Analyzing unequally spaced familial-longitudinal and familial-spatial data

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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.