Diagnostics for mixture regression models: applications to public health

在许多公共卫生研究中，有限混合回归模型经常被用来分析来自异质人群的数据。重要的是要评估参数估计的稳定性和统计推断的有效性时，基本假设似乎被违反，但适当的诊断缺乏文献。本研究旨在发展有效的诊断方法，以评估混合回归模型的充分性和伴随的检验统计量的敏感性。所开发的方法将使医疗保健专业人员能够专注于实质性问题，并从相关和过度分散的结果中得出准确和有效的结论。在存在异常观测的情况下，影响诊断可以提供对异质性来源和明显过度分散的见解，同时适应由于纵向研究设计或嵌套数据结构而产生的固有相关性。该研究的意义在于其科学新奇和实际应用的广泛性。对公共卫生的好处将在国家和国际两级累积。对于激励并与本研究相关的实证研究，健康结果的评估对预防和控制复发性尿路感染、医院战略规划以及卒中后护理和康复管理具有重要意义。此外，对老年人的身体活动干预进行适当的评估与久坐老年人的福尔斯预防和减少肌肉骨骼疾病有关。

In many public health studies, finite mixture regression models are often used to analyse data arising from heterogeneous populations. It is important to assess the stability of parameter estimates and the validity of statistical inferences when the underlying assumptions appear to be violated, but appropriate diagnostics are lacking in the literature. This research aims to develop effective diagnostic methods for assessing the adequacy of mixture regression models and the sensitivity of accompanying test statistics. The methodology developed will enable health care professionals to focus on substantive issues and to draw accurate and valid conclusions inferred from correlated and over-dispersed outcomes. In the presence of anomalous observations, the influence diagnostics can provide insights into the source of heterogeneity and the apparent over-dispersion, while accommodating the inherent correlation due to the longitudinal study design or nested data structure. Significance of the research lies in its scientific novelty and the breadth of its practical applications. The benefits to public health will accrue both nationally and internationally. For the empirical studies that motivated and are linked to this research, evaluation of health outcomes has significant implications in the prevention and control of recurrent urinary tract infections, hospital strategic planning, and post-stroke care and rehabilitation management. Moreover, appropriate assessment of a physical activity intervention for older adults is pertinent to falls prevention and reduction of musculoskeletal disorders among sedentary seniors.