background mutation Model is needed
Prob(X=k)=\binom{n}{r}P_{c,g}^{k}(1-P_{c,g})^{n-k} \\
center nucleotide mutation rate in a trinucleotide(t)
P_t=\frac{C_t}{F_t} \\\text{ }C_t:\#of\_mut;F_t:\#of\_trinucleotide
codon mutation rate P_{c,g} of codon c and gene g:
P_{c,g}=\frac{\frac{C_g}{N_{sample}}}{\sum_{t \in g}{N_{t,g}P_t}} \sum_{t \in c}{\frac{n_{t,c}}{n_c}P_t}
$N_{t,g}$ : #of tri in gene;
$N_{sample}$ : sample size ;
$n_{t,c}$ : # of mut in site t of codon c;
$n_c$ : # of mut in codon c
Chang, Matthew T., Saurabh Asthana, Sizhi Paul Gao, Byron H. Lee, Jocelyn S. Chapman, Cyriac Kandoth, JianJiong Gao, et al. 2016. “Identifying Recurrent Mutations in Cancer Reveals Widespread Lineage Diversity and Mutational Specificity.” Nature Biotechnology 34 (2): 155–63. doi:10.1038/nbt.3391.
Lawrence, Michael S., Petar Stojanov, Paz Polak, Gregory V. Kryukov, Kristian Cibulskis, Andrey Sivachenko, Scott L. Carter, et al. 2013. “Mutational Heterogeneity in Cancer and the Search for New Cancer-Associated Genes.” Nature 499 (7457): 214–18. doi:10.1038/nature12213.