SCORE: Principal Differential Analysis with Covariates for Functional Data

描述（由申请人提供）：本提案的重点是扩展主差分分析（PDA）来分析曲线数据。听觉研究中的几个应用正在推动这种方法的扩展，它允许协变量调整。目前，所有已发表的听觉脑干反应曲线（ABR）和皮层听觉诱发电位曲线（CAEP）分析方法都描述了该曲线的特征，如突出波形的位置和振幅。提出的统计方法将允许使用整个ABR和CAEP曲线进行分析，而不仅仅是选择特征，从而有助于理解与年龄相关的、多发性硬化症或糖尿病相关的听觉刺激时间处理变化，并更好地预测人工耳蜗植入的临床结果。该方法具有用于创伤性脑损伤（TBI）早期检测的潜力。了解噪音引起的听力损失和创伤性脑损伤之间的相互作用，创伤性脑损伤是暴露在爆炸中的“伊拉克自由行动”/“持久自由行动”士兵常见的疾病（Meyers, Wilmington, Gallun, and Henry, 2009; Jordan, Lee, and Helfer, 2009），在伊拉克和阿富汗部署军事人员的这段时间至关重要。PDA是一种通过首先估计接近于湮灭噪声曲线数据的线性微分算子来获得曲线的低维表示的方法。在具体目标(1)中，主差分分析将扩展到包括使用局部线性平滑的协变量调整。分析研究了系数函数的非参数估计量的渐近偏差和方差性质。偏差和方差的渐近表达式将用于提出基于数据的平滑参数选择方法。提出了协变量显著性的检验统计量。在Specific Aim(2)中，开发的方法将在Splus或R中的一种中实现，并公开提供。将进行计算机模拟研究，以验证系数估计量的偏差和方差的渐近理论在指导平滑参数选择和研究所提出的检验统计量的性质方面是有用的。在分析理解扩展PDA的特性并实现扩展PDA软件之后，将与听觉研究人员协商对特定目标(3)和(4)进行听觉研究数据分析。PI具有发展的学术和专业目标。学术目标是发展听觉研究的能力，以推进解决该领域数据分析问题的新颖统计方法。专业目标是通过以下方式在UTEP建立一个强大的统计学研究环境：涉及来自新的计算科学博士课程的博士生和统计学硕士研究生；在研究会议上发言；并与国内听觉研究专家建立合作关系。在她的指导下，在统计学和最近批准的UTEP计算科学项目中，发展目标的进展将以增加的出版率和学生论文数量来衡量。1

DESCRIPTION (provided by applicant): This proposal focuses on extending principal differential analysis (PDA) for analysis of curve data. Several applications in auditory research are motivating this methodological extension, which allows for covariate adjustment. Currently, all published methods for analysis of auditory brainstem response curves (ABR) and cortical auditory evoked potential curves (CAEP) describe features of the curve, such as location and amplitude of prominent waveforms. The proposed statistical methods will allow for an analysis that uses the entire ABR and CAEP curves, rather than just selected features, to contribute to the understanding of age-related, multiple sclerosis- or diabetes-related changes in temporal processing of auditory stimuli, and better prediction of clinical outcomes from cochlear implantation. The methods have the potential to be used for the early detection of traumatic brain injury (TBI). Understanding the interaction of noise induced hearing loss and TBI, disorders common to Operation Iraqui Freedom/Operation Enduring Freedom soldiers exposed to explosive blasts (Meyers, Wilmington, Gallun, and Henry 2009; Jordan, Lee, and Helfer 2009), is vital during this time of ongoing deployment of military personnel in Iraq and Afghanistan. PDA is a method for obtaining a low-dimensional representation of a curve by first estimating a linear differential operator that comes close to annihilating the noisy curve data. In Specific Aim (1), principal differential analysis will be extended to include covariate adjustments using local linear smoothing. The asymptotic bias and variance properties of the nonparametric estimators of the coefficient functions will be investigated analytically. The asymptotic expressions for bias and variance will be used to propose data-based methods for smoothing parameter selection. Test statistics for the significance of covariates are proposed. In Specific Aim (2), the methods developed will be implemented in one of Splus or R and made publicly available. Computer simulation studies will be executed to verify that the asymptotic theory for the bias and variance of the estimators of the coefficients is useful in guiding the smoothing parameter selection, and for studying the properties of the proposed test statistics. After the properties of the extended PDA are understood analytically and the extended PDA software is implemented, auditory research data will be analyzed for Specific Aims (3) and (4) in consultation with auditory researchers. The PI has developmental scholarly and professional objectives. The scholarly objective is to develop competency in auditory research in order to advance novel statistical methodologies that solve data analysis problems in the field. The professional objective is to build a strong research environment in statistics at UTEP by: involving doctoral students from the new Computational Sciences Ph.D. program and masters students in statistics; presenting at research conferences; and establishing collaborations with national experts in auditory research. Progress on developmental objectives will be measured in terms of an increased publication rate and numbers of student theses under her direction in statistics and within the recently approved Computational Sciences Program at UTEP. 1 PUBLIC HEALTH RELEVANCE: Narrative The proposed statistical methods will allow for a statistical analysis that uses the entire auditory brainstem response (ABR) and cortical auditory evoked potential (CAEP) curves, rather than just selected features, to contribute to the understanding of age-related changes, multiple sclerosis- or diabetes-related changes in temporal processing of auditory stimuli, and better prediction of clinical outcomes from cochlear implantation. The methods have the potential to be used for the early detection of traumatic brain injury (TBI). Understanding the interaction of noise induced hearing loss and TBI, disorders common to Operation Iraqui Freedom/Operation Enduring Freedom soldiers exposed to explosive blasts (Meyers, Wilmington, Gallun, and Henry 2009; Jordan, Lee, and Helfer 2009), is vital during this time of ongoing deployment of military personnel in Iraq and Afghanistan.