Hypothetically there are four subjects in the control group of a clinical trial. There are two deaths (day 2 and day 4) and two censored cases (day 3 and day 5). At the beginning all four subjects are at risk of death. In day 2 one out of four at risk subjects die, giving a probability of death P_t (death)=0.25 and reducing the number at risk to three for the next day. One subject is lost to follow-up in day 3; the censoring is assumed to happen at the end of the day. So in day 4 the number at risk is two. One out of two at risk subjects dies, so P_t (death)=0.5. P_t(surv), the probability of survival, is equal to 1-P_t(death). The cumulative survival probability, S(t), is initially 1. Multiplying S(t) and P_t+1(surv) gives S(t+1). For instance, S(4)=S(3) x  P₄(surv)=0.75 x 0.50=0.38, rounded to two significant digits. The KM method utilises information from censored cases prior to their censoring time. Also see Chapter 12 of Statistics at Square one.