Statistical methods for informative and outcome-dependent data

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In many practical data settings, the way in which we observe data is related to the data themselves. When complete data exist (e.g. a full cohort) but some are unobserved, this is treated as a missing data problem. Elsewhere, when there is no notion of complete data, the phenomenon goes by various names. In cluster-correlated settings when cluster sizes are related to outcomes, this is known as informative cluster size. In longitudinal settings when measurement frequency is related to outcomes, this is known as an informative visit process. In each case, the observation mechanism is informative in that how and whether we observe data is related to the outcomes themselves. While informativeness is typically a challenge to be accounted for, the same principle can be harnessed to one's advantage: outcome-dependent sampling designs are informative by design to improve efficiency relative to simple random sampling-as in the classic case-control study. Informative and outcome-dependent observation mechanisms pose several analysis challenges as well as opportunities. The long-term goal of this program is to investigate and develop statistical tools for modelling data under informative or outcome-dependent observation mechanisms. In the near term, this program will develop estimation methods for data subject to informative observation mechanisms or collected via outcome-dependent sampling designs, propose novel outcome-dependent designs for efficient estimation when data are subject to informative cluster size or visit processes, and leverage the logic of outcome-dependent designs in modern machine learning analyses. This program will contribute to the field by developing a statistical toolbox for analyzing the messy and informatively observed data that are all too common outside of idealized scenarios. Moreover, the proposed methods are motivated by applications in epidemiology, public health and beyond, and the proposed research will have many secondary effects. For example, proposed designs for data subject to informative cluster size can permit researchers to effectively study exposures with multigenerational effects-ones that not only affect those exposed but have cascading effects as the population reproduces. And methods for analyzing data subject to complex and informative visit processes would empower scientists to investigate relationships between complex diseases via electronic health records databases in a principled way. A key priority of the proposed research will be to support and train nine students to become well-rounded statisticians and thinkers, each of whom will make major creative contributions toward the program goals. In so doing, they will not only gain expertise in cutting-edge statistical tools and in how to conduct methodological research but will learn to clearly communicate statistical phenomena to colleagues and non-statistician stakeholders alike-precisely the skills needed to succeed as independent statisticians.