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

这项提议是为在许多应用领域中出现的一种重要数据提供统计模型和推断工具的举措。具体地说，该建议旨在处理数据集的统计分析，其中感兴趣的结果是一长串时间和空间相关的计数，具有称为长期相关性(LRD)或长记忆行为的复杂特征。*一般而言，在以下应用领域产生计数时间序列形式的数据：卫生保健业绩分析(例如，在医院急诊科就诊或入院的病人数量分析)；环境污染物监测；金融市场数据分析(例如，某一特定股票的每日交易量)；公共卫生监测(例如，具体原因死亡率的监测)。*尽管对计数时间序列的统计建模和分析引起了越来越多的关注，但它的许多复杂方面，如LRD特征，还没有得到充分解决。LRD特征通过数据的相关性结构表现出来，这种行为已经在金融市场和医疗保健服务的一些数据中观察到。例如，几年来每天观察上午8点急诊科的病人数量，有时可能会表现出LRD行为。除了时间LRD特征外，当在感兴趣的地理区域的几个设施收集时，这种数据还可能具有空间相关性。*在本提案中，我打算提供一套统计建模、推理和监视工具以及软件包，以实现具有LRD特征的时空计数数据。具体地说，我将研究通过空间和时间ARMA(p，q)建模方法处理计数的短期(空间和时间)相关性的回归模型，而时间LRD特征通过分数高斯噪声(FGN)和相关的长记忆过程来处理。这是一种有吸引力的方法，因为劳资关系通常是由于背景潜伏的过程，调查人员对估计不感兴趣，尽管统计方法必须将其作为一个滋扰过程来考虑。FGNs是只使用一个称为赫斯特指数的参数来引入LRD的过程。因此，FGNs提供了一种处理LRD的方法，同时将模型中要估计的参数数量保持在较低水平。这一研究项目产生的方法有望帮助卫生保健服务和出现此类数据的其他应用领域的利益相关者根据正确的统计推断做出适当的决定。

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.