误差公式。我们进行了蒙特卡罗模拟研究，以评估我们程序的有限样本性能。所提出的方法通过对戒烟数据的实证分析来说明，其中感兴趣的问题是调查吸烟冲动、持续反应和饮酒状态、二元反应之间的关联，以及这种关联如何随着时间的推移而变化。时间。