Negative binomial distribution mixture model

Dear R community

I'm new to R and I'd like to ask for hints how to approach the following 
problem:

I have two vectors of count data 'observed_S' and 'observed_A'. Whereas 
'observed_S' follows a neg. binomial distribution but 'observed_A' is a 
mixture of an unknown variable 'A' (also from a neg. binomial 
distribution) and a shadow of 'observed_S', so to say.

Therefore my model can be expressed by: observed_A = factor*observed_S + A

I d like to find the factor explaining my two data vector most 
coherently. but I m overwhelmed by the different packages dealing with 
neg. binomial distribution regression. Can someone please point me which 
package is most useful for the above described purpose?

Thank you very much in advance

Regards
Fabian