The current one-dose-fits-all viewpoint, dosing for the 'average' human, and empirical derivations of dosing regimens are clearly not sufficient to effectively treat a diverse population. Personalised medicine, with the determination of treatment plans influenced by genetic factors and historical cases of toxicity, represents a step towards improving clinical outcomes. However, when an individual is deemed not suitable for treatment with the standard medicine/dose based on pharmacogenetics, an alternative must be found which is likely to either be costlier, less effective or potentially toxic. This scenario can be improved by having a greater understanding of both the mechanisms of toxicity in subpopulations and a proper quantification of risk and efficacy. Mathematical modelling can help to improve the understanding of the mechanisms of toxicity, simulate different dosing scenarios and propose optimal treatment. Statistical techniques can be applied to define and quantify uncertainties within model output and define risk when translating to optimised treatment strategies incorporating different genetic and non-genetic factors associated with variability in drug-induced adverse reactions. The integration of applied mathematics and statistics in this project comprises a potentially exciting new field bringing together two quantitative modelling approaches to better quantify uncertainty and inform drug development, testing and therapy.