Recent laser shock wave experiments by Da Silva et al. have raised new interest in hydrogen and its isotopes at high pressure. Those are the first measurements in a region of pressure where hydrogen has been predicted to undergo a plasma-phase transition. The existence and the properties of this transition are topic of current discussions. In this paper, we report path-integral Monte Carlo simulations and compare with the experimental results for the equation of state. Further, we identify the number molecules, atoms, and free particles in hydrogen using cluster analysis, which can be compared with chemical models. At high densities, the analysis provides information on the nature of the phase transition.