Statistical methods for multilevel data with informative cluster size

大规模聚类纵向研究现在更频繁地进行，其中属于一个聚类的一个单元的数据是在两个以上的时间点上获得的。当簇的大小发生变化并且与感兴趣的结果相关时，就会出现信息簇大小。例如，在牙周病的纵向研究中，单位是牙齿，集群是人，在多个时间点测量每个人的口腔健康状况。由于严重的牙周病可导致牙齿脱落，因此关注的结果，疾病进展的时间，与群集大小（一个人体内的牙齿数量）有关；牙齿少的人的牙齿比牙齿完整的人的牙齿更容易出现这种情况。在这种情况下，取所有人随时间的所有牙齿测量值的平均值将低估疾病的发病率。考虑信息簇大小的统计方法对于纵向数据是有限的。提出的研究包括三个目标，将开发新的方法和工具，以适当地分析复杂的纵向数据。1)属于一个集群的单位可以经历不同的疾病阶段或生命状态，但在某些情况下，从一种状态过渡到另一种状态的时间可能与集群大小有关。因此，我们建议开发一个聚类多状态模型来考虑信息聚类大小。我们将创建一个灵活的软件包，在集群多状态模型中合并权重。2)在纵向研究中，我们可以根据对每个单元的纵向测量来估计某一事件发生的概率。我们将两种动态预测模型-联合建模和地标-扩展到聚类数据集。所提出的聚类动态预测模型能够很好地考虑聚类内各单元之间的相关性，从而做出准确的聚类特定预测和种群平均预测。3)在大规模、长期的纵向研究中，数据缺失是不可避免的。我们将评估各种多重输入方法，以从具有信息簇大小的聚类纵向数据中输入缺失结果。我们还将研究丢失的数据模式与集群大小相关的情况。每个目标的结果将作为期刊文章分发，并附带用于分析和会议演示的软件包或代码。所提出的方法在许多研究领域都有应用：例如对关节炎患者的多中心纵向研究和对儿童和青少年的多学校纵向研究。我们拟议的研究将加强复杂相关数据分析领域，并为研究人员提供适当的方法和工具来分析数据、转化知识和制定政策，以改善加拿大人的健康和福祉。

Large-scale clustered longitudinal studies are conducted more frequently now, where data on a unit that belongs to a cluster is obtained for more than two time points. Informative cluster size occurs when the sizes of the clusters vary and are related to the outcome of interest. For example, in a longitudinal study of periodontal disease, where a unit is a tooth and a cluster is a person, each person's oral health status is measured at multiple timepoints. Because severe periodontal disease can lead to tooth loss, the outcome of interest, time to disease progression, is related to cluster size (number of teeth within a person); a tooth that belongs to a person with few teeth is more likely to experience the outcome than a tooth that belong to a person with a full set of teeth. In this case, taking the average of all the teeth measurements of all the people over time will underestimate the rate of disease. Statistical methods that account for informative cluster size are limited for longitudinal data. The proposed research includes three objectives that will develop new methods and tools to appropriately analyze complex longitudinal data. 1) A unit that belongs to a cluster can go through various stages of disease or status in life, but in some situations, time to transition from one state to another can be related to cluster size. Therefore, we propose to develop a clustered multistate model that accounts for informative cluster size. We will create a flexible software package that incorporates weights in clustered multistate models. 2) In a longitudinal study, we can estimate the probability of a certain event based on the longitudinal measurements made on each unit. We will extend two dynamic prediction models - joint modelling and landmarking - to the clustered data setting. The proposed clustered dynamic prediction models will properly account for the correlation between units within a cluster to make accurate cluster-specific and population-averaged predictions. 3) Missing data is unavoidable in large-scale and long-term longitudinal studies. We will evaluate various multiple imputation approaches to impute missing outcomes from clustered longitudinal data with informative cluster size. We will also investigate the case when the missing data pattern is related to cluster size. The results from each objective will be disseminated as journal articles accompanied by software packages or code for analysis and conference presentations. The proposed methods have applications in many areas of research: examples include a multi-center longitudinal study of arthritis patients and a multi-school longitudinal study of children and adolescents. Our proposed research will strengthen the field of complex correlated data analysis and provide researchers with the appropriate methods and tools to analyze data, translate knowledge, and create policies that will improve the health and well-being of Canadians.