Statistical methods for time series of counts with long-range dependence arising from health care settings

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This proposal is an initiative to provide statistical models and inferential tools to an important type of data that arises in many fields of applications. Specifically, this proposal is intended to deal with the statistical analysis of data sets in which the outcome of interest is a long series of temporally and spatially correlated counts with a complex feature known as Long-Range Dependence (LRD) or Long-Memory behavior. In general, data in the form of time series of counts arise in fields of applications such as: health care performance analysis (e.g., analysis of number of patients served at the emergency department of a hospital or admitted to the hospital); monitoring of environmental pollutants; analysis of data from financial markets (e.g., counts of daily transactions for a given stock); public health surveillance (e.g., surveillance of cause-specific mortality). Although there is a considerable and growing attention directed to the statistical modeling and analysis of time series of counts, many of its complex aspects such as the LRD feature have not been fully addressed. The LRD feature manifests itself through the correlation structure of the data, and such behavior has been observed in some data arising from financial markets and from health care services. For instance, the number of patients at an emergence department at 8am, observed daily over several years, may sometimes exhibit an LRD behavior. In addition to the temporal LRD feature, such data may also have spatial correlations when collected at several facilities over a geographical area of interest. In this proposal, I intend to provide a suite of statistical modeling, inference, and surveillance tools along with software packages to implement it for spatio-temporal count data with LRD features. Specifically, I will study regression models that handle short-term (spatial and temporal) dependencies in counts through spatial and temporal ARMA(p,q) modeling approach while the temporal LRD feature is dealt with via fractional Gaussian noises (FGN) and related long-memory processes. This is an appealing approach, as often the LRD is due to a background latent process in which investigators are not interested in estimating, although statistical methods must account for it as a nuisance process. The FGNs are processes that introduce LRD by using only one parameter, known as the Hurst exponent. Thus, FGNs provide a way of handling LRD while keeping low the number of parameters to be estimated in the model. The methodologies resulting from this research project are expected to aid stakeholders in health care services, and in other areas of applications where such data arise, in making proper decisions based on the correct statistical inferences.