Modelling formulations using gene expression programming – A comparative analysis with artificial neural networks

Abstract

This study has investigated the utility and potential advantages of gene expression programming (GEP) – a new development in evolutionary computing for modelling data and automatically generating equations that describe the cause-and-effect relationships in a system- to four types of pharmaceutical formulation and compared the models with those generated by neural networks, a technique now widely used in the formulation development. Both methods were capable of discovering subtle and non-linear relationships within the data, with no requirement from the user to specify the functional forms that should be used. Although the neural networks rapidly developed models with higher values for the ANOVA R² these were black box and provided little insight into the key relationships. However, GEP, although significantly slower at developing models, generated relatively simple equations describing the relationships that could be interpreted directly. The results indicate that GEP can be considered an effective and efficient modelling technique for formulation data.

Introduction

Formulation development is a complicated problem set in a design space that is multidimensional in nature and difficult to conceptualise. In order to reduce the development timescale within a framework of quality by design research into advanced computational techniques have resulted in the use of expert and knowledge base systems for the generation of initial formulations (Rowe and Roberts, 1998) and data mining for modelling formulation and process data. (Ekins, 2006, Balakin, 2010). Statistical methods have been used for over thirty years in pharmaceutical formulation to derive equations expressing the relevant cause-and-effect relationships, and over the last fifteen years artificial neural networks (ANN) have gained increasing usage in this area as a means of developing useful models from experimental data allowing predictions to be made and formulations optimised (Achanta et al., 1995, Bourquin et al., 1997, Takayama et al., 2003, Colbourn and Rowe, 2005). Neural networks cope well with complex non-linear relationships with the added advantage that the functional form between the dependent and independent variables need not be chosen a priori as with statistical techniques. However, the developed models are invariably ‘black-boxes’ and difficult to interpret except indirectly by examining response surfaces.

In order to overcome this specific disadvantage Do et al. (2008) proposed the use of a new technique – genetic programming (GP). This method based on evolutionary computing (Koza, 1998) is also able to generate mathematical equations and Do et al. (2008) showed that it could be applied to modelling drug dissolution from controlled release formulations. They showed that it was capable of not only providing equations relating the variables that could be interpreted directly but also the models exhibited comparable predictive power to statistics. The results support work carried out by Gusel and Brezocnik (2006) on modelling the impact toughness of a copper alloy; although in their case the GP models were more precise than the statistical models, the equations were very complex.

In this paper gene expression programming (GEP), an extension of GP recently proposed by Ferreira (2001) and claimed (Ferreira, 2006) to produce models more quickly, has been evaluated as a modelling technique for four different types of pharmaceutical formulations and the models compared with those generated using multi-layer perceptron (MLP) neural networks.