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

该提案是一项倡议，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。具体而言，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，具有称为长距离依赖性（LRD）或长记忆行为的复杂特征。 * 一般来说，计数的时间序列形式的数据出现在应用领域中，例如：医疗保健性能分析（例如，分析在医院急诊部服务的或入院的患者的数量）;监测环境污染物;分析来自金融市场的数据（例如， 给定股票的每日交易计数）;公共卫生监视（例如， 具体原因死亡率的监测）。** 虽然有一个相当大的和越来越多的关注针对统计建模和分析的时间序列的计数，其许多复杂的方面，如LRD功能尚未得到充分解决。 LRD特征通过数据的相关性结构表现出来，并且已经在来自金融市场和医疗保健服务的一些数据中观察到这种行为。例如，几年来每天早上8点在急诊室观察的患者数量有时可能会表现出LRD行为。 除了时间LRD特征之外，当在感兴趣的地理区域上的多个设施处收集时，这样的数据还可以具有空间相关性。** 在本提案中，我打算提供一套统计建模、推理和监视工具，沿着软件包，以实现具有LRD功能的时空计数数据。具体来说，我将研究回归模型，通过空间和时间的阿尔马（p，q）建模方法处理短期（空间和时间）的依赖性计数，而时间的LRD功能是通过分数高斯噪声（FGN）和相关的长记忆过程处理。这是一个有吸引力的方法，因为LRD通常是由于背景潜在的过程中，调查人员不感兴趣的估计，虽然统计方法必须考虑它作为一个滋扰过程。FGN是通过仅使用一个参数（称为Hurst指数）引入LRD的过程。因此，FGN提供了一种处理LRD的方式，同时保持模型中待估计的参数的数量较低。从这个研究项目产生的方法，预计将帮助利益相关者在医疗保健服务，并在其他领域的应用程序中出现这样的数据，在正确的统计推断的基础上作出适当的决定。

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.