Analyzing chromatographic data using multilevel modeling
It is relatively easy to collect chromatographic measurements for a large number of analytes, especially with gradient chromatographic methods coupled with mass spectrometry detection. Such data often have a hierarchical or clustered structure. For example, analytes with similar hydrophobicity and dissociation constant tend to be more alike in their retention than a randomly chosen set of analytes. Multilevel models recognize the existence of such data structures by assigning a model for each parameter, with its parameters also estimated from data. In this work, a multilevel model is proposed to describe retention time data obtained from a series of wide linear organic modifier gradients of different gradient duration and different mobile phase pH for a large set of acids and bases. The multilevel model consists of (1) the same deterministic equation describing the relationship between retention time and analyte-specific and instrument-specific parameters, (2) covariance relationships relating various physicochemical properties of the analyte to chromatographically specific parameters through quantitative structure–retention relationship based equations, and (3) stochastic components of intra-analyte and interanalyte variability. The model was implemented in Stan, which provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods.
KeywordsLiquid chromatography pH Multilevel modeling Bayesian analysis
This project was supported by the National Science Centre, Poland (grant 2015/18/E/ST4/00449).
Compliance with ethical standards
Conflict of interest
The author declares that he has no competing interests.
- 2.Kubik Ł, Struck-Lewicka W, Kaliszan R, Wiczling P. Simultaneous determination of hydrophobicity and dissociation constant for a large set of compounds by gradient reverse phase high performance liquid chromatography-mass spectrometry technique. J Chromatogr A. 2015;1416:31–7.CrossRefPubMedGoogle Scholar
- 8.Park SH, Haddad PR, Amos RIJ, Talebi M, Szucs R, Pohl CA, et al. Towards a chromatographic similarity index to establish localised quantitative structure-retention relationships for retention prediction. III combination of Tanimoto similarity index, logP, and retention factor ratio to identify optimal analyte training sets for ion chromatography. J Chromatogr A. 2017;1520:107–16.CrossRefPubMedGoogle Scholar
- 11.Wiczling P, Bartkowska-Śniatkowska A, Szerkus O, Siluk D, Rosada-Kurasińska J, Warzybok J, et al. The pharmacokinetics of dexmedetomidine during long-term infusion in critically ill pediatric patients. A Bayesian approach with informative priors. J Pharmacokinet Pharmacodyn. 2016;43(3):315–24.CrossRefPubMedPubMedCentralGoogle Scholar
- 12.Lin C, Gelman A, Price PN, Krantz DH. Analysis of local decisions using hierarchical modeling, applied to home radon measurement and remediation. Stat Sci. 1999;14(3):333–7.Google Scholar
- 23.Snyder LR, Kirkland JJ, Dolan JW. Introduction to modern liquid chromatography. 3rd ed. Oxford: Wiley-Blackwell; 2010.Google Scholar
- 24.Gelman A. Bayesian data analysis. 2nd ed. Boca Raton: CRC; 2004.Google Scholar
- 26.Gelman A, Hill J. Data analysis using regression and multilevel/hierarchical models. Cambridge: Cambridge University Press; 2007.Google Scholar
- 27.McElreath R. Statistical rethinking: a Bayesian course with examples in R and Stan. Boca Raton: CRC; 2016.Google Scholar
- 32.Haddad PR. Seeking the holy grail—prediction of chromatographic retention based only on chemical structures. LCGC. 2017;35(8):499–502.Google Scholar