Some psychiatric studies indicate that among distinguished artists

Some psychiatric studies indicate that among distinguished artists the rates of manic depression and major depression are ten to thirteen times as prevalent as in the population at large.

(A) the rates of manic depression and major depression are ten to thirteen times as prevalent as in
(B) the rates of manic depression and major depression are ten to thirteen times more prevalent than in
(C) the rates of manic depression and major depression are ten to thirteen times more prevalent when compared to
(D) manic depression and major depression are ten to thirteen times as prevalent when compared to
(E) manic depression and major depression are ten to thirteen times more prevalent than in

E is perfectly fine
"rates" cannot be "more prevalent than" or "as prevalent as" something else although they can be "greater" or "less" than something else. On that basis, A, B and C are out
As for D, once again, I explained this earlier in another post; when you have a difference in relative values, you can not use "as prevalent as". Instead, you have to use "more prevalent than"
ie X is as prevalent as Y --> ok
ie X is two times as prevalent as Y --> no!
ie X is two times more prevalent than Y is --> ok
On this basis, D is out.