The composting process destroys pathogens by several mechanisms. The first is heat: in the pile, thermophilic bacteria raise the temperature through their own biological heat, killing E. coli, Salmonella, etc. My current pile was 149F (65C) yesterday. In a compost pile, those temps will kill pathogens in less than an hour. As a general rule of thumb the following temps/times kill pathogens in compost piles: 140F/60C for 1 hour; 130F/54C for 1 day; 120F/49C for 1 week. To measure this, you get a compost thermometer from a garden store and keep it in the center of the pile at all times, year-round. (The thermometer also serves another function: it indicates the degree to which your pile is biologically active, providing hints about moisture, carbon, and nitrogen levels.) So heat is the first mechanism for killing pathogens. Another is competition: the pathogens are directly killed by other bacteria in the pile.
Once my compost bin is fully built, I let it sit for at least 1 year.
The only thing to be really concerned with is certain chemotherapy drugs. Some of them not only don't break down in a compost pile, but they can cause cancer in people who don't already have it.
The composting process is pretty amazing. It's vastly more hygienic than sewage (lol).