I've got a situation where I have a series of individuals who have two factors describing their health.  Factor A has 3 levels while factor B has 4 levels.  Biologically, level 1 of factor A appears if and only if factor B is level 1.  Therefore, I have data structured like this:

    ID   Factor A  Factor B   Score
    1      a        alpha       0.1
    2      a        alpha       0.2
    3      b        beta        0.3
    4      b        gamma       0.4
    5      b        delta       0.5
    6      c        beta        0.6
    7      c        gamma       0.7
    8      c        delta       0.8

I'm interested in studying the effects of both factors, but I'm struggling with how to properly code this.  Giving each factor their own full set of dummy codes is rank deficient and leaving out a level of either factor creates a model with impossible combinations (ie level *a* ONLY occurs with level *alpha*, and vice versa).  **How could I code these fixed effects so that I can investigate the impact of both factors on our score?  Additionally, how would I interpret this coding scheme?**

EDIT:  To give some further context on how this happens, Factor A is series of related diseases (each phenotypically similar, but genetically different) while Factor B is severity of that diseased state.  So *a* is the control group while *alpha* is healthy severity.  These two occur contemporaneously by necessity (ie a healthy severity must be a control while a control can be nothing but healthy).