"despite these facts" is correct and usable in written English.
You can use it, for example, when there are two sides of an issue and you are acknowledging one side but then continuing on with the other side. For example: "Despite these facts, there is still evidence to suggest the opposite."
Despite these facts, she still faces a jail sentence, while some other more infamous actors in this matter do not.
Despite these facts, the Lockean notion that the estimation of time depends on the succession of sensations is still to some degree true.
Despite these facts, the vaccine, sold by Merck as Gardasil, has been mired in controversy, and many parents remain wary about using it for the girls and young women it was meant to protect.
Despite these facts, the Senate reform bill, like the bill that House Republicans passed earlier this year, would hollow out or terminate coverage for tens of millions of Americans who rely on Medicaid or the private-insurance exchanges set up by the A.C.A.
It is somehow among the top-rated shows this season despite these facts: In raw numbers ABC's 10 p.m. show, "Six Degrees," inherits 24.2 million viewers watching the preceding "Grey's Anatomy" while "ER" inherits only 9.9 million viewers watching NBC's "Deal or No Deal".
Despite these facts, patients' needs still are unmet.
Despite these facts, diagnostic and therapeutic errors are frequently reported in the literature [6].
Despite these facts, the preparations for the return of the Fischer-Tropsch technology proceeded slowly.
However, despite these facts, good photo-catalytic activity was observed for the polymer-supported CDs.
Despite these facts, the text contains a treasure trove of argument concerning Cartesian ideas.
Despite these facts, physical inactivity is increasing, not only in high-income, but also in middle- and low-income countries.
