Mathematical Modeling Of Cancer Occurrence Rate

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Mathematical and statistical models are capable of integrating biological knowledge that is outside of the observational data. In a number of applications, the use of Bayesian methods that integrate a prioriknowledge into the model have been shown to improve model behaviors and predictive output. We have described applications of BNs which incorporate expert advice from radiologists, which can be viewed as a model prior (Kahn et al., 1995). In metabolic modeling, flexible Bayesian priors have been used to guide the parameter estimation process. In this context, priors favor parameter estimates which respect known physiology of the system, e.g., steady-state, dynamic trends, feasible bounds on concentration levels, and fluxes (Calvetti and Somersalo, 2006; Calvetti et al., 2006). In graphical models, priors have been developed in the form of energy functions to guide network inference (Imoto et al., 2004). Priors have been used to encode known relational information from databases such as KEGG into the network inference process (Werhli and Husmeier, 2007; Mukherjee and Speed, 2008). Priors have also been used to enforce sparsity in the network structure and prevent over-fitting (Hageman et al., 2011).

Developing mathematical models which are consistent with and predictive of the true underlying biological mechanisms is a central goal of systems biology. The experimental design and perturbations have been shown to have major influence on parameter estimation, and subsequently the output and accuracy of the computational model (Apgar et al., 2010). Graphical model network inference can be subject to a large proportion of false positive edges (Li et al., 2010). Environmental and experimental design factors that are not accounted for in the model can further misguide models (Remington, 2009). Assessing and improving the utility of mathematical models in the context of systems biology will continue to be an active area of research.

A continuous cycle between mathematical modeling and the wet-bench is critical to move systems biology forward. As George Box famously stated, “all models are wrong, but some are useful” (Box and Draper, 1987). Sensitivity analysis should routinely be performed to assess how sensitive the model output (predictions) are to model parameters and input (data). However, this is often not routine. Sensitivity analysis can also be used to guide model reductions and expansions, e.g., marginalizing over quantities that play little to no role in the system dynamics. Mathematical models can provide, via model driven predictions and hypotheses generation, a cheap and fast catalyst for experimental advances in systems biology. On the other hand, models which are more “wrong” than “useful” can lead to the design and execution of experiments and studies which are unlikely to be successful. Contrary to in silico studies, this can waste a lot of time and money, and ultimately promote skepticism in the modeling approach.

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