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

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，线性混合效应模型是 用于连续响应的建模，而广义线性混合模型适用于非高斯 数据除了这种似然方法，基于广义估计的拟似然方法 当分布假设不现实且不容易指定时，通常使用GEE方程。我们 建议扩展这些方法，以处理协变量效应为非线性或非线性时的情况 易于参数化建模。这类似于广义加性模型，其中平滑曲线是 用于预测协变量对单变量结果的影响。本研究的目的是开发 两个领域相关数据的统计软件。第一种是广义样条光顺方法 加法混合模型，它联合收割机了广义加法模型中的半参数方法， 相关数据的平滑方法和混合效应建模。第二种是半参数GEE 方法，扩展了核平滑相关数据的GEE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、算法开发和应用 真实的健康问题。这项研究需要创新的半参数统计分析的发展 计算密集型方法的方法和算法开发。目前，还没有软件 这些地区其目的是克服这一缺陷，并扩大使用平滑方法的好处， 模型非线性协变量效应。结果是一个软件包，平滑效果，用于处理相关的 数据一个全面的案例研究指南使用的问题，从纵向研究和其他人将来 用软件。还将编写技术报告和模拟研究报告。 本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 聚类数据，如纵向数据、小组调查或空间数据。兴趣的焦点是分析 来自相同实验单元的记录相关的这种聚类数据， 健康结果的预测值呈现非线性平滑曲率，不易参数化。

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 softwarefor 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.