contributions on Quantifying Cancer Progression with Conjunctive Bayesian Networks
Notes
Beerenwinkel (one of the authors) previously put some assumptions and followed them when modelling the accumulative evolutionary process. Such assumptions are:
1. Substitutions do not occur independently. There are preferred evolutionary pathways in which mutations are fixed
2. The fixation mutations into the population is definite. This means that substitutions are non-reversible
3. At each time point, the virus population is dominated by a single strain and clones are independent and (sometimes erroneous) copies of this genotype
Improvements
As mentioned in the paper, an improvement on the proposed model would be to use different parameters [math]\displaystyle{ \varepsilon^+ }[/math] and [math]\displaystyle{ \varepsilon^- }[/math] for false positives and false negatives in the error model. Beerenwinkel and Drton have developed this idea.
Let [math]\displaystyle{ \varepsilon^+ = (\varepsilon_1^+,...,\varepsilon_M^+) \in [0, 1]^M }[/math] and [math]\displaystyle{ \varepsilon^- = (\varepsilon_1^-,...,\varepsilon_M^-) \in [0, 1]^M }[/math] be parameter vectors that contain the mutation specific probabilities of observing a false positive and a false negative respectively. False positives (negatives) are mutations observed in clones derived from a virus population that is in mutant state at such time point. The false positive and false negative negative rates summarize differences from the population state. Then, these parameters quantify the expected genetic diversity of the virus population. Conditionally upon the hidden state [math]\displaystyle{ X_{jm} }[/math], the probabilities of observing mutation [math]\displaystyle{ m }[/math] in clone [math]\displaystyle{ k }[/math] at time point [math]\displaystyle{ t_j }[/math] are as follows:
[math]\displaystyle{ }[/math]