If you did, you would create a list of three things: (1) a daily schedule of pills, (2) their risks, (3) expense. The patient would be free of each of these things: they would be free of expense, in particular. I don't think this is meant.
As it stands, the sentence contains a list of two things: (1) a daily schedule of pills, (2) their risks and expense. Item (2) internally contains another two-item list, with 'their' covering both sub-items. The patient is free of their expense [i.e. the expense of the pills]. There might or might not be other expenses.
That said, few people know how to punctuate lists coherently. (He said, going by sad experience at work.)