Modeling longitudinal binary data is challenging but common in practice. Existing methods on modeling of binary responses take no account of the fact that the correlation coefficient of binary responses must have an upper bound which is smaller than one. Ignoring this fact can lead to incorrect statistical inferences for longitudinal binary data. A novel method is proposed to model the mean and within-subject correlation coefficients for longitudinal binary data, simultaneously, by taking into account the constraints of the upper bounds. By introducing latent normally distributed random variables, the correlation coefficients of binary responses are connected to those for the latent variables, of which the correlation coefficients are modeled accordingly. A joint generalized estimating equation (GEE) method is developed for this purpose and the resulting correlation coefficients are shown to satisfy the constraints. Asymptotic normality of the parameter estimators is derived and simulation studies are made under various scenarios, showing that the proposed joint GEE method works very well even if the working covariance structures are misspecified. For illustration, the proposed method is applied to two real data practices to assess the effects of covariates on the mean and within-subject correlation coefficients.

中文翻译：

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纵向二进制数据的联合广义估计方程

纵向二进制数据建模具有挑战性，但在实践中很常见。现有的二元响应建模方法没有考虑到二元响应的相关系数必须具有小于 1 的上限这一事实。忽略这一事实可能会导致对纵向二进制数据的统计推断不正确。提出了一种新方法，通过考虑上限的约束，同时对纵向二进制数据的平均值和主体内相关系数进行建模。通过引入潜在的正态分布随机变量，二元响应的相关系数与潜在变量的相关系数相关联，其中的相关系数被相应地建模。为此目的开发了联合广义估计方程 (GEE) 方法，结果相关系数显示为满足约束条件。推导出参数估计量的渐近正态性并在各种场景下进行模拟研究，表明即使工作协方差结构被错误指定，所提出的联合 GEE 方法也能很好地工作。为了说明，所提出的方法应用于两个实际数据实践，以评估协变量对平均值和受试者内相关系数的影响。表明即使工作协方差结构被错误指定，所提出的联合 GEE 方法也能很好地工作。为了说明，所提出的方法应用于两个实际数据实践，以评估协变量对平均值和受试者内相关系数的影响。表明即使工作协方差结构被错误指定，所提出的联合 GEE 方法也能很好地工作。为了说明，所提出的方法应用于两个实际数据实践，以评估协变量对平均值和受试者内相关系数的影响。