The application of Gaussian processes in the predictions of permeability across mammalian and polydimethylsiloxane membranes

Abstract

The problem of predicting the rate of percutaneous absorption of a drug is an important issue, particular with the increasing use of the skin as a means of moderating and controlling drug delivery. One key feature of this problem domain is that human skin permeability to penetrants (often characterised by K p , the permeability coefficient) has been shown to be inherently non-linear when mathematically related to the key physicochemical parameters of penetrants. The aims of the current study were to apply and validate Gaussian process regression methods to datasets for membranes other than human skin, and to explore how the nature of the dataset may influence its analysis. Permeability data for absorption across rodent and pig skin, and polydimethylsiloxane Silastic ® membranes was collected from the literature. Two QSPR methods were applied to compare to the Gaussian process models. The results demonstrated that Gaussian process models with different covariance functions outperform the QSPR model for human, pig and rodent datasets, but in general are not good for Silastic ® membranes. These results suggest that the physicochemical parameters employed in this study might not be appropriate for developing models that represent this membrane. In addition, the results show the size of the datasets, in both absolute and comparative senses, appears to influence model quality.

Model fitting for small skin permeability data sets: hyperparameter optimisation in Gaussian Process Regression

“…That the data range should be as wide as possible also has an implication on the descriptor choice, despite previous GPR studies [11,14] indicating that a certain degree of interchangeability between parameters due to covariance might be significant in flexibly generating models of the same statistical quality. For example, an examination of previously published data sets [29,32,36] indicates that the majority of chemicals present in those data sets have a small number of hydrogen bonding groupsusually from zero to three.…”

“…[11,[18][19][20][21][22] This technique has been reported on and reviewed extensively elsewhere, and the reader is directed to those sources for further information. [12][13][14][20][21][22][23][24][25][26][27] It is possible that inferring the hyperparameters from the data could be particularly problematic with small data sets. To resolve this, various optimisation methods have been used to obtain the hyperparameters that minimise negative log marginal likelihood values.…”

“…The correlation coefficient (r), MSLL [22] and improvement over the na€ ıve model (ION, where the na€ ıve model always predicts the mean of the target value in the training set independently of the input) were used, as in previous studies, to determine the model performance. [11,13,14] The correlation coefficient is a widely used performance measure in this problem domain. Our experiences from our previous work tell us that ION is a good indicator and measures how much better a predictor is than the na€ ıve predictor.…”

“…[22] The correlation coefficient ranges from À1 to 1, and in this study, a high positive value defines good prediction performance. [14] Results and Discussion…”

“…Despite studies which in different ways address this issue, [11,12] the uptake of such methods in the field of percutaneous absorption has been limited and is due mostly to the lack of ease of use of what can often be quite advanced computation techniques by non-specialists. Nevertheless, despite their more rudimentary nature when compared to Machine Learning methods, and previous studies highlighting comparatively poor performance for QSPR methods compared to Machine Learning methods, [11,13,14] QSPRs are still considered by many researchers in this field to be the benchmark predictive method and are used in this study in that regard.…”