My periods would make me very, very sick so my OB started having me take my pills straight through about 10 years ago. I just skip the placebo week and it halts my fake period week. I'll do the period week maybe every 3-4 months to avoid spotting in between and the period is less severe than it used to be. I do know this strategy doesn't work at all with the triphasic brands.
My OB went to a conference where they discussed this strategy and the research showed it was totally safe. I had no problems at all conceiving when I wanted to and my gyn. health has been fine doing this long-term.
There are pills on the market now that just don't have the placebo week in them at all that do basically the same thing as I'm doing. You're not ovulating anyway, so the fake period week isn't a real period anyway, so there's no medical benefit to having it.