Flexible methods for mixed longitudinal responses measured at irregular time intervals

为了测量两个纵向响应之间的关联，在传统统计不感兴趣或可能需要一些限制性假设（例如，Pearson相关系数）。在本提案中，我们打算开发灵活的方法来研究不同纵向指标的关联和时间顺序，其中指标可能是混合类型（例如，一个是连续的，另一个是二进制的），并记录在不均匀的网格上和彼此不同的时间点上。该建议建立在提出双变量连续纵向响应相关性度量的工作基础上（Dubin和Müller，2005）。在这项先前的工作中，该方法被应用于肾脏学蛋白质数据，在连续的规模上测量，并且在一个人体内测量的时间点是相同的。 该方法采用基于曲线的方法，从而允许测量具有滞后的关联的能力，即使测量不是在个体内的相同和均匀设计上测量的。 我们将继续使用基于曲线的方法，这是一种与Dubin和Müller（2005）方法相关的非参数模型，但我们也将提出一种半参数方法，该方法基于相关数据的广义线性模型框架，在灵活性和易于将该方法与标准软件结合的能力之间提供平衡。目前的建议是由一个纵向的例子，也在肾脏病学，它是不知道是否在一个响应，连续测量的蛋白质，是炎症的标志物，之前或之后的不同的反应，一个二元测量感染的变化。这些测量是混合类型的，并且在不同和不均匀的场合测量。我们希望，所提出的方法将证明是有用的跨各种科学学科。

For measuring the association between two longitudinal responses, it is quite useful to have flexible methods in case traditional statistics are not of interest or may require somewhat restrictive assumptions (e.g., using Pearson correlation coefficient). In this proposal, we intend to develop flexible methods to look at both association and temporal sequencing of distinct longitudinal measures, where the measures may be of mixed type (e.g., one continuous, the other binary) and recorded on non-uniform grids and different time points from one another. This proposal builds off work which proposed a measure of correlation for bivariate continuous longitudinal responses (Dubin and Müller, 2005). In this prior work, the method was applied to nephrology protein data, measured on a continuous scale, and where the time points for measurements within a person were the same.  This method took a curve-based approach, thereby allowing for the ability to measure associations with lags, even when the measurements were not measured on an identical and uniform design within an individual.   We will continue to use a curve-based approach, a nonparametric model related to the approach from Dubin and Müller (2005), though we will also propose a semiparametric approach, grounded in the framework for generalized linear models for correlated data, which provides a balance between flexibility and the ability to easily incorporate the method with standard software. The current proposal is motivated by a longitudinal example, also in nephrology, where it is not known whether changes in one response, a continuous measured protein that is a marker of inflammation, precedes or follows a different response, a binary measured infection. These measurements are of mixed type, and are measured at different and non-uniform occasions. We hope that the proposed methodology will prove useful across various scientific disciplines.