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

本提案旨在为许多应用领域中出现的重要数据类型提供统计模型和推理工具。具体来说，本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，这些计数具有称为远程依赖（LRD）或长记忆行为的复杂特征。***一般而言，时间序列计数形式的数据出现在以下应用领域：卫生保健绩效分析（例如，分析在医院急诊科服务或住院的患者人数）；监测环境污染物；分析来自金融市场的数据（例如，某只股票的每日交易计数）；公共卫生监测（例如，针对特定原因的死亡率监测）。******虽然对计数时间序列的统计建模和分析有相当多的关注，但其许多复杂方面，如LRD特征尚未得到充分解决。LRD特征通过数据的相关结构表现出来，在金融市场和医疗保健服务产生的一些数据中已经观察到这种行为。例如，多年来每天早上8点急诊科的患者数量可能有时会表现出LRD行为。除了时间LRD特征外，当在感兴趣的地理区域上的几个设施收集这些数据时，这些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。具体来说，我将研究回归模型，该模型通过空间和时间ARMA（p,q）建模方法处理计数中的短期（空间和时间）依赖关系，而时间LRD特征通过分数高斯噪声（FGN）和相关的长记忆过程处理。这是一种吸引人的方法，因为LRD通常是由于背景潜在过程，其中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讨厌的过程来考虑。fgn是通过仅使用一个参数（称为Hurst指数）来引入LRD的过程。因此，FGNs提供了一种处理LRD的方法，同时保持模型中需要估计的参数数量较低。这一研究项目产生的方法预计将帮助保健服务领域的利益攸关方，以及出现此类数据的其他应用领域的利益攸关方，根据正确的统计推断作出适当的决定。

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.