Radiomic image features are becoming a promising non-invasive method to obtain quantitative measurements for tumour classification and therapy response assessment in oncological research. However, despite its increasingly established application, there is a need for standardisation criteria and further validation of feature robustness with respect to imaging acquisition parameters. In this paper, the robustness of radiomic features extracted from computed tomography (CT) images is evaluated for liver tumour and muscle, comparing the values of the features in images reconstructed with two different slice thicknesses of 2.0 mm and 5.0 mm. Novel approaches are presented to address the intrinsic dependencies of texture radiomic features, choosing the optimal number of grey levels and correcting for the dependency on volume. With the optimal values and corrections, feature values are compared across thicknesses to identify reproducible features. Normalisation using muscle regions is also described as an alternative approach. With either method, a large fraction of features (75-90%) was found to be highly robust (< 25% difference). The analyses were performed on a homogeneous CT dataset of 43 patients with hepatocellular carcinoma, and consistent results were obtained for both tumour and muscle tissue. Finally, recommended guidelines are included for radiomic studies using variable slice thickness.