I am trying to find what the percentage or even general odds of a baby being born with a cleft chin, whose parents don't have cleft chins, and whose grandparents didn't have cleft chins. From what I've read, virtually any mutation is possible with or without the genetic history. So, I'm not asking if it's possible, but apart from terms like "rare" or "uncommon", is there any data or calculation that can suggest just how rare it is? From what I've perused, it is suggested that it is more common for a mother or father with a cleft chin to birth a child without one than the opposite. Any thoughts on any of this?

From the point of a person with some clinical genetics background, empiric or population risk is used here. It's really simplified outlook on reality, but since we often do not know much, it has to be enough. (Some examples can be taken from this site: http://www.nchpeg.org/index.php?option=com_content&view=article&id=120&Itemid=118 , note that it there are also other numbers), but let's say incidence of schizophrenia is 1% . This means that if you are going to be a parent, you have 1% chance of having a child with schizophrenia (or cleft palate). It's based on many families where schizophrenia occured.

 

If a 1st degree relative, such as sibling or parent has the disease, the risk is calculated by Edwards equation: $R=/sqrt(P) * N$ where P is the population risk and N is number of affected 1st degree individuals. If individuals are farther (such as grandparents) the risk is taken as "slightly higher" than populational.

 

It's still very imprecise, but better than nothing. Hope this helps