Usually there is a data safety monitoring board that reviews data periodically to ensure that SAEs are not arising of a size and frequency that would call for the trial to be shut down - or in the case of a serious indication, the DSMB could be looking for a total absence of efficacy or even a general worsening that would justify the same thing. Occasionally, the DSMB sees incredible efficacy and recommends stopping the trial because it would be unethical not to offer it to the placebo patients too. This latter case happens very, very rarely - like in the case of 100% fatal childhood leukemia where there is 100% efficacy of the therapy.
Is your DMC - DSMB?