The explanation could be simple, as follows: (1)di=niis the proportion (or
estimated probability of having an event in the interval fromti 1 toti, (2)
1 di=nirepresents the proportion (or estimated probability of surviving that
same interval), and (3) the product in the formula forSS^ðtÞfollows from the
product rule for probabilities of Chapter 3.
Example 11.1 The remission times of 42 patients with acute leukemia were
reported from a clinical trial undertaken to assess the ability of the drug 6-
mercaptopurine (6-MP) to maintain remission (Figure 11.4). Each patient was
randomized to receive either 6-MP or placebo. The study was terminated after
one year; patients have di¤erent follow-up times because they were enrolled
sequentially at di¤erent times. Times in weeks were:
6-MP group:6, 6, 6, 7, 10, 13, 16, 22, 23, 6þ,9þ,10þ,11þ,17þ,19þ,
20 þ,25þ,32þ,32þ,34þ,35þ
Placebo group:1, 1, 2, 2, 3, 4, 4, 5, 5, 8, 8, 8, 8, 11, 11, 12, 12, 15, 17, 22,
23in whichtþdenotes a censored observation (i.e., the case was censored after
tweeks without a relapse). For example, ‘‘10þ’’ is a case enrolled 10 weeks
before study termination and still remission-free at termination.
According to the product-limit method, survival rates for the 6-MP group
are calculated by constructing a table such as Table 11.1 with five columns;
Figure 11.4 Survival curve: drug 6-MP group.INTRODUCTORY SURVIVAL ANALYSES 385