This paper investigates one- and two-sample problems comparing survival times when an individual may experience an intermediate event prior to death or reaching some well defined endpoint. The intermediate event may be polychotomous. Patients experiencing the intermediate event may have an altered survival distribution after the intermediate event. Score tests are derived for testing if the occurrence of the intermediate event actually alters survival. These models have implications for evaluating therapies without randomization as well as strengthening the log rank test for comparing two survival distributions. The exact distribution of the score tests can be found by conditioning on both the waiting time and occurrence of the intermediate event.