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A frequent problem in statistical science is how to properly handle missingdata in matched paired observations. There is a large body of literature copingwith the univariate case. Yet, the ongoing technological progress in measuringbiological systems raises the need for addressing more complex data, e.g.,graphs, strings and probability distributions, among others. In order to fillthis gap, this paper proposes new estimators of the maximum mean discrepancy(MMD) to handle complex matched pairs with missing data. These estimators candetect differences in data distributions under different missingnessmechanisms. The validity of this approach is proven and further studied in anextensive simulation study, and results of statistical consistency areprovided. Data from continuous glucose monitoring in a longitudinalpopulation-based diabetes study are used to illustrate the application of thisapproach. By employing the new distributional representations together withcluster analysis, new clinical criteria on how glucose changes vary at thedistributional level over five years can be explored.

Hypothesis testing for matched pairs with missing data by maximum mean discrepancy: An application to continuous glucose monitoring