Nonparametric Methods in Statistics with SAS Applications

124 TIME-TO-EVENT ANALYSIS

The log-rank test was first proposed in 1966 by an American biostatistician Nathan

Mantel (1919-2002).

1

6.2.1 Testing Procedure

The theoretical background behind the log-rank test is as follows. Let t

1

< t

2

< .. . <

t

k

denote the distinct ordered event times in both samples pooled together. At each

time t

i

, the observations may be summarized in a 2 ×2 table with the two samples

represented by the rows, and the columns representing the number of individuals who

experienced the event at time t

i

(Event) and the number of those who were at-risk but

didn’t experience the event (No Event). Thus, there are a total of k 2 ×2 tables of