What to say if a decision problem is not NP?

Let $ O$ be an optimisation problem and $ P$ its decision variant. I know that $ O$ is said to be NP-hard if $ P$ is $ NP-$ complete. However, what to say about $ O$ when the decision problem $ P$ is no more in the class $ NP$ , and thus it’s no more $ NP-$ complete(the algorithm of deciding is pseudo-polynomial and there is no better alternatives)?