Can I use published data to do my analyses and publish?
They've published their data. The way academia works is that people build on other people's work. You're just expected to reference their work properly.

Copyright is not particularly relevant here. Copyright law varies from country to country, but in any case copyright does not prohibit you from, e.g., adding two numbers just because those two numbers appeared in a copyrighted paper. Here in the US, copyright applies to the presentation of a work, not to ideas or data. For example, telephone directories have been found not to be copyrightable in the US. Since copyright is not very relevant, neither is licensing. Copyright law is specifically constructed so that it will not interfere with activities like scholarly commentary.

You will of course want to behave well toward the people whose data you're using. It won't hurt to talk it over with them. They know it intimately, and they may be able to warn you against misinterpreting it. For example, you don't want to be in the position of publishing a "gee whiz, amazing!" conclusion based on their data, only to find later that it was a misunderstanding. It may be appropriate for them to be coauthors on any resulting paper. Even if the purpose of your analysis is to contradict the conclusions they drew from their own data, it still doesn't hurt you to tell them what you're doing, and be above board and respectful.