Statistical Methods for the Design and Analysis of Studies with Incomplete Data

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Missing data is a common problem that can be encountered in any research setting due to unanticipated problems in the implementation of a study. Conclusions drawn from such a study are only valid if the missing data are appropriately handled in the statistical analyses. However, statistical methodology is underdeveloped in settings where there are multiple mechanisms contributing to missingness. If interest lies in a composite score that is constructed from several potentially missing variables, then the missing data mechanism will be complex and model misspecification becomes a real concern. I will develop statistical methodologies and provide practical recommendations for effective analysis strategies in these settings.Additionally, missing data can arise by design. When a variable is particularly expensive to assess, it is increasingly common to measure it only for a prespecified validation subset. Optimal selection of the validation subset can lead to great efficiency gains. However, statistical methods for determining such optimal subsamples are underdeveloped in longitudinal studies. I will develop efficient multiphase response-dependent designs to guide selection of individuals for measurement of expensive exposure variables at each wave of data collection in longitudinal cohort studies. These procedures will be adaptive and will exploit information gathered at previous time points. Optimal designs will be derived that result in the most informative completely-observed subsample to maximize the precision of parameter estimates and greatly increase the power of significance tests.This innovative research program will capitalize on my expertise to develop novel statistical methodology for efficient design and analysis of studies with incomplete data and to provide advanced statistical research training for 8 statistics and biostatistics graduate students. This program will provide powerful design tools for researchers conducting longitudinal cohort studies with expensive covariates and provide important insight into appropriate analysis strategies when there may be distinct sources of missingness within a single study. This theoretical statistics research has been motivated by collaborations with applied researchers throughout Canada; the results from this program will provide novel tools to researchers designing studies such as the Canadian Longitudinal Study on Aging, and will offer increased validity to engaged researchers performing analyses of studies involving complex risk factors for both infectious disease (eg, HIV) and non-infectious diseases (eg, heart disease). In short, this research program will benefit many fields of research which struggle with challenges arising from missing data and budgetary constraints in data collection.