Statistical analysis of isocratic chromatographic data using Bayesian modeling

Chromatographic retention times are usually modeled considering only one analyte at a time. However, it has certain limitations as no information is shared between the analytes, and consequently the model predictions poorly generalize to out-of-sample analytes. In this work, a publicly available dataset was used to illustrate the benefits of pooling the individual data and analyzing them simultaneously utilizing Bayesian hierarchical approach. Statistical analysis was carried out using the Stan program coupled with R, which enables full Bayesian inference with Markov chain Monte Carlo sampling. This methodology allows (i) incorporating prior knowledge about the likely values of model parameters, (ii) considering the between-analyte variability and the correlation between the model parameters, (iii) explaining the between-analyte variability by available predictors, and (iv) sharing information across the analytes. The latter is especially valuable when only limited information is available in the data about certain model parameters. The results are obtained in the form of posterior probability distribution, which quantifies uncertainty about the model parameters and predictions. Posterior probability is also directly relevant for decision-making. In this work, we used the Neue model to describe the relationship between retention factor and acetonitrile content in the mobile phase for 1026 analytes. The model was parametrized in terms of retention factor in 100% water, retention factor in 100% acetonitrile, and curvature coefficient, and considered log P and pK_a as predictors. From this analysis, we discovered that the analytes formed two clusters with different retention depending on the degree of analyte dissociation. The final model turned out to be well calibrated with the data. It gives insight into the behavior of analytes in the chromatographic column and can be used to make predictions for a structurally diverse set of analytes if their log P and pK_a values are known.