Analyzing unequally spaced familial-longitudinal and familial-spatial data

在纵向研究中，随着时间的推移，从大量实验/家庭单位中收集少量重复观察结果以及相关协变量。例如，许多研究人员研究了59例癫痫患者的反复发作次数，将其作为各种协变量（如年龄和基线发作率等）的函数。为了适应重复计数数据之间的相关性，研究人员使用等间隔泊松计数的动态模型来研究重复发作计数。很明显，癫痫发作可以发生在不规则间隔的时间，同一家庭的成员，这可能导致不规则间隔重复计数的一些家庭成员。由于调查的设计、预约的间隔不均匀以及测量之间的公共假期或周末，也可能出现间隔不均匀的家庭纵向（FL）反应。我们注意到，一般来说，不等间隔的FL测量可以是二元（如哮喘状态），连续（如家庭（HH）债务）或计数（就诊次数）。据我们所知，由于非等间隔重复响应之间的复杂相关性，分析非等间隔FL数据的方法的发展尚未得到充分解决。因此，在本研究的第一部分中，我们将开发和研究考虑到FL连续、计数和二进制数据中响应之间关联的复杂结构的动态模型。我们研究计划的第二个目标将是分析多变量响应，以及从大量空间位置收集的多维协变量。例如，在一项关于HH债务的全国性研究中，可以收集来自不同空间位置的大量HH的多变量响应以及协变量信息，如住宅价值、HH规模和HH收入等。显然，来自每个HH的多变量响应和来自同一邻域的HH的响应可能是相关的。在离中心位置固定距离内的HHs自然会构成相关位置的集群。一些HHs也可能属于多个集群。然后，这些HHs将在数据中引起移动的空间相关性。我们的目标是开发和测试用于分析多变量/家族空间（FS）数据的模型，该模型将考虑到相邻位置的观测结果之间基于移动簇的空间相关性，也考虑到来自同一位置的响应之间的家族相关性。我们将通过密集的模拟研究来检查我们的方法的性能，并演示如何将这些方法应用于实际数据。硕士生和博士生代表着不同的背景和性别平等，期望他们在培训期间为研究做出贡献。

In longitudinal studies, a small number of repeated observations, along with associated covariates are collected over time from a large number of experimental/family units. As an example, many researchers have studied repeated seizure counts of 59 individuals with epilepsy as a function of various covariates such as age and baseline seizure rate, amongst others. In order to accommodate the correlations among the repeated count data, researchers have used dynamic models for equally spaced Poisson counts to study the repeated seizure counts. Clearly, seizures can occur at irregularly spaced time intervals for members of the same family which may lead to irregularly spaced repeated counts for some individuals in the family. Unequally spaced familial-longitudinal (FL) responses can also occur due to the design of an investigation, unequally spaced appointments and public holidays or weekends between measurements. We note that, in general, unequally spaced FL measurements can be binary (e.g. asthma status), continuous (e.g. household (HH) debt), or counts (number of physician visits). To the best of our knowledge, the development of methods for analysis of unequally spaced FL data have not been adequately addressed because of the complicated correlation between unequally spaced repeated responses. Therefore, in the first part of this research, we will develop and study dynamic models that will take into account the complicated structure of the correlation between responses in FL continuous, count and binary data. A second objective of our program of research will be the analysis of multivariate responses, along with multidimensional covariates that are collected from a large number of spatial locations. For instance, in a national study on HH debt, one may collect multivariate responses from a large number of HHs at different spatial locations along with covariate information such as value of dwelling, HH size and HH income, amongst others. Clearly, the multivariate responses from each HH and the responses from HHs in the same neighborhood are likely to be correlated. HHs within a fixed distance from a central location will then naturally constitute a cluster of correlated locations. It is also possible for some HHs to belong to more than one cluster. These HHs will then induce a moving spatial correlation in the data. Our objective is to develop and test models for the analysis of multivariate/familial-spatial (FS) data, that will take into account the moving-cluster based spatial correlation between observations at neighboring locations and also account for the familial correlation between responses from the same location. We will examine the performance of our methods through an intensive simulation study and also demonstrate how the methods can be applied to real data. Masters and doctorate students, representing diverse backgrounds and gender equity, are expected to be trained and contribute to the research during their training.