Advancing Statistical Models for Complex and Correlated Data

在小区域估计(SAE)中，关于将资源分配给人口亚群的决策取决于对其基本参数的可靠预测。然而，在一些子组中，由于相对于总体的样本量较小，称为小区域，可靠预测所需的信息通常不可用。因此，较粗略的测量(或行政)数据被用来预测小区域的特征。混合模型主要用于从替代来源(例如，以前的调查、行政和普查数据集)借用信息，以提供可靠的预测。这种预测有很多应用，例如，在疾病地图中，主要目标是在小范围内找到可靠的发病率，如癌症。它还在农业、经济、政策制定和资金分配方面有其他应用。在接下来的5年里，我将继续在SAE的背景下开发新的和原创的模型。我的计划是致力于10个项目，涉及不可忽略的缺失协变量；分位数响应；稳健统计；纵向数据中协变量的测量误差；广义线性混合模型类的非参数响应。在空间统计学方面，我正在研究空间和时间上的发病率分析。总体而言，这些时空模型属于混合模型的范畴。时空模型主要用于疾病地图绘制，通过借用邻近地理分区的力量来提供对潜在疾病风险的可靠估计。发病率空间和时空模型开发背后的想法对于模拟真实发病率的变化和更好地将系统可变性与随机噪声区分开来至关重要，随机噪声是通常使粗发病率图黯然失色的一个组成部分。在接下来的5年里，我将继续在我的研究计划中开发新的和原创的空间和时间模型。我的计划是致力于9个项目，涉及点参考数据集的复杂时空模型的最大似然估计(MLE)；空间或时空模型混合的稳健版本；两种或更多相关疾病的联合建模的MLE；不可忽略的缺失协变量；协变量中的测量误差；健康结果的稳健混合，以及个人或区域一级传染病统计模型中的多种健康结果。忽视数据应用程序的适当建模(如上所述)可能会导致错误的结论，这可能会对调查、抽样和公共卫生产生明显的政策影响。这些进展还将使统计科学的研究人员能够对他们的假设模型进行更可靠的拟合和评估，这些模型对于向公众和决策者报告可靠的结果非常重要，以便更好地规划，最终帮助人们。我预计在未来五年内培训13名HQP。

In small area estimation (SAE), policy decisions regarding the allocation of resources to sub-groups of a population depend on reliable predictors of their underlying parameters. However, in some sub-groups, called small areas due to small sample sizes relative to the population, the information needed for reliable prediction is typically not available. Consequently, survey (or administrative) data on a coarser scale is used to predict the characteristics of small areas. Mixed models are mainly used to borrow information from alternative sources (e.g., previous surveys, administrative and census data sets) to provide a reliable prediction. Such predictions have many applications, e.g. in disease mapping the main objective is to find reliable rates of disease such as cancer in small areas. It also has other applications in agriculture, economics, policymaking, and allocation of funds. Over the next 5 years, I will continue to develop new and original models in the context of SAE. My plan is to work on 10 projects dealing with non--ignorable missing covariates; quantile responses; robust statistics; measurement error in covariates in longitudinal data; non-parametric responses in the class of generalized linear mixed models. In spatial statistics, I am pursuing research on the analysis of disease rates over space and time. In general, these spatio--temporal models fall under the umbrella of mixed models. The spatio--temporal models are mainly used in disease mapping to provide a reliable estimate of the underlying disease risk by borrowing strength from neighboring geographic sub-regions. The idea behind developments on spatial and spatio--temporal modeling of disease rates is essential to model variations in true rates and better separate systematic variability from random noise, a component that usually overshadows crude rate maps. Over the next 5 years, I will continue to develop new and original spatial and temporal models in my research program. My plan is to work on 9 projects dealing with maximum likelihood estimation (MLE) for complex spatio--temporal models of point- referenced datasets; robust version of the mixture of spatial or spatio--temporal models; MLE for joint modeling of two or more relevant diseases; non--ignorable missing covariates; measurement error in covariates, a robust mixture of health outcome, and multiple health outcomes in the context of the individual- or area -level infectious disease statistical models. Ignoring proper modeling of data applications (as explained above) may lead to wrong conclusions that can have clear policy implications in survey sampling and public health. These developments will also enable researchers in the statistical sciences to engage in more reliable fitting and evaluation of their hypothesized models which are important to report reliable results to the public and policy-makers for better planning to ultimately help people. I expect to train 13 HQP in the next five years.