Statistical methods for multilevel data with informative cluster size

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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.