Statistical methods for screening individual childhood growth paths

儿科生长发育图被广泛用于临床和医疗中心，用于监测婴儿、儿童和青少年的生长发育，以比较个体价值和参考人群。现有的方法侧重于在固定时间进行单次测量的筛选。由于婴儿和儿童经常得到定期跟踪，以确保正常成长，每个儿童通常都有一条成长道路。拟议研究的主要目标是开发统计方法来构建用于筛选个体成长路径的成长图表。这里的关键挑战是对潜在的增长路径进行排名，这些增长路径只能在不同的测量时间间隔下观察到有限的次数。提出了两种可能的方法。第一种方法获得成长路径的低维近似值，并根据个人成长路径在该较低空间中的预测分数对其进行排名。第二个定义了增长路径的统计深度，进而提供了单个路径的排名。对于这两种方法，研究人员将研究它们的理论性质，如一致性、收敛速度和渐近分布，并开发相关的推理工具。由于增长数据通常是在全国范围内收集的，因此样本量很大。为了使所提出的方法在实践中可行，计算时间是一个关键问题。因此，研究人员还计划为这两种方法开发快速算法，以提高计算效率。此外，如以往的研究表明，协变量调整方法可以有效地提高筛选性能。例如，父母信息对孩子的成长起着重要作用。研究人员将扩展为这两种方法开发的方法，以纳入协变量信息。总体而言，本建议采用的统计方法包括：构建增长图的统计方法、纵向数据分析、功能数据分析、奇异值分解和主成分分析、统计深度、分位数回归、非参数和半参数建模以及混合效应模型。拟议的研究将产生广泛的跨学科贡献。虽然这项研究的动机是儿科生长筛查，但所提出的方法的应用肯定不止于此。在流行病学、艾滋病毒研究、遗传学、癌症研究和环境科学方面，PI和合作调查员都参与了各种合作项目。增长数据可以看作是变化位置的纵向数据，这些数据通常存在于这些应用程序中。因此，所提出的方法可以为这些研究领域的问题提供更准确和更全面的方法。此外，要制定的一般方法具有明确的统计重要性，迄今尚未得到令人满意的研究。本提案中描述的研究计划具有广泛的方法和应用价值。该项目的成果预计将通过在统计、公共卫生和医学等国际科学期刊上发表的出版物、在国内和国际会议上的陈述、在大学的研讨会演讲以及与临床研究人员的合作来广泛传播。研究人员计划开发与分位数回归和数据深度相关的新课程，部分课程材料将基于拟议的研究。此外，调查人员还认为，传播新方法的一个重要途径是提供易于获得和方便使用的计算机软件。拟议的方法将以R包的形式实施，可在网上免费获得。

Pediatric growth charts have been widely used in clinics and medical centers to monitor the growth of infants, children, and adolescents to compare individual values with the reference population. The existing methods focus on screening of a single measurement at a fixed time. As infants and children are often followed up regularly to ensure normative growth, each child usually exhibits a growth path. The main objective of the proposed research is to develop statistical methods to construct growth charts for screening individual growth paths. The key challenge here is to rank the underlying growth paths, which are only observed limited number of times with varying measurement time spacings. Two potential approaches are proposed. The first one obtains a lower dimensional approximation of growth paths, and ranks the individual growth paths based on their projection scores in this lower space. The second one defines statistical depth for growth paths, which in turn provides a ranking of individual paths. For both approaches, the investigators will study their theoretical properties, such as consistency, convergence rate, and asymptotic distributions, and develop related inference tools. As growth data are often collected nation wide, they have large sample sizes. To make the proposed methods feasible in practice, computing time is a critical issue. Therefore, the investigators also plan to develop fast algorithms for both methods to improve the computational efficiency. In addition, as shown in previous studies, covariate-adjusted methods can effectively enhance screening performance. For example, parental information plays a significant role in children's growth. The investigators will extend the developed methods for the two approaches to incorporate covariate information. Overall, the statistical methods to be employed for this proposal cover: statistical methods for growth chart construction, longitudinal data analysis, functional data analysis, singular value decomposition and principal component analysis, statistical depth, quantile regression, nonparametric and semi-parametric modeling, and mixed effect models. The proposed research will produce broad interdisciplinary contributions. Although the study was motivated by pediatric growth screening, the applications of the proposed methods certainly go beyond that. Both the PI and the co-investigator have been involved in various collaborative projects in epidemiology, HIV research, genetics, cancer research and environmental science. Growth data can be viewed as varying-location longitudinal data, which commonly exist in those applications. Hence, the proposed methods can lead to more accurate and more comprehensive approaches for problems in these areas of research. Additionally, the general methodologies to be developed are of definite statistical importance and have not been studied satisfactorily to date. The research plan described in this proposal has both broad methodological and applied merits. The results obtained from this project are expected to be widely disseminated through publications in international scientific journals in statistics, public health and medicine, presentations in domestic and international conferences, seminar talks in universities, and collaborations with clinical researchers. The investigators plan to develop new courses related to quantile regression and data depth, and part of the course materials will be based on the proposed research. In addition, the investigators also believe that an important way of disseminating new methodology is to provide easily available and user-friendly computer software. The proposed methods will be implemented as an R package which will be freely available on-line.