Introductory Biostatistics

then

lðt;nonexposedÞ¼l 0 ðtÞeb

lðt;exposedÞ¼l 0 ðtÞeb

so that

RR¼

lðt;exposedÞ

lðt;nonexposedÞ

¼e^2 b

and its 95% confidence interval

exp½ 2 ðbb^G 1 :96 SEðbb^Þފ

Of course, the estimate ofbunder the new coding scheme is only half of that
under the former scheme; therefore, the estimate of RR remains unchanged.
The following example, however, will show the clear e¤ect of measurement
scale on the value of the relative risk in the case of a continuous measurement.

Example 11.4 Refer to the data for patients with acute myelogenous leukemia
in Example 11.3 (Table 11.3) and suppose that we want to investigate the rela-
tionship between survival time of AG-positive patients and white blood count
(WBC) in two di¤erent ways using either (a)X¼WBC or (b)X¼logðWBCÞ.
(a) ForX¼WBC, we find that

bb^¼ 0 : 0000167

from which the relative risk forðWBC¼ 100 ; 000 ÞversusðWBC¼ 50 ; 000 Þ
would be

RR¼exp½ð 100 ; 000  50 ; 000 Þð 0 : 0000167 ފ

¼ 2 : 31

(b) ForX¼logðWBCÞ, we find that

bb^¼ 0 : 612331

from which the relative risk forðWBC¼ 100 ; 000 ÞversusðWBC¼ 50 ; 000 Þ
would be

RR¼expf½logð 100 ; 000 Þlogð 50 ; 000 ފð 0 : 612331 Þg

¼ 1 : 53

394 ANALYSIS OF SURVIVAL DATA