As StoneyB says, in this particular sentence factor (or factor into) is the verb
factor (v): to consider or include (something) in making a judgment or calculation, The company would have made a lot of money, but they neglected to factor the rising cost of the raw materials into their business model.
However, it is possible to rewrite the sentence using factor as a noun:
Studies indicate that many patient and doctors are uncomfortable with the idea of having the cost-of-care factor (be) a part of end-of-life decisions"
Here, of course, the article is required. Plus it's kind of a clumsy sentence. Both mean more or less the same thing, so whether you choose the noun or the verb is a question of style, not substance.