Bayesian multilevel modeling of retention data informed by structural similarity of analytes

In chromatographic retention time modeling, a common assumption is that analyte retention times are conditionally independent given molecular descriptors. In practice, however, analytes frequently exhibit structural similarities that induce dependencies. Explicitly modeling these dependencies can enhance predictive accuracy. In this study, I present a multilevel multi-output Gaussian process modeling approach that incorporates a Tanimoto similarity matrix to address these dependencies. I evaluate the proposed model using a publicly available data set of isocratic RP-HPLC retention time measurements for 1026 analytes. The high structural similarity among many of these analytes makes them particularly suitable for evaluating the impact of incorporating analyte similarity into the modeling framework. A central component of the model is its use of a matrix normal distribution to describe between analyte variability. This distribution is parameterized by a mean matrix and two covariance matrices, one capturing covariance across analytes and the other capturing covariance across chromatographic parameters. The mean matrix includes molecular predictors, such as logP values and the number of functional groups. The row covariance matrix is structured according to the similarity matrix, which controls the effect of structural similarities on analyte-specific chromatographic parameters. The column covariance matrix captures the correlation among analyte-specific chromatographic parameters. This study demonstrates that structural similarity can be integrated into the retention time model to offer improved predictive performance, especially when experimental data from structurally related analytes are available.