Smoothing Methods to Investigate Non-linear Effect in Correlated Data Studies

描述(申请人提供)：相关数据在健康研究中非常常见。这些数据可能来自纵向研究、社区小组调查、遗传家族研究或空间研究。通常，线性混合效应模型用于对连续响应进行建模，而广义线性混合模型用于非高斯数据。除了这种似然方法外，当分布假设不现实且不容易指定时，还经常使用基于广义估计方程GEE的拟似然方法。我们建议扩展这些方法，以处理协变量效应是非线性的或不容易用参数建模的情况。这类似于广义相加模型，在广义相加模型中，使用平滑曲线来预测协变量对单变量结果的影响。这项研究的目标是开发两个领域相关数据的统计软件。第一种是广义可加混合模型的样条平滑方法，它结合了广义可加模型中的半参数方法和相关数据的混合效应建模。第二种是半参数GEE方法，它扩展了相关数据的GEE方法和核平滑方法，以模拟非线性对健康结果的影响。研究内容包括统计方法、算法开发以及在实际健康问题中的应用。这项研究需要对创新的半参数统计方法进行分析开发，并对计算密集型方法进行算法开发。目前，还没有针对这些领域的软件。目的是克服这一不足，并扩大使用平滑方法对非线性协变量效应进行建模的好处。结果是一个处理相关数据的软件包SmoothEffect。该软件将提供一本全面的案例研究指南，其中使用了纵向研究中的问题和其他问题。还将编写技术报告和模拟研究。这项研究旨在开发灵活的统计平滑方法和软件，用于分析相关数据或聚集数据，如纵向数据、面板调查或空间数据。感兴趣的焦点是分析这种聚集的数据，其中来自同一实验单位的记录是相关的，并且来自某些预测因子对健康结果的影响显示出非线性平滑曲率，这不容易被参数化。

DESCRIPTION (provided by applicant): Correlated data are very common in health studies. Such data could come from longitudinal studies, community panel surveys, genetic family studies or spatial studies. Typically, linear mixed-effect models are used for modeling continuous response, and generalized linear mixed models are applied to non-Gaussian data. In addition to such likelihood approaches, quasi-likelihood methods based on generalized estimating equations GEE are often used when the distributional assumption is not realistic and not easy to specify. We propose to extend these methods to handle the situations when the covariate effect is non-linear or is not easy to be modeled parametrically. This is similar to generalized additive models, where a smooth curve is used to predict the impact of a covariate on a univariate outcome. The goal of this study is to develop statistical software for correlated data in two areas. The first is the spline smoothing methods for generalized additive mixed models, which combine the semiparametric methods in generalized additive models using smoothing methods and mixed-effect modeling for correlated data. The second is the semiparametric GEE methods, which extend the GEE methods for correlated data with kernel smoothing to model the non-linear impact on health outcome. The research includes statistical methods, algorithm development and application to real health problems. The study requires analytic development on innovative semiparametric statistical methods and algorithm development on computational intensive methods. Currently, there is no software for these areas. The aim is to overcome this deficiency and extend the benefits of using smoothing methods to model non-linear covariate effect. The result is a software package, SmoothEffect, for handling correlated data. A comprehensive case study guidebook using problems from longitudinal studies and others will come with the software. Technical reports and simulation studies will also be developed. This study is to develop flexible statistical smoothing methods and software for analyzing correlated data or clustered data such as longitudinal data, panel surveys or spatial data. The focus of interest is to analyze such clustered data where records from the same experimental unit are related and the impact from some predictor on health outcome shows a non-linear smoothing curvature, which is no easy to be parameterized.