Bayesian Calibration, Validation and Uncertainty Quantification for Predictive Modelling of Tumour Growth: A Tutorial.

In this work, we present a pedagogical tumour growth example, in which we apply calibration and validation techniques to an uncertain, Gompertzian model of tumour spheroid growth. The key contribution of this article is the discussion and application of these methods (that are not commonly employed in the field of cancer modelling) in the context of a simple model, whose deterministic analogue is widely known within the community. In the course of the example, we calibrate the model against experimental data that are subject to measurement errors, and then validate the resulting uncertain model predictions. We then analyse the sensitivity of the model predictions to the underlying measurement model. Finally, we propose an elementary learning approach for tuning a threshold parameter in the validation procedure in order to maximize predictive accuracy of our validated model.

A hierarchical Bayesian approach to calibrating the linear-quadratic model from clonogenic survival assay data.

We propose a Bayesian hierarchical model applicable to the calibration of the linear-quadratic model of radiation dose-response. Experimental data used in model calibration were taken from a clonogenic survival assay conducted on human breast cancer cells (MDA-MB-231) across a range of radiation doses (0-6Gy). Employing Markov-chain Monte Carlo methods, we calibrated the proposed Bayesian hierarchical model, computed posterior distributions for the model parameters and survival fraction dose-response probability densities. Key contributions include the proposal of a model that incorporates multiple sources of inter- and intra-experiment variability commonly neglected in the standard frequentist approach and its subsequent application to in vitro experimental data.

Molecular, proteomic and immunological parameters of allergens provide inclusion criteria for new candidates within established grass and tree homologous groups.

BACKGROUND: Our knowledge of allergen structure and function continues to rise and new scientific data on the homology and cross-reactivity of allergen sources should be considered to extend the work of Lorenz et al., 2009 (Int Arch Allergy Immunol. 148(1):1-1, 2009) and the concept of homologous groups. In addition to this, sophisticated techniques such as mass spectrometry (MS) are increasingly utilised to better characterise the complex mix and nature of allergen extracts. METHODS: Homology models were used of Fag s 1 (Beech) and Cyn d 1 (Bermuda grass) and compared with template crystal structures of Bet v 1 and Phl p 1 from the 'exemplar' species of Birch and Timothy grass, respectively. ELISA experiments were performed to assess cross-reactivity of Beech (tree) and Bermuda (grass) extracts to rabbit sera raised to either "3-Tree" (Birch, Alder and Hazel) extract or "Grass" (12-grass mix extract), respectively. The comparability of biochemical stability of different allergen sources was assessed through statistical methods for a range of tree and grass species. RESULTS: Allergen cross-reactivity and/or structural homology have been described providing justification for inclusion of Beech within the Birch homologous tree group. Data from Bermuda grass (Cyn d 1) provides further justification for the inclusion of this species into the homologous group of the sweet grasses. However, further characterisation of relevant allergens from Bermuda grass and, in particular, comparison of cross-reactive patterns between subjects specifically in areas with high abundance of both Pooideae and Chloridoideae is sought. CONCLUSION: MS allows the possibility to identify individual proteins or allergens from complex mixes by mass and/or sequence, and this has been extensively applied to the allergen field. New data on the homology, cross-reactivity and biological parameters of allergen sources have been considered to extend the work of Lorenz et al., 2009 in the context of tree and grass species. The concept of homologous groups is certainly dynamic allowing the flexibility and potential in streamlining quality parameters, such as stability profiles, due to extrapolation of exemplar data to a wider range of allergens.