Introductory Biostatistics

low-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,

23

in whichtþdenotes a censored observation (i.e., the case was censored aftert
weeks without a relapse). For example, ‘‘10þ’’ is a case enrolled 10 weeks
before study termination and still remission-free at termination.
Since the proportional hazards model is often assumed in the comparison of
two survival distributions, such as in this example (see also Example 11.2), it is
desirable to check it for validity (if the proportionality is rejected, it would lend
support to the conclusion that this drug does have some cumulative e¤ects). Let
X 1 be the indicator variable defined by

X 1 ¼

0 if placebo

1 if treated by 6-MP



and

X 2 ¼X 1 t

representing treatment weeks (timetis recorded in weeks). To judge the valid-
ity of the proportional hazards model with respect toX 1 , it is the e¤ect of this
newly defined covariate,X 2 , that we want to investigate. We fit the following
model;

l½tjX¼ðx 1 ;x 2 ފ¼l 0 ðtÞeb^1 x^1 þb^2 x^2

and from the results shown in Table 11.5, it can be seen that the accumulation
e¤ect or lack of fit, represented byX 2 , is insignificant; in other words, there is
not enough evidence to be concerned about the validity of the proportional
hazards model.

TABLE 11.5

Factor Coe‰cient

Standard

Error zStatistic pValue

X 1 1.55395 0.81078 1.917 0.0553
X 2 0.00747 0.06933 0.108 0.9142

404 ANALYSIS OF SURVIVAL DATA