Consider heuristic for genes with lots of benign variants

[pnrobinson]

Currently, we do not downweight genes that have say 10 benign and one called pathogenic variant. However, experience shows that often these cases result in false positive results. We can consider a heuristic that would downweight the score for the numerator by

(0.95)^n

where n is the number of benign variants. It would be nicer to frame this as a probability distribution.

[pnrobinson]

This is apparent in the example for HEREDITARY MYOPATHY WITH EARLY RESPIRATORY FAILURE, which has ten variants (TTN) including one with a pathogenicity score of 0.96 0.97. λdisease=1. λbackground=9.4235. P(G|D)=0.3731. P(G|¬D)=0.0007. log10(LR): 2.72.

[pnrobinson]

The problem is that although it makes sense to say that the P(G|D)=0.3731, because we found one variant, the P(G|¬D)=0.0007 is not a good way to calculate this probabilty with the background lambda of 9.4. This is prob related to the way we are calculating the background frequency (which is an overestimate)

[pnrobinson]

Let's try this heuristic: The background score ranged from 0 to 20.8 (for {\it MUC16}). Numerous disease-associated genes displayed scores over 1.0, including for example {\it TTN} with a score of 9.4. According to our model, it is not surprising to observe a predicted pathogenic variant in a gene such as {\it TTN}, whether or not the gene is associated with the disease being investigated in any particular case. We can best achieve this by setting $\lambda^{\mathcal{B}}_g=\min(\lambda^{\mathcal{D}}_g,\lambda^{\mathcal{B}}_g)$ in cases where $\lambda^{\mathcal{B}}_g\geq 1$. For instance, if one predicted pathogenic variant is identified in {\it TTN}, this scheme would lead to a likelihood ratio of one -- the observation of the predicted pathogenic variant in this gene neither adds to nor detracts from the probability of the differential diagnosis (note that we treat known disease-associated variants differently, see below).

[pnrobinson]

I have implemented this and it takes care of the artefacts with TTN apparently. I think we can close this issue, but we need to assess this heuristic once we have all the phenopackets.