Let $S$ be a ring with involution (with 2 invertible). Suppose that the non connective algebraic K-theory $K(S)$ is 0 (i.e. $K_{n}(S)=0$, for all $n$).

Can we say something about the (higher) Witt groups $W_{n}(S)$ ? 

**Edit:** I was wondering if this kind of questions is tractable in general? What kind of articles or books can be recommended to have some insight about these questions? I will be grateful to any indication. Thank you in advance for any help in this direction.