Flexible methods for mixed longitudinal responses measured at irregular time intervals

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For measuring the association between two longitudinal responses, it is quite useful to have flexible methods in case traditional statistics are not of interest or may require somewhat restrictive assumptions (e.g., using Pearson correlation coefficient). In this proposal, we intend to develop flexible methods to look at both association and temporal sequencing of distinct longitudinal measures, where the measures may be of mixed type (e.g., one continuous, the other binary) and recorded on non-uniform grids and different time points from one another. This proposal builds off work which proposed a measure of correlation for bivariate continuous longitudinal responses (Dubin and Müller, 2005). In this prior work, the method was applied to nephrology protein data, measured on a continuous scale, and where the time points for measurements within a person were the same.  This method took a curve-based approach, thereby allowing for the ability to measure associations with lags, even when the measurements were not measured on an identical and uniform design within an individual.   We will continue to use a curve-based approach, a nonparametric model related to the approach from Dubin and Müller (2005), though we will also propose a semiparametric approach, grounded in the framework for generalized linear models for correlated data, which provides a balance between flexibility and the ability to easily incorporate the method with standard software. The current proposal is motivated by a longitudinal example, also in nephrology, where it is not known whether changes in one response, a continuous measured protein that is a marker of inflammation, precedes or follows a different response, a binary measured infection. These measurements are of mixed type, and are measured at different and non-uniform occasions. We hope that the proposed methodology will prove useful across various scientific disciplines.