Analysis of Isocratic-Chromatographic-Retention Data using Bayesian Multilevel Modeling

The objective of
this work was to develop a multilevel (hierarchical)
model based on isocratic-reversed-phase-high-performance-chromatographic
data collected in methanol and acetonitrile for 58 chemical compounds.
Such a multilevel model is a regression model of the analyte-specific
chromatographic measurements, in which all the regression parameters
are given a probability model. It is a fundamentally different approach
from the most common approach, where parameters are separately estimated
for each analyte (without sharing information across analytes and
different organic modifiers). The statistical analysis was done with
Stan software implementing the Bayesian-statistics inference with
Markov-chain Monte Carlo sampling. During the model-building process,
a series of multilevel models of different complexity were obtained,
such as (1) a model with no pooling (separate models were fitted for
each analyte), (2) a model with partial pooling (a common distribution
was used for analyte-specific parameters), and (3) a model with partial
pooling as well as a regression model relating analyte-specific parameters
and analyte-specific properties (QSRR equations). All the models were
compared with each other using 10-fold cross-validation. The benefits
of multilevel models in inference and predictions were shown. In particular
the obtained models allowed us to (i) better understand the data and
(ii) solve many routine analytical problems, such as obtaining well-calibrated
predictions of retention factors for an analyte in acetonitrile-containing
mobile phases given zero, one, or several measurements in methanol-containing
mobile phases and vice versa.